B.1 Introduction.
B.2 Cumulative particles.
B.3 Description of polarized states of particles with spin 1 5 B.4 Brief review of data on the reaction of fragmentation of deuterons into cumulative protons.
B.5 Purpose and structure of the dissertation work.
I SETUP OF THE EXPERIMENT
1.1 Motivation.
1.2 Experimental setup.
1.3 Methodological measurements and modeling
1.4 Organization and principle of operation of the trigger.
II SOFTWARE
II. 1 Introductory remarks
11.2 qdpb data collection and processing system
11.3 Configurable data and hardware views
11.4 Session dependent presentations
11.5 DAQ system SPHERE.
II. 6 Data acquisition systems for polarimeters.
III EXPERIMENTAL RESULTS AND THEIR DISCUSSION
III. 1 Analysis of sources of systematic errors.
111.2 Experimental data.
111.3 Discussion of experimental data.
Recommended list of dissertations
The study of spin and isospin effects in reactions of the production of cumulative particles 2007, Doctor of Physical and Mathematical Sciences Litvinenko, Anatoly Grigorievich
Study of interactions of polarized deuterons with protons and nuclei in the momentum range 0.7-9.0 GeV/c 2006, Doctor of Physical and Mathematical Sciences Ladygin, Vladimir Petrovich
Study of the angular dependence of the analyzing abilities of the reactions -dd→3Hen and -dd→3H p at a deuteron energy of 270 MeV 2007, Candidate of Physical and Mathematical Sciences Janek, Marian
Tensor analyzing power Ayy in the reactions A(d, p)x and A(d, d)x at 9 GeV/c and the structure of the deuteron at short distances 1998, Candidate of Physical and Mathematical Sciences Ladygin, Vladimir Petrovich
Study of the analyzing abilities Ay, Ayy and Axx of the reaction of deuteron-proton elastic scattering at energies of 880 and 2000 MeV 2010, Candidate of Physical and Mathematical Sciences Kurilkin, Pavel Konstantinovich
Introduction to the thesis (part of the abstract) on the topic "Measurements of the tensor analyzing power of T20 in the reaction of deuteron-to-pion fragmentation at zero angle and development of software for data acquisition systems of installations on polarized beams"
B.1 Introduction
The dissertation paper presents experimental results of measuring the tensor analyzing power T20 in the reaction of fragmentation of tensor polarized deuterons into cumulative (sub-threshold) pions. The measurements were carried out by the SPHERE collaboration on a beam of tensor polarized deuterons at the accelerator complex of the High Energy Laboratory of the Joint Institute for Nuclear Research (LHE JINR, Dubna, Russia). The study of polarization observables provides more detailed, compared to reactions with non-polarized particles, information about the interaction Hamiltonian, reaction mechanisms, and the structure of the particles involved in the reaction. To date, the question of the properties of nuclei at distances smaller than or comparable to the size of a nucleon has not been adequately studied both from the experimental and theoretical points of view. Of all the nuclei, the deuteron is of particular interest: firstly, it is the most studied nucleus from both experimental and theoretical points of view. Secondly, for the deuteron, as for the simplest nucleus, it is easier to understand the reaction mechanisms. Third, the deuteron has a nontrivial spin structure (spin equal to 1 and a nonzero quadrupole moment), which provides wide experimental possibilities for studying spin observables. The measurement program, within which the experimental data presented in the dissertation work were obtained, is a natural continuation of studies of the structure of atomic nuclei in reactions with the production of cumulative particles in the collision of unpolarized nuclei, as well as polarization observables in the deuteron decay reaction. The experimental data presented in the dissertation work make it possible to advance in understanding the spin structure of the deuteron at small internucleon distances and supplement the information on the structure of the deuteron obtained in experiments with a lepton probe and in the study of the breakup reaction of tensor polarized deuterons, and therefore seem to be relevant. To date, the data presented in the dissertation work are the only ones, since such studies require beams of polarized deuterons with an energy of several GeV, which at present and in the next few years will be available only at the JINR LHE accelerator complex, where it is natural to continue research in this direction. The mentioned data were obtained as part of an international collaboration, were reported at a number of international conferences, and also published in peer-reviewed journals.
Further in this chapter, we give the information about cumulative particles necessary for further presentation, the definitions used in the description of polarization observables, and also give short review known in the literature results on the deuteron decay reaction.
B.2 Cumulative particles
Studies of the regularities of the birth of cumulative particles have been carried out since the beginning of the seventies of the XX century, , , , , , , , , , , , . The study of reactions with the production of cumulative particles is interesting in that it provides information about the behavior of the high-momentum (> 0.2 GeV/c) component in fragmenting nuclei. These large internal momenta correspond to small ones (< 1 ферми) межнуклонным расстояниям. На таких (меньших размера нуклона) расстояниях использование нуклонов как квазичастиц для описания свойств ядерной материи представляется необоснованным, и могут проявляться эффекты ненуклонных степеней свободы в ядрах , , , . В глубоконеупругом рассеянии лептонов упомянутый диапазон внутренних импульсов соответствует значениям переменной Бьоркена хъ >1, where the cross sections become very small.
First of all, let us define what will be further understood by the term "cumulative particle" (see, for example, the references therein). Particle c, born in the reaction:
Ar + Ac.^c + X, (1) is called "cumulative" if the following two conditions are satisfied:
1. the particle c was born in a kinematic region inaccessible in the collision of free nucleons having the same momentum per nucleon as the nuclei Ai and Ac in reaction (1);
2. particle c belongs to the fragmentation region of one of the colliding particles, i.e. must be done either
St, - Yc\< \YAii - Ус| , (2) либо
YA„-Ye\ YA„ - Yc\ «- Ye\ = - Ye\ + \YAii - YAi\ . (4) It follows from the experimental data (see, for example, , , , , , , , ) that for experiments on a fixed target, the shape of the spectrum of cumulative particles weakly depends on the collision energy, starting from the energies of the incident particles Tb > 3-1-GeV. This statement is illustrated in Fig. 1, reproduced from the paper , which shows the dependences on the energy of the incident proton: (b) the ratio of the outputs of pions of different signs 7r~/7r+ and (a) the parameter of the inverse slope of the spectrum To for approximating Eda/dp - C exp(-Tx/To ) cross sections for the production of cumulative pions measured at an angle of 180°. This means that the independence of the shape of the spectra from the primary energy begins with the difference in the speeds of the colliding particles \YAii - YAi\> 2. Another established pattern is the independence of the spectra of cumulative particles from the type of particle on which fragmentation occurs (see Fig. 2). Since the dissertation paper considers experimental data on the fragmentation of polarized deuterons into cumulative pions, the regularities established in reactions with the production of cumulative particles (dependence on atomic mass fragmenting nucleus, the dependence on the type of detected particle, etc.) will not be discussed. If necessary, they can be found in the reviews: , , , . Rice. 1: Energy dependence of the incident proton (Tp) of (a) the reciprocal slope parameter To and (b) the ratio of outputs tt~/tt+ integrated starting from a pion energy of 100 MeV. Figure and data marked with circles are taken from . Data marked with triangles are cited from . B.3 Description of polarized states of particles with spin 1 For the convenience of further presentation, we give a brief overview of the concepts , , which are used in describing the reactions of particles with spin 1. Under ordinary experimental conditions, an ensemble of particles with a spin (a beam or a target) is described by a density matrix p, the main properties of which are as follows: 1. Normalization Sp(/5) = 1. 2. Hermitianity p = p+. Present experiment r Reference 6 P-1-1-1-1-S f Present experiment T ▼ Reference 6 L-S O - Si - Rb f d sh Cumulative scale variable xs Rice. Fig. 2: Dependence of the cross section for the production of cumulative particles on the cumulative scaling variable xc (57) (see Section III.2) for the fragmentation of a deuteron beam on various targets into pions at zero angle. Picture taken from work. 3. The average of the operator O is calculated as (O) = Sp(Op). The polarization of an ensemble (for definiteness, a beam) of particles with spin 1/2 is characterized by the direction and average value of the spin. As regards particles with spin 1, one should distinguish between vector and tensor polarizations. The term "tensor polarization" means that the description of particles with spin 1 uses a tensor of the second rank. In general, particles with spin I are described by a tensor of rank 21, so for I > 1 one should distinguish between the polarization parameters of the 2nd, 3rd ranks, etc. In 1970, at the 3rd International Symposium on Polarization Phenomena, the so-called Madison Convention was adopted, which, in particular, regulates the notation and terminology for polarization experiments. When recording nuclear reaction A(a, b)B above the particles that react in the polarized state or whose polarization state is observed, arrows are placed. For example, the notation 3H(c?,n)4He means that the unpolarized 3H target is bombarded by polarized deuterons d and that polarization of the resulting neutrons is observed. When we talk about measuring the polarization of a particle b in a nuclear reaction, we mean the process A(a,b)B, i.e. in this case, the beam and the target are not polarized. The parameters describing the changes in the reaction cross section when either the beam or the target (but not both) are polarized are called the analyzing powers of the A(a, b)B reaction. Thus, apart from special cases, polarizations and analytical abilities must be clearly distinguished, since they characterize different reactions. Reactions like A (a, b) B, A (a, b) B, etc. are called polarization transfer reactions. The parameters relating the spin moments of the particle b and the particle o are called the polarization transfer coefficients. The term "spin correlations" is applied to experiments on reactions of the form A(a, b)B and A(a, b)B, in which case the polarization of both resulting particles must be measured in the same event. In beam experiments polarized particles(measurements of analyzing abilities), in accordance with the Madison Convention, the z-axis is directed along the momentum of the beam particle kjn, the y-axis is directed along k(n x kout (i.e., perpendicular to the reaction plane), and the x-axis must be directed so that the resulting coordinate system was right handed. The polarization state of a system of particles with spin / can be completely described by (21+1)2 - 1 parameters. Thus, for particles with spin 1/2, the three parameters pi form a vector p, called the polarization vector. The expression in terms of the spin 1/2 operator, denoted by c, is the following: Pi = fa) , i = x,y,z , (5) where the angle brackets mean averaging over all particles of the ensemble (in our case, the beam). The absolute value of p is limited< 1. Если мы некогерентно смешаем п+ частиц в чистом спиновом состоянии, т.е. полностью поляризованных в некотором данном направлении, и частиц, полностью поляризованных в противоположном направлении, поляризация составит р - , или p = N+-N- , (6) если под iV+ = и AL = п™+п понимать долю частиц в каждом из двух состояний. Since the polarization of particles with spin 1 is described by a tensor, its representation becomes more complicated and less visual. The polarization parameters are some observable quantities of the spin operator 1, S. Two different sets of definitions for the corresponding polarization parameters are used - the Cartesian tensor moments Pi, pij and the spin tensors tkq . In Cartesian coordinates, according to the Madison Convention, the polarization parameters are defined as Pi - (Si) (vector polarization), (7) 3 u - -(SiSj + SjSi) - 25ij (tensor polarization), (8) = 5(5 + 1) =2 , (9) r we have the connection Pxx+Pyy+Pzz = 0 . (ten) Thus, tensor polarization is described by five independent quantities(pxx, pyy, pxy, pxz, pyz), which, together with the three components of the polarization vector, gives eight parameters for describing the polarized state of a particle with spin 1. The corresponding density matrix can be written as: P = \( 1 + + SjSi)) . (eleven) The description of the polarization state in terms of spin tensors is convenient, since they are easier than Cartesian ones, they are transformed during rotations of the coordinate system. The spin tensors are related to each other by the following relationship (see): tkq - N Y,(kiqik2q2\kq)ikiqiik2qz > (12) 9192 where q\k2q2\kq) are the Clebsch-Gordan coefficients, and N is the normalization coefficient chosen so that the condition Sp(MU) = (2S + l)6kkl6qqi . (thirteen) The lowest spin moments are: Yu \u003d 1 5 h o - Sz, h -1 \u003d ^ (Sx - iSy) . For the spin I, the index k ranges from 0 to 21, and |d|< к. Отрицательные значения q могут быть отброшены, поскольку имеется связь tk q = (-1)Ч*к + . Для спина 1 сферические тензорные моменты определяются как Thus, the vector polarization is described by three parameters: the real tw and the complex tw, and the tensor polarization is described by five parameters: the real tw and the complex tw hi Next, we consider the situation when the spin system has axial symmetry about the axis ((we will leave the notation l for the coordinate system associated with the reaction under consideration, as described above). Such special case is interesting in that beams from sources of polarized ions usually have axial symmetry. Let us imagine such a state as an incoherent mixture containing the fraction N+ of particles with spins along C, the fraction AL of particles with spins along, and the fraction No of particles with spins uniformly distributed in directions in the plane perpendicular to. In this case, only two polarization moments of the beam are nonzero, t\o (or p^) and t2o (or p^). Let us direct the quantization axis along the axis of symmetry £ and replace t with r and z with (. It is obvious that (5^) is simply equal to N+ - N-, and in accordance with (15) and (7): 15) vector polarization), t2i = -^((Sx.+ iSy)Sg.+ Sg(Sx+iSy)) , t22 = f((Sx + iSy)2) tensor polarization). 17) (N+ - N-) (vector polarization). From (16) and (8) it follows that T20 = ^=(1 - 3Nq) or PCC = (1-3b) where it is used that (N+ + N-) = (1 - No). If all moments of the 2nd rank are absent (N0 = 1/3), one speaks of a purely vector beam polarization. The maximum possible values of the polarization of such a beam are r0ax- - y2/3 or (19) pmax. 2/3 (purely vector polarization). For the case of purely tensor polarization (mu = 0), from equations (17) and (18) we obtain -\/5<Т2О<-7= ИЛИ (20) л/2 2 < рсс < +1 . The lower limit corresponds to No - 1, the upper - AG+ = AL = 1/2. In the general case, the symmetry axis ξ of a polarized beam from a source can be arbitrarily oriented with respect to the coordinate system xyz associated with the reaction under consideration. Let us express the spin moments in this system. If the orientation of the axis (is given by the angles /3 (between the z and C axes) and φ (rotation by -φ around the z axis brings the C axis to the yz plane), as shown in Fig. 3, and in the C frame the beam polarizations are equal to T20, then the tensor moments in the xyz system are: Vector moments: Tensor moments: 10 = r10COS/3 , t20 = -7p(3cOS2/? - 1) , (21) itn = ^Lsin/fe4*-. t2l = sinPcosRe(f, l/2 l/2 In the general case, the invariant cross section a = Eda/dp of the reaction A(a, b)B is written as: st = ao(Etkqnq) . (22) k,q The values of Tkq are called the analyzing abilities of the reaction. The Madison Convention recommends designating tensor analyzing powers as Tkq (spherical) and A;, Lu (Cartesian). Four analyzing abilities - vector gTz and tensor Ty, T2\ and T22 Rice. 3: Orientation of the symmetry axis £ of the polarized beam with respect to the xyz coordinate system associated with the reaction, xz is the reaction plane, (3 is the angle between the z axes (direction of the incident beam) and rotation na-f around the z axis brings the £ axis into the yz plane. They are valid due to parity conservation, and Ty = 0. Taking into account these restrictions, equation (22) takes the form: sg =<70-. In Cartesian coordinates, the same section is written as: 3 1 2 1 a - one hundred tkq , (25) i.e. the vector analyzing power is equal to the vector polarization in the reverse reaction: T2l = -^r.reaction. ^(2?) For elastic scattering, when the response is identical to its inverse, the vector polarization is equal to the vector analyzing power. Therefore, in some papers on the study of the scattering of polarized particles, one speaks of polarization measurements, when, strictly speaking, the analyzing power was measured. Nevertheless, for elastic scattering of deuterons it is necessary to distinguish between the analyzing power and the polarization £21 due to the difference in sign. B.4 Brief review of data on the reaction of fragmentation of deuterons into cumulative protons Let us briefly summarize the currently known results of studying the reaction of fragmentation of deuterons into protons d(pd > 1 GeV/c) + А р(® = 0°) + X , (28) since they will be required when motivating the measurements considered in the thesis work and discussing the obtained results. Over twenty years of research into reaction (28) with polarized and unpolarized deuterons, a large amount of experimental data has been accumulated, which initiated the emergence of a number of theoretical models aimed at describing the structure of the deuteron and the reaction mechanism. This reaction has the largest, in comparison with fragmentation into other hadrons, cross section, and a clear interpretation within the framework of the impulse approximation. In this case, the main contribution to the cross section comes from the spectator mechanism, which is depicted by the diagram shown in Fig. 4. Rice. 4: Spectator diagram for the fragmentation of a deuteron into a proton. For a two-component (S- and D-wave) deuteron wave function (hereinafter referred to as "WFD"), the differential cross section (Eda/dp) and the tensor analyzing power T20 are written as follows: E~(p)^(u2(k)+w2(k)) , . , 2u(k)w(k) -w2(k)/V2 da u2(k) + w2(k) Here p is the momentum of the detected proton, and and w are the radial components of the PFD for the S and D waves, respectively. Due to the essential role of relativistic effects, the relationship between the variable k, which plays the role of the internal momentum of the nucleon in the deuteron, and the momentum of the registered proton depends on the method of describing the deuteron. This is due to the fundamental impossibility to separate , the movement of the center of mass and the relative movement in a system of particles moving with relativistic velocities. Generally speaking, the WFD relativization method, i.e. the way in which relativistic effects are taken into account in it is one of the main differences between the theoretical models used to describe the reaction (28). Therefore, when comparing experimental data with theoretical models, the specific method of PFD relativization will be specially stipulated, but here we will rely on the so-called minimum relativization scheme. The scheme of minimal relativization is the consideration of WFD in dynamics on the light front with a fixed choice of the direction of the light front (z + t = 0). This approach, apparently, was first proposed in and widely used in the description of composite relativistic systems (see, for example, , , , ). In this approach, the momentum p of the detected proton and the internal momentum k of the nucleon in the deuteron are related by the relationship: m, M are the masses of the proton and deuteron, p, d are their three-dimensional momenta. Nonrelativistic functions depending on A are used as the wave function; and multiplied by the normalization factor 1/(1 - a). The fragmentation cross section of unpolarized deuterons into protons at zero angle was studied in the range from 2.5 to 17.8 GeV/c of the momentum of primary deuterons in the works , , , , , , . On the whole, the experimental spectra obtained are well described by the spec 32) by a tator mechanism using generally accepted WFD, for example, Reid or Paris WFD. 0.0 0.2 0.4 0.6 0.8 1.0 k. GeV/c Rice. 5: Nucleon relative momentum distribution in the deuteron extracted from experimental data for various reactions involving the deuteron. Picture taken from work. So, from Fig. Figure 5 shows that the momentum distributions of nucleons in the deuteron are in good agreement, extracted from the data for the reactions: inelastic scattering of electrons on the deuteron d(e,e")X , elastic proton-deuteron backscattering p(d,p)d , and breakup deuteron.Except for the range of internal momenta k from 300 to 500 MeV/c, the data are described by the spectator mechanism using the Paris PFD.To explain the discrepancy in this region, additional mechanisms were used.In particular, taking into account the contribution from pion rescattering in the intermediate state , , makes it possible to satisfactorily describe However, the uncertainty in the calculations is about 50% due to the uncertainty in the knowledge of the vertex function irN, which, moreover, in such calculations must be known off-shell.In order to explain the experimental spectra, we took into account the fact that for large internal momenta (i.e. small internucleon distances 0.4 1.2 2.0 2. Inn - 0.2/k), non-nucleon degrees of freedom may appear. In particular, in that work, an admixture of the six-quark component \6q) was introduced, the probability of which was ~ 4%. Thus, it can be noted that, on the whole, the spectra of protons obtained during the fragmentation of deuterons into protons at zero angle can be described up to internal momenta of ~ 900 MeV/c. In this case, it is necessary either to take into account the diagrams following after the momentum approximation, or to modify the PFD taking into account the possible manifestation of nonnucleon degrees of freedom. The polarization observables for the deuteron breakup reaction are sensitive to the relative contribution of the PFD components corresponding to different angular momenta, so experiments with polarized deuterons provide additional information about the deuteron structure and reaction mechanisms. At present, there are extensive experimental data on the tensor analyzing power of T20 for the breakup reaction of tensorically polarized deuterons. The corresponding expression in the spectator mechanism is given above, see (30). Experimental data for Tad, obtained in the works , , , , , , , , , are shown in Fig. 6, which shows that starting from internal momenta of the order of 0.2 - f - 0.25 GeV/c, the data are not described by conventional two-component PFDs. Accounting for interaction in the final state improves agreement with experimental data up to momenta of the order of 0.3 GeV/c. Accounting for the contribution of the six-quark component in the deuteron allows one to describe the data up to internal momenta of the order of 0.7 GeV/c. The behavior of T20 for momenta of the order of 0.9 -f-1 GeV/c is in best agreement with calculations within the framework of QCD using the method of reduced nuclear amplitudes , , which takes into account the antisymmetrization of quarks from different nucleons. So, summing up the above: 1. Experimental data for the cross section for the fragmentation of unpolarized deuterons into protons at zero angle can be described in terms of the nucleon model. 2. The data for T20 have so far been described only with the involvement of non-nucleon degrees of freedom. B.5 Purpose and structure of the thesis The purpose of this dissertation work was to obtain experimental data on the tensor analyzing ability of the T20 reaction Ta, for df *12C-> p(O") + X 0 200 400 600 800 1000 k (MeV/c) Rice. 6: Tensor analyzing power of the T2o deuteron decay reaction. Picture taken from work. 60) fragmentation of tensor polarized deuterons into cumulative (subthreshold) pions at zero angle on various targets, as well as the creation software for data acquisition systems of experimental facilities conducting polarization measurements at the LHE accelerator complex. Structurally, the dissertation work consists of an introduction, three chapters and a conclusion.
Similar theses in the specialty "Physics of the atomic nucleus and elementary particles", 01.04.16 VAK code
Study of the angular dependence of the analyzing abilities of the reaction dd→3Hp at an energy of 200 MeV 2010, Candidate of Physical and Mathematical Sciences Alexey Konstantinovich Kurilkin
Measurement of tensor and vector analyzing abilities of inelastic scattering of polarized deuterons on protons in the region of Roper resonance and delta isobar excitation energies 2001, candidate of physical and mathematical sciences Malinina, Lyudmila Vladimirovna
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Creation of a polarized hydrogen-deuterium gas target for the ANKE experiment on the internal beam of the storage ring of the COZY accelerator 2007, candidate of physical and mathematical sciences Grigoriev, Kirill Yurievich
Dissertation conclusion on the topic "Physics of the atomic nucleus and elementary particles", Isupov, Alexander Yurievich
CONCLUSION
Let us formulate the main results and conclusions of the dissertation work:
1. For the first time, the value of the tensor analyzing power Т2о was measured in the reaction d + А -7Г±(@ = 0°) + X fragmentation of tensor polarized deuterons into cumulative pions at zero angle in two formulations:
For a fixed pion momentum pn = 3.0 GeV/c for deuteron momentum pd in the range from 6.2 to 9.0 GeV/c;
For a fixed deuteron momentum pa = 9.0 GeV/c for pion momenta Pt in the range from 3.5 to 5.3 GeV/c.
2. The measured value of the tensor analyzing power T20 does not depend on the atomic mass A of the target nucleus in the interval A = 1->-12.
3. The measured value of T2o does not depend on the sign of the detected pion.
4. The measured value of T20 is not even qualitatively described by currently known theoretical calculations in the momentum approximation in the nucleon model of the deuteron.
5. A distributed data collection and processing system qdpb has been created, which provides the basis for building data collection systems for experimental installations.
6. Based on the qdpb system, a data acquisition system DAQ SPHERE was created, which has been used so far in 8 sessions on the extracted beam of the Synchrophasotron and Nuclotron LHE.
7. On the basis of the qdpb system, data collection systems were created for LHE polarimeters: high-energy on the extracted beam, as well as on the internal target of the Nuclotron - the vector polarimeter and subsequently - the vector-tensor polarimeter.
In conclusion, I would like to thank the leadership of the High Energy Laboratory and personally A.I. Malakhov, as well as the staff of the accelerator complex and the POLARIS source, who for many years provided the opportunity to conduct experimental work, the results of which formed the basis of the presented dissertation work.
I express my deep gratitude to my supervisors - A. Glitvinenko, without whose help this dissertation work would not have been completed in work and life, and L. S. Zolin, who initiated both the setting of the described experiments and many of the technical developments included in this work.
I consider it a pleasant necessity to express my sincere gratitude to I.I. Migulina for moral support, which cannot be overestimated, as well as for many years of work as part of the SPHERE collaboration, the results of which greatly facilitated the preparation of the dissertation work.
I consider it my duty to thank my colleagues K.I. Gritsai, S.G. Reznikov, V.G. Olshevsky, S.V. Afanasiev, A.Yu. on professional (and not only) topics, as well as all participants of the SPHERE collaboration over the past decade, because without them it would be absolutely impossible to obtain the results presented in this paper.
Special thanks to the author - L.S. Azhgirey and V.N. Zhmyrov, employees of the LHE high-energy polarimeter, and also to the late G.D. Stoletov for fruitful cooperation, which led to the creation of modern polarimetric software.
I am grateful to Yu.K. Pilipenko, N.M. Piskunov and V.P. Ladygin, who at different times initiated some of the developments included in the dissertation work.
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If the applied field E0 has an arbitrary direction, then the induced dipole moment can be easily found from the superposition
Where, are the field components with respect to the principal axes of the ellipsoid. In scattering problems, the coordinate axes are usually chosen to be fixed with respect to the incident beam. Let x" y" z" be such a coordinate system where the propagation direction is parallel to the z-axis". If the incident light
x" is polarized, then from the optical theorem we have:
To carry out calculations using formula (2.2), it is necessary to write out the p components with respect to the axes drawn by dashed lines. Equality (2.1) can be written in matrix form:
We write column vectors and matrices in a more compact form in accordance with the following notation:
With this notation, 2.3 takes the following form:
The components of an arbitrary vector F are transformed in accordance with the formula:
Where, etc. As a result, from (2.5) and transformation (2.6) we have:
where, due to the orthogonality of the coordinate axes, the matrix inverse to is the transposed matrix. Thus, the polarizability of an ellipsoid is a Cartesian tensor; if its components in the principal axes are given, then its components in the rotated coordinate axes can be determined by formula (2.8). The absorption cross section for incident - polarized light is determined simply by the formula:
Where. Similarly, if the incident light is polarized, then
If the vector scattering amplitude
for a dipole illuminated by -polarized light, substitute into the cross section equation, then we obtain the scattering cross section
Where we used the matrix identity. A similar expression holds for the scattering cross section and for incident polarized light.
Application.
Polarized light was proposed to be used to protect the driver from the blinding light of the headlights of an oncoming car. If film polaroids with a transmission angle of 45o are applied to the windshield and headlights of a car, for example, to the right of the vertical, the driver will clearly see the road and oncoming cars illuminated by their own headlights. But for oncoming cars, the polaroids of the headlights will be crossed with the polaroid of the windshield of this car, and the headlights of oncoming cars will go out.
Two crossed polaroids form the basis of many useful devices. Light does not pass through crossed polaroids, but if you place an optical element between them that rotates the plane of polarization, you can open the way for light. This is how high-speed electro-optical light modulators are arranged. They are used in many technical devices - in electronic rangefinders, optical communication channels, laser technology.
The so-called photochromic glasses are known, darkening in bright sunlight, but not able to protect the eyes with a very fast and bright flash (for example, during electric welding) - the darkening process is relatively slow. Polarized glasses have an almost instant "reaction" (less than 50 microseconds). The light of a bright flash enters miniature photodetectors (photodiodes), which supply an electrical signal, under the influence of which the glasses become opaque.
Polarized glasses are used in stereo cinema, which gives the illusion of three-dimensionality. The illusion is based on the creation of a stereo pair - two images taken at different angles, corresponding to the angles of view of the right and left eyes. They are considered so that each eye sees only the image intended for it. The image for the left eye is projected onto the screen through a polaroid with a vertical transmission axis, and for the right eye with a horizontal axis, and they are precisely aligned on the screen. The viewer looks through polaroid glasses, in which the axis of the left polaroid is vertical, and the right one is horizontal; each eye sees only “its own” image, and a stereo effect arises.
For stereoscopic television, the method of rapidly alternating dimming of glasses is used, synchronized with the change of images on the screen. Due to the inertia of vision, a three-dimensional image arises.
Polaroids are widely used to dampen glare from glass and polished surfaces, from water (the light reflected from them is highly polarized). Polarized and light screens of liquid crystal monitors.
Polarization methods are used in mineralogy, crystallography, geology, biology, astrophysics, meteorology, and in the study of atmospheric phenomena.
-- [ Page 1 ] --
THE RUSSIAN ACADEMY OF SCIENCES
PETERSBURG INSTITUTE OF NUCLEAR PHYSICS
them. B.P. KONSTANTINOV
As a manuscript
Mikirtychyants Maxim Sergeevich
UDC 539.128, 539.188
Development and research of a source of atomic hydrogen and deuterium with nuclear polarization for experiments on internal beams of accelerators 01.04.01 – devices and methods of experimental physics
Scientific supervisors:
Candidate of Physical and Mathematical Sciences V.P. Koptev Candidate of Physical and Mathematical Sciences A.A. Vasiliev Gatchina Contents Introduction............................................... ................................................. ..........................- nine Chapter 1.
Methods for obtaining atomic beams.................................................................... ...................................... 13 1.1 Introduction .......................... ................................................. ..................................- 13 1.2 The mechanism of dissociation in a gas discharge .......... ...............................................- 14 1.3 Theoretical consideration of the formation gas jet ..............................- 17 1.3.1 Molecular regime (outflow) .............. ...............................................- 17 1.3.2 Formation beam with a long channel .............................................. - 18 1.3.3 Hydrodynamic flow regime. Supersonic jet...................................- 20 1.3.4 Estimation of source intensity ............................. ...................................- 24 Chapter 2
Methods for creating polarization in atomic beams.................................................................. .- 27 2.1 Introduction............................................... ................................................. ............- 27 2.2 Sources using the Lamb shift (LSS) .................................. ..........- 31 2.3 Optically pumped sources (OPPIS) .................................................. ........................................... 33 2.4 Sources of polarized atomic beams (PABS) .................................. ..............- 35 Chapter 3
Source of polarized atomic hydrogen and deuterium for the internal gas target of the ANKE spectrometer........................................................... ..................................- 38 3.1 Brief description of the design .............................. ................................................. .........- 38 3.2 Vacuum system .................................. ................................................. .....- 42 3.2.1 Construction of the vacuum chamber ..................
42 3.2.2 Differential pumping system .............................................................. .........- 44 3.3 Dissociator ..................................... ................................................. ..............- 47 3.3.1 Mechanical design .............................. ...............................................- 48 3.3.2 RF system.... ................................................. ...................- 51 3.3.3 Nozzle cooling system .............................. ...............................................- 52 3.4 Forming system gas jet ............................................... ............- 54 3.4.1 Construction .................................. ................................................. .........- 54 3.5 Spin-separating magnet system .................................. ..............................- 56 3.5.1 Basic principles ............................... ................................................. .........- 56 3.5.2 Spin-separating sextupole magnets ANKE ABS...................- 57 .................................................- 59 3.6.1 Principles of operation............................................... ...................................- 60 -2 3.6.2 ANKE ABS.. .........................................- 62 Chapter 4
Optimizing Source Characteristics .................................................................. ..................- 66 4.1 Intensity of the atomic beam .............................. .........................................- 66 4.1.1 Instruments and measurement technique ................................................. ..........- 66 4.1.2 Absolute calibration method .................................. ...............................- 69 4.1.3 Device for measuring the intensity of an atomic beam .......... ...- 74 4.1.4 Obtained results .......................................... ..................................- 78 4.1.5 Conclusions............. ................................................. ...............................................- 81 4.2 Spatial distribution of the beam density.... ...................................- 82 4.2.1 Instruments and measurement technique .............. ................................................. ....- 82 4.2.2 Nozzle adjustment ....................................... ................................................ ........- 86 4.2.3 Findings .............................................. ...............................- 88 4.2.4 Conclusions....... ................................................. ...............................................- 89 4.3 The degree of dissociation of the atomic beam ................................................. .......- 90 4.3.1 Instruments and measurement technique .................................. .........................- 90 4.3.2 Degree of dissociation of a free atomic jet ............... .................................................. 92 4.3.3 Spatial distribution of the degree of dissociation in a polarized beam .............................. ................................................. .................- 95 4.3.4 Conclusions .............................. ................................................. .......................- 97 4.4 Polarization ............................... ................................................. ...............................- 98 4.4.1 Instruments and measurement technique .............................. ................... .........................- 98 4.4.2 Findings .............................. ................................................. .... - 100 4.4.3 Conclusions............................................... ................................................. ........ - 102 Chapter 5
Perspectives of use .................................................................. ................................... - 104 5.1 Jet targets .......... ................................................. ............................... - 104 5.2 Polarized gas targets. Accumulation box .......................... - 106 Conclusion .................. ................................................. ............................................... - 110 Literature... ................................................. ................................................. .......... - 115 -3 List of illustrations i Fig. 1. Cross sections s in of inelastic processes 16 as a function of the electron energy . - 15 Fig. 2. Scheme of splitting the nozzle into elementary tubes .......................................................... ...- 24 Fig. 3: Energy level diagram of a hydrogen atom in a magnetic field B. For the ground state Bc = 507 G, for the 2S1/2 state Bc = 63.4 G. The energy W is measured in units of DW = h1420.4 MHz (= 5.9 10-6 eV) ............................... ..............- 28 Fig. 4: Energy level diagram of a deuterium atom in a magnetic field B. For the ground state Bc = 117 G, for the 2S1/2 state Bc = 14.6 G. The energy W is measured in units of DW = h327.4 MHz (= 1.4 10-6 eV) ............................... ...............................- 28 Fig. 5. Nuclear polarization of the levels of the hyperfine splitting of the hydrogen atom as a function of the external magnetic field.................................................................. .........................................- 30 Fig. 6. Nuclear polarization of the levels of hyperfine splitting of the deuterium atom as a function of the external magnetic field .................................................................. .........................................- 30 Fig. Fig. 7. Diagram of energy levels of hyperfine splitting for 2S1 / 2 and 2P1 / 2 states of the hydrogen atom .................................................. ................................................. ...- 31 Fig. Fig. 8. The main elements of a polarized source at the Lamb shift......- 32 Fig. 9. Operating principle of the source with optical pumping ..............................................- 34 Fig. Fig. 10. Energy levels of the hyperfine splitting of the hydrogen atom in the 2S1 / 2 state as a function of the external magnetic field.................................................... ...............................- 34 Fig. 11: Block diagram of a source of polarized atomic hydrogen/deuterium.
1 - gas flow regulator;
4 - the first group of spin-separating magnets;
6 - the second group of spin-separating magnets;
8 - storage cell (target) .............................................. ................- 35 Fig. 12. ANKE ABS and a special vacuum chamber for mounting various types of targets on the COZY storage ring. The source of polarized atomic hydrogen and deuterium is located between the deflecting magnet D1 and the central magnet of the spectrometer D2. Direction of the COZY beam from left to right .......................... 38 Fig. 13. ANKE ABS drawing. Explanations are given in the text............................................... .- 40 Fig. 14. Photo of ANKE ABS in the laboratory. Height of the upper vacuum chamber – 80 cm ....................................... ................................................. .................................- 41 Fig. 15. Upper movable baffle .............................................. .........................- 43 Fig. 16. Scheme of the vacuum system of the ANKE ABS source. A complete list of vacuum equipment is given in Table 1.................................................... ...................................- 44 Fig. 17. Various schemes for pumping chamber I .................................................. ...................- 45 Fig. 18. ANKE ABS RF dissociator.................................................................. ..........- 47 Fig. 19. Sectional view of the ANKE ABS dissociator. 1: gas supply flange, 2: coolant inlet, 3: HF entry, 4: HF sliding connection, 5: inductor, 6: capacitors, 7: lower cooling circuit seal, 8:
nozzle, 9: part of the nozzle cooling system (copper thermal bridge).................................- 49 -4 fig. 20. The lower end of the dissociator and the gas jet formation system. one:
discharge tube and cooling tubes, 2: lower cooling circuit seal, 3: Teflon heat flow restrictor, 4: sliding joint, 5:
nozzle and cooling system support, 6: heater, 7: copper thermal bridge, 8:
nozzle mount, 9: nozzle, 10: window in upper vacuum baffle, 11: skimmer, 12: collimator12, 13: first sextupole magnet, 14: lower vacuum baffle ................................................. ................................................. - 50 Fig. 21. Structural diagram of the radio frequency system .................................................... ...- 51 Fig. Fig. 22. Characteristic dependence of the nozzle temperature on time during stabilization using a PID controller .................................................................. ................................................. .......- 53 Fig. 23. Losses in the gas jet formation system .......................................................... ...- 55 Fig. 24. Sextupole magnet used in ABS. An atom flying into a magnet with r = 0 at an angle a0 is shown on the left;
on the right, several lines of force are shown.....- 56 Pic. 25. Dependence of the effective magnetic moment of an atom on the external magnetic field for four levels of hyperfine splitting .................................................................. ..............- 57 Fig. 26. Part of a cylindrical permanent sextupole magnet, consisting of segments .............................................................. ................................................. ...............................- 58 Fig. 27. Scheme of the block of high-frequency transitions .............................................. ..........- 60 Fig. Fig. 28. Structure of the ANKE ABS ultra-thin transition block...................................- 62 29. Scheme of winding a coil of a gradient field (Bgrad) .............................................. - 63 Fig. Fig. 30. Simplified wiring diagram for switching on the WFT and MFT units ...............- 64 31. Photograph of the MFT ultrafine transition unit (center) installed in the ANKE ABS polarized source. One of the three spin-separating magnets of the first group is seen from above. ..............- 65 Fig. Fig. 32: Device for absolute measurements of beam intensity - compression tube .............................................................. ................................................. ........- 67 Fig. 33: Electron impact ionization cross sections for atomic () and molecular () hydrogen .................................................... ................................................. .......................- 71 Fig. 34: Experimental data of PSV and PCV pressures versus time...- 74 Pic. 35. Assembly drawing of a device based on a compression tube. one:
guide support .................................................................. ...............................- 76 Fig. 36. Scheme of the non-polarized gas supply system .............................................. .- 77 Fig. Fig. 37. Photograph of the ABS lower vacuum chamber with devices for measuring the absolute beam intensity (below) and the degree of dissociation (left).................................................- 78 Fig. 37. Fig. 38: Dependence of the intensity of the atomic beam on the input flow of molecular hydrogen at nozzle temperature Tnozzle = 62 K, dissociator RF power Wdisso = 350 W and additional oxygen flow q(O2) = 1 10-3 mbar l/s..... ................................................. ...............................- 79 Fig. Fig. 39: Dependence of the intensity of the atomic beam on the RF power supplied to the dissociator at the nozzle temperature Tnozzle = 62 K, the input flow of molecular hydrogen q(H2) = 1.2 mbar l/s and the additional flow of oxygen q(O2) = 1 10-3 mbar l/s ............................................... ................................................. ...- 80 -5 Fig. Fig. 40: Dependence of the atomic beam intensity on the nozzle temperature for different nozzle diameters (D = 2.0, 2.3, 2.5 mm). The radio frequency power supplied to the dissociator is Wdisso = 350 W, the input flow of molecular hydrogen is q(H2) = 1.2 mbar l/s, and the additional oxygen flow is q(O2) = 1 10-3 mbar l/s. For comparison, the results of measuring the intensity of the sources HERMES (), PINTEX () and the source of polarized ions of the University of Munich ()...- 81 are shown. Fig. 41. Scheme of the installation for measuring the profile of an atomic beam ..................................- 83 42. Block diagram of a quadrupole mass spectrometer. Solid lines are stable, dash-dotted lines are unstable ion trajectories ..........................- 84 Fig. 43. Simplified scheme of the mass filter .............................................. .........................- 84 Fig. 44. System of control and data collection used in the measurements of the degree of dissociation .................................................................. ................................................. ...............................- 86 Fig. 45. Density distribution of atomic hydrogen in a beam. The shaded area corresponds to the geometrical dimensions of the vertical tube of the storage cell.................................................................. ................................................. .................................- 86 Fig. 46. Atomic hydrogen beam profiles in the X and Y planes corresponding to the distribution maximum in Figs. Fig. 45. The shaded area corresponds to the geometrical dimensions of the vertical tube of the storage cell...............- 87 Fig. 45. Fig. 47. Dependence of the signal of the quadrupole mass spectrometer on the position of the adjusting screw N1 .................................................................. ................................................. ...- 88 Fig. 48. Density distribution of atomic hydrogen in the beam after nozzle adjustment. The shaded area corresponds to the geometrical dimensions of the vertical tube of the storage cell.................................................................. ...............................................- 88 Fig. 49. Atomic hydrogen beam profiles in the X and Y planes corresponding to the distribution maximum in fig. Fig. 48. The shaded area corresponds to the geometric dimensions of the vertical tube of the accumulative cell...............- 89 Fig. 48. Fig. 50. Dependence of the degree of dissociation (a) on the inlet gas flow for various nozzle temperatures and radio frequency power W = 300 W.................................................... 93 Fig. 51. Dependence of the degree of dissociation (a) on the RF power at low input flows and nozzle temperature T = 70 K................................................. .................- 93 Fig. Fig. 52. Dependence of the degree of dissociation (a) on the RF power at high input fluxes and nozzle temperature T = 70 K....................................................... ................- 94 Fig. Fig. 53. Dependence of the degree of dissociation (a) on the temperature of the nozzle at various input flows and RF power W = 300 W............................................ .............- 94 Fig. 54. Degree of dissociation as a function of time for typical operating conditions of ANKE ABS .................................................................. ................................................. ..............- 95 Fig. 55: Distribution of the degree of dissociation in the beam in the plane of the compression tube. The shaded area corresponds to the geometrical dimensions of the compression tube.................................................................. ................................................. ...- 96 Fig. 56: Density distribution of molecular hydrogen in the beam in the plane of the compression tube. The shaded area corresponds to the geometrical dimensions of the compression tube.................................................................. ...................................- 96 Fig. 57: Profiles of the degree of beam dissociation in the X and Y planes along the center of the compression tube. The shaded area corresponds to the geometric dimensions of the compression tube....... ................................................. .......................- 97 -6 Fig. Fig. 58. Scheme of setup for measuring beam polarization...............................................- 99 Fig. 59. Dependence of the number of Ly-a photons on the magnetic field in the spin filter...... - 100 60. Dependence of the number Ly-a of photons on the magnetic field in the spin filter in the case of a polarized hydrogen beam. The left peak corresponds to atoms with mI = +1/2, the right one with mI = –1/2 .............................. ................................................. ......................... - 101 Fig. Fig. 61. Dependence of the number Ly-a of photons on the magnetic field in the spin filter in the case of a polarized deuterium beam: (a) and (b) - vector polarization, (c) and (d) - tensor polarization. The left peak corresponds to atoms with mI = +1, the middle one with mI = 0, the right one with mI = –1................................ ................................................. ............................... - 101 Fig. Fig. 62. Distribution of the magnetic and HF fields in the blocks of radio frequency transitions MFT (a), WFT (b) and SFT (c)............................................... ................................................. ............... - 102 Fig. Fig. 63. Principal diagram of a jet target (jet target) .................................................. - 105 Fig. 64. Storage cell for a polarized source............................................... - 106 65. Idea of storage gas cell and distribution of pressure in it....... - 108 -7 List of tables Table 1. List of ANKE ABS vacuum equipment.......... .......................- 46 Table 2. Parameters of the original and optimized beamforming systems and the obtained maximum intensities. Dimensions are in mm..............- 55 Table 3. Dimensions of sextupole magnets and magnetic field on the surface.....- 59 Table 4. Main characteristics of radio frequency transition blocks..... ...................... 61 Table 5. High-frequency equipment of hyperfine junction blocks ..............- 64 -8 Introduction Despite the great success of modern nuclear physics in explaining various properties of of nuclear matter, the question of the high-momentum component of the nuclear wave function, or, in other words, of the structure of nuclear matter at distances of the order of or less than the nucleon radius, is still open. At present, the main problem is the experimental detection of this structure and the determination of the interval of the internal moment of the relative motion of nucleons in the nucleus, in which the traditional description of the nucleus as a collection of nucleons is valid.
It is expected that at distances RNN 0.5 fm there is a certain transition region between the meson-nucleon and quark-gluon degrees of freedom in the nucleus. One of the confirmations of the existence of such a region at high transferred momenta can be a violation of the traditional picture based on the phenomenological potential of the NN interaction corresponding to the NN phase shift. In this sense, the problem of the high-momentum component of the nuclear wave function is closely related to the problem of choosing the nucleon-nucleon interaction potential at close distances.
A special role in the study of these problems is played by polarization experiments, which make it possible to establish the spin dependence of nuclear forces.
Carrying out such experiments requires the use of both a high-intensity beam of polarized protons and a high-density polarized target.
Traditionally, such targets were solid-state polarized targets. However, over the past decade, a new type of polarized targets, gaseous polarized targets, has been rapidly developed, which makes it possible to avoid the problems of radiation damage and the presence of unpolarized impurities (for example, N in NH3) that are typical for solid targets. The most common r r r polarized gas targets are H -, D - and 3 He targets that do not contain impurities. Since the spatial density of such targets is low, they have found wide application in accelerating storage rings. In this case, it is possible to achieve a sufficiently high value of the lifetime of the accelerator beam, and the high luminosity of the experiment is ensured due to the repeated passage of the beam through the target.
9 Currently, several experiments are being carried out using both a polarized accelerator beam and a polarized target consisting of a polarized atomic beam source (PABS1) and a cryogenic storage cell in which the interaction under study occurs.
For the first time, a gaseous polarized deuterium target was used in Novosibirsk on the VEPP-3 electron storage ring.
The HERMES experiment at DESY (Hamburg, Germany) studies the spin structure of the nucleon. For this purpose, inclusive and semi-inclusive reactions of deep inelastic scattering of a longitudinally polarized 27.5 GeV r r HERA positron beam on polarized H, D, and 3 He gas targets are studied.
Hydrogen and deuterium targets are a source of a polarized atomic beam and a storage cell. Such setups make it possible to create an atomic beam with a sufficiently high (close to 100%) nuclear polarization, and the use of an open storage cell does not destroy the accelerator beam.
Experiments were carried out on the polarized beam of the IUCF storage ring (Bloomington, USA) to study nucleon-nucleon interactions, also using an internal polarized gas target. Their goal was to improve modern ideas about the potential of the nucleon-nucleon interaction. For this purpose, the spin-correlation coefficients were measured and pion production near the threshold was studied.
A special role in the study of issues related to the study of NN interactions at close distances is played by the deuteron, as the simplest nuclear system. Despite the fact that the deuteron is a rather loosely bound system, it has become the main object of study in both theoretical and experimental nuclear physics.
One of the experiments aimed at studying the pd interaction at a moment of relative motion of nucleons inside the nucleus q = 0.3 0.5 GeV/c is the COSY2-Jlich storage ring experiment dedicated to the breakup of the deuteron. Of particular interest is the polarization experiment rr (pd ® ppn), aimed at determining the dependence of five polarization (A yp, Ay, A yy, C yy, C yyy) d d observed on the internal moment of relative motion of nucleons in the deuteron breakup reaction. This will allow the new Polarized Atomic Beam Source COoler SYnchrotron - 10 to obtain information about the structure of the deuteron wave function, since the polarization observables depend on the ratio of the S- and D-components of the wave function. Taking into account the features of the ANKE3 spectrometer, the experiment can be carried out in conditions of collinear geometry: protons emitted backwards close to 180 will be registered in coincidence with protons emitted forward at small angles (close to 0). In this geometry, the S- and D-wave functions of the deuteron can be studied up to an internal moment of 0.5 GeV/c.
This experiment will require the use of both a polarized accelerator beam and a polarized target.
At present, a beam intensity of 5·1016 particles/s for unpolarized and 5·1015 particles/s for polarized protons has been achieved on the COZY storage ring. However, modernization of the source of polarized ions, beam transport path and injection system should lead to an increase in the intensity of the beam of polarized protons up to 1 1016 particles/s. In addition, it is planned to inject unpolarized, and later polarized deuterium.
In the experiment, it is planned to use an internal gas target, which is a cryogenic storage cell. The polarized gas, hydrogen or deuterium, enters the target from a source of polarized atomic hydrogen and deuterium (ANKE ABS).
Since one of the main factors determining the efficiency of the experiment at the accelerator is the statistics collection time, which is proportional to the target density, determined by the source atomic beam intensity, and has a quadratic dependence on the target polarization. Therefore, these parameters are subject to special requirements:
· high nuclear polarization of the atomic beam (more than 80%);
· fast change of polarization sign (positive/negative) and, in the case of a deuterium beam, polarization type (vector/tensor);
high intensity of the atomic beam (more than 61016 atoms/s).
· In addition to physical parameters, the source must meet the high requirements for experimental setups on modern storage rings (vacuum conditions, limited space, rapid integration into an existing experimental setup, etc.).
Apparatus for studies of Nucleon and Kaon Ejectiles - 11 Achieving high values of source parameters is impossible without studying the characteristics of atomic beams. The latter implies the need to develop methods and create a number of instruments for measuring and optimizing source parameters.
This work is devoted to the creation of a source of polarized atomic hydrogen and deuterium, as well as the development of instruments for studying and optimizing the parameters of an atomic beam, such as the intensity of the atomic beam, the degree of polarization, and the spatial distribution of the beam density.
The paper presents various methods that make it possible to create atomic beams with nuclear polarization. A detailed description of both the principles of operation and the design of the structural elements of the source of polarized atomic hydrogen and deuterium is given. The results of studies of the properties of an atomic hydrogen beam are presented. The prospects for using a source of polarized atomic hydrogen and deuterium as a source for gas targets used in experiments on storage rings are considered.
Chapter 12
Methods for producing atomic beams 1.1 Introduction For many years, experiments with molecular and atomic beams have been a source of valuable information about the properties of molecules, atoms, and nuclei. The first experiments with molecular beams were carried out at the beginning of the 20th century by Dunoyer. In the 1920s, Stern and Gerlach, in their experiments on the deflection of atomic beams in inhomogeneous magnetic fields, showed the presence of spatial quantization. A little later, in the 1950s, Lamb and Riserford discovered a shift in the 2S1/2 and 2P1/2 levels relative to each other. This phenomenon is called the Lamb shift. A decade later, a method was proposed for creating polarized atomic beams, which has found wide application in modern nuclear physics. In this, far from complete, list, the main objects of study were beams of neutral atoms and molecules.
Quite often, it becomes necessary to obtain beams of atoms, such as H, D, Cl, etc., despite the fact that under normal conditions these atoms form molecules (H2, D2, Cl2, etc.). If the creation of molecular beams is not particularly difficult, then the methods for obtaining beams of similar atoms are in themselves a separate physical problem for the dissociation of molecules into atoms.
Traditionally, the most commonly used methods for dissociating molecules into atoms are:
· Dissociation under the influence of high temperatures, as, for example, in the work where molecular hydrogen was fed into a tungsten furnace, which was heated to a temperature of 2500 K. At a pressure in the furnace of the order of 1 mbar, the degree of dissociation was ~64%.
· Dissociation in a strong electric field, as, for example, in the work , where a Wood tube was used to dissociate hydrogen. The degree of dissociation was ~7080% at a pressure in the tube of about 1 mbar.
13 · Dissociation under the action of a high-frequency field (see, for example, , where at a pressure in the discharge tube of ~0.25 mbar, the degree of dissociation was ~60%).
In modern installations, the latter method is most widely used. To create and maintain a gas discharge, standard high-frequency or microwave industrial generators are used. At characteristic pressures inside the discharge tube at a level of 12 mbar, the degree of dissociation in such devices reaches 90%.
In addition to the dissociation of molecules, the task of creating atomic beams also includes issues of beam formation. The conditions necessary to create a beam of atomic hydrogen can be very different for each specific case under study. The need to keep the recombination rate low requires that the beamforming systems operate at low density (1017 atoms/cm3) and, moreover, at fairly large nozzle openings. Therefore, the parameters of the formation system cannot be chosen a priori, but rather must be a compromise solution, taking into account the limitations imposed by other parameters of the installation.
1.2 Mechanism of dissociation in a gas discharge The degree of dissociation in a gas discharge is determined by the density of the created atomic component and various recombination mechanisms. The mechanism of these processes is determined by the macroscopic parameters of the discharge, such as the gas pressure in the discharge tube, the power of the radio-frequency field scattered by the plasma, the properties of the material of the discharge tube, and so on. Usually, to obtain and maintain a discharge, an oscillatory circuit is used, fed by a radio frequency generator and dissipating the power of the electromagnetic field on the plasma through inductive coupling with a dielectric discharge tube. The degree of ionization, defined as the ratio of the electron or ion density to the density of neutral particles (atoms and molecules), is rather low and lies in the range of 10-510-3.
The mobility of electrons is much greater than the mobility of ions, and this leads, given the low degree of ionization, to the fact that the temperature of the electron gas is much higher than the temperature of neutral particles and ions. The characteristic temperature range is 14 neutral and ionic components 5002000 K, which corresponds to energies in the range of 0.080.35 eV, while the average electron energy lies within 210 eV. That.
the properties of the discharge are determined by the kinetics of electrons: being in a high-frequency electromagnetic field, free electrons acquire energy and dissipate it on neutral particles through elastic and inelastic collisions.
The following inelastic interactions (with cross section s iin) of free electrons with neutral particles are dominant:
1) Excitation of vibrational levels of molecules (s 1in) e- + H 2 ® H 2 + e-.
ex 2) Dissociation of molecules (s 2) in e- + H 2 ® H + H + e-.
3) Ionization of molecules (s 3) in e - + H 2 ® H 2+ + 2e -.
4) Ionization of atoms (s 4) in e - + H ® H + + 2e -.
5) Excitation of 2p states of atoms (s 5) in e - + H ® H (2 p) + e -.
6) Excitation of 2s states of atoms (s 6) in e - + H ® H (2s) + e -.
0. s2in s in 0. s1in s5in siin 10-15 cm s4in 0. 0. 0. s in 0. 10 20 30 40 Electron energy, eV i 1. Cross sections s in of inelastic processes 16 as a function of the electron energy .
15 As can be seen from fig. 1, the dissociation process (threshold electron energy 8.8 eV) is dominant in the electron energy range 1020 eV.
Taking into account the energy dependence of the cross sections and the Maxwellian spectrum of electron energies, it was shown in the work that, at an average electron energy of less than 5 eV, in addition to the dominant process (1), the intensity of the dissociation process (2) is an order of magnitude higher than the intensity of ionization processes (3) and ( 4).
This leads to the conclusion that, under the typical discharge conditions described above, dissociation rates of up to 90% can be expected. For given atomic and molecular densities, the degree of dissociation is defined as na a= (1) na + 2n m or nm a =1+ (2) off nm off where nm is the molecular density in the absence of discharge and then (3) na = 2(nm - n m) off In addition to the main processes, for charged particles formed as a result of ionization processes (3 and 4), in the above reasoning, diffusion losses, two- and three-particle recombination were taken into account. The calculations presented in show that, in the range of a from 0 to 100% and a dissipated power density of 125 W/cm3, the average electron energy lies below 5 eV. This also confirms the possibility of obtaining a high degree of dissociation.
The density of the atomic fraction created as a result of the dissociation of molecules decreases due to the recombination 2H + M ® H 2 + M + E where M is the third body required to fulfill the conservation laws and E0 4.5 eV is the binding energy of the hydrogen molecule. In the work, an estimate was made of the recombination coefficient (the probability of recombination in a collision with a wall) and it was shown that under typical discharge conditions, i.e. gas pressure, temperature and plasma volume, the predominant process is surface recombination.
Traditionally, borosilicate or quartz glass is used as the material of the discharge tube; these materials are suitable for high temperature applications and have a low surface recombination coefficient. However, existing experimental data show that - 16 the recombination coefficient for hydrogen on borosilicate and quartz glass increases rapidly with increasing temperature. Thus, during operation, it is necessary to cool the discharge tube. Additionally, to reduce the recombination coefficient, a special treatment of the inner surface of the discharge tube, described in the works, is used, as well as a small additional (~ 0.10.5% of the main) oxygen flow.
1.3 Theoretical consideration of the formation of a gas jet In order to correctly estimate the intensity of an atomic beam, as well as to explain the measurement results, it is necessary to answer the questions that arise when considering the formation of a beam. The theory, unfortunately, has not yet reached a consensus on the formation of a gas jet in the hydrodynamic regime. Therefore, for the time being, we have to talk not about intensity calculations, but only about its estimation.
1.3.1 Molecular regime (outflow) Simple outflow prevails over other modes if the density of the gas behind the hole is low enough, i.e. Knudsen coefficient Kn = l / d 1 , where l is the mean free path, d is the hole diameter. In this case, there is no interaction between the particles both during the outflow and after it4. The differential beam intensity I(q) per unit solid angle dW at angle q (relative to the normal to the hole plane) is given by the cosine distribution :
I (q) = n0 A0 v f (v) cos(q)dWdv, (4) where n0 is the gas density in the source, A0 is the hole area f(v) is the Maxwell-Boltzmann velocity distribution, which is written as:
v v f (v)dv = p exp - dv, (5) z z3 with a viscosity coefficient h having a velocity v inside a pipe with a diameter d.
At R 2200, the flow regime becomes turbulent.
17 z = (2kT0 / m)1 / 2 corresponds to where is the most probable particle velocity at the source temperature T0.
The total flow f 0 through the hole is obtained by integrating over velocities and solid angle 2p:
f0 = n0 A0 v 1/s, (6) where v = (8kT0 / pm)1 / 2 is the average particle velocity in the source at temperature T0.
The beam intensity in the direction of the normal to the hole plane I(q = 0) is maximum and is given by:
f I (0) = 1/s ster. (7) p The fundamental disadvantages of a simple hole as a beam source are the low peak intensity proportional to the density n0, as well as the weak beam directivity.
1.3.2 Beam shaping by a long channel The weak directivity of a beam formed by a simple hole can be significantly improved by replacing the hole with a long channel, usually of a cylindrical cross section. The requirement for a molecular regime of gas flow in a long channel entails a loss in beam intensity. Therefore, usually, when considering the formation of a beam by a long channel, only partial fulfillment of the molecular flow conditions is required. The assumptions for such a model can be formulated as follows:
· Even for a sufficiently high pressure in the gas source, there is a section of the channel in which the conditions of the molecular flow regime are satisfied. Usually, the existence of such a section at the outlet of the channel is implied, while at the beginning of the channel, the gas is in the conditions of a hydrodynamic or intermediate flow regime with (Kn 1).
· In the section of the channel with a molecular flow regime, the density as a function of the distance z along the channel decreases linearly and reaches zero at the exit from it.
Two processes contribute to the peak intensity of the beam (in the forward direction). The first contribution is due to particles that pass through the channel without experiencing - 18 collisions. The second contribution comes from particles that have been scattered by other gas particles but have reached the end of the channel.
The described model has two specific modes depending on the ratio of the particle free path l at the gas density in the source n 0 to the channel length L:
1. Transparent channel: l L/2. For a sufficiently low gas pressure in the source, only the first process contributes to the beam intensity.
Therefore, the peak intensity is:
I (0) = n0 A0 v 1/s ster. (8) 4p It can be expressed in terms of the total gas flow f t using the Clausing formula ft = K n0 A0 v, (9) where K = 4d/3L is the geometric factor, d and L are the channel diameter and length, f t 1/ s ster.
I (0) = (10) pK Expression (10) is a formula for calculating the peak intensity of a beam formed by a long channel. It should be noted that the gas flow in the forward direction in relation to the total flow is greater compared to a simple outflow from the hole (7).
2. Opaque channel: l L/2. This regime corresponds to the case when particles have negligible probability to pass through the channel without collisions.
The criterion for opacity is the condition L/l 12 . In this case, the peak intensity is lower than with a transparent channel, and is given by :
1/ v d I (0) = 0.065 f t1 / 2 1/s ster, (11) s () - where s = 2ln is the particle collision cross section. It can be seen that in the above expression, the peak intensity does not depend on the channel length.
Based on the cases considered, it can be concluded that at a sufficiently low gas density in the source, the peak intensity I(0) is proportional to f t, and at a high density, to f t1 / 2.
19 I (0) µ f t1 / 2, The analysis of the described model shows that the dependence arising as a consequence of the linear law of change in the gas density in the channel, in fact, does not depend on this assumption. Therefore, this relationship can be extended to the case when the "opacity" continues beyond the channel, forming a cloud between the nozzle and the skimmer. In this case, the gas density decreases linearly along the channel axis z at distances less than two nozzle diameters;
and then drops to very small values at a distance of several l. This allows such a model to be used despite the unrealistic assumption of n = 0 at the channel output. As a consequence, expression (11) is a reliable approximation, even if the conditions of the molecular flow regime are not satisfied. A contradiction is expected only in the case when the transition of the gas to the molecular regime occurs at a large distance from the exit from the channel or the gas jet acquires hydrodynamic features as a result of formation.
1.3.3 Hydrodynamic flow regime. Supersonic jet As soon as the gas density in the source becomes so high that the mean free path l becomes small compared to the nozzle diameter, the gas passes into an intermediate flow regime close to laminar. After exiting the nozzle, the gas undergoes adiabatic expansion. Assuming thermalization of gas particles on the nozzle surface and setting a typical nozzle temperature of about 100 K, nozzle diameter of 2 mm, and pressure in the dissociator discharge tube of about 1 mbar, l » 0.04 mm and Kn » 0.02. Here l is defined as kT l=, (12) 4p 2 pr where k is the Boltzmann constant, T is the gas temperature, p is the source pressure and r = 1.87·10-8 cm is the kinetic radius .
A simple orifice or a long channel used to produce a gas jet in the molecular flow regime is replaced by a conical nozzle in the case of hydrodynamic jet formation. The second "hole", usually called a skimmer and located behind the nozzle, theoretically allows the formation of a supersonic particle beam.
Under the conditions described, the gas jet emitted by the nozzle moves towards the skimmer at a hydrodynamic velocity that can greatly exceed the simple thermal velocity of the gas. This shaping method is very interesting from the point of view of obtaining beams with high intensity, as well as monochromatic beams.
Under ideal conditions of steady gas flow, it leaves the tank through a small opening and experiences adiabatic expansion. The initial enthalpy H 0 of the particles is converted into the kinetic energy of the directed flow mu 2 and the residual enthalpy H = U + PV, where U is the internal energy, P is the mass pressure, and V is the volume. The law of conservation of energy gives:
H0 = H + mu 2. (13) With the specific heat capacity of the gas at constant pressure c p, the temperature of the initial reservoir T0 and the local gas temperature T on the axis of the expanding beam, we obtain :
c p T0 = c p T + mu 2, (14) whence - 1 T = T0 1 + (g - 1) M 2, (15) 2 cp where g =. The Mach number M is the ratio of the jet velocity u to the local sound velocity cV in the gas c = (gkT / m)1 / 2. M2 is the fraction of the energy of directed motion from the thermal energy of the gas.
If the residual gas pressure p1 in the chamber directly behind the nozzle satisfies the condition:
g p1 2 g +1 (16), p 0 g - then the Mach number reaches the value M = 1 in the narrowest part of the nozzle. Here p 0 is the gas pressure in the original reservoir. Under such conditions, the gas flow reaches its maximum value.
The specific heat capacity at constant pressure c p for a monatomic gas is equal to kT. Then - 21 5 1 kT0 = mu 2 + kT + kT. (17) 2 2 The first term on the right side is the kinetic energy of the directed mass flow, the second term is the kinetic energy of thermal motion5. The third term is related to the energy contained in an ideal gas at temperature T, which forces the gas to expand.
All three terms can be written as functions of the Mach number, in particular, the kinetic energy is written as:
1 mu = c p (T0 - T) = c pT0 1 - 1 + (g - 1) M.
(18) 2 2 The Mach number increases with increasing distance l from the nozzle, since with the expansion of the gas, not only the gas temperature, but also the density (and, accordingly, the number of particle collisions per unit time) decreases with increasing distance. Finally, at a certain distance l m, the beam cooling stops and the Mach number reaches its maximum value M T and remains `frozen'.
For the distance l m, the empirical relation is given in the work:
p l m = 0.67d t 1, (19) p where d t is the nozzle throat diameter. Further, the maximum Mach number can be approximated by the expression:
g - (20) g M T = 1.2 Kn 0, where Kn 0 is the Knudsen coefficient determined by the nozzle conditions. As already mentioned, for a nozzle with a diameter of 2 mm at a temperature of 100 K, Kn 0 » 0.02, and thus the maximum Mach number is 6.
Approximately the same value under these conditions is given in the work, in which the dependence of the Mach number on the distance, measured in units of nozzle diameter, is derived.
At a distance l m there is a transition from hydrodynamic to molecular flow. Not earlier than this transition has taken place, the beam must pass the skimmer into the region of better vacuum. However, the transition to the region of better vacuum can be done in a frame of reference moving at a speed u relative to the laboratory one.
22 to influence the shock waves arising due to the interaction of the gas jet and the residual gas. Therefore, the location of the skimmer must be chosen with extreme care in order to avoid strong impact from the shock waves that form the Mach disk.
Let us assume that the beam structure is not disturbed by the presence of a skimmer, and, in addition, after the skimmer, the beam is in the molecular flow regime. Then the peak intensity on the beam axis per unit solid angle is given by the following expression:
I (v) = n s As v f (v)dWdv, (21)
(v - Ws) v f (v)dv = p exp - dv, (22) z s3 z s where z s = (2kTs / m)1 / 2 and Ws = M s (gkTs / m)1 / 2 . The index s of the variables reflects their calculation when the beam enters the neck of the skimmer. From expression (22) it is easy to find the most probable velocity of the supersonic beam:
v0 = (23) 2 gMs
gM s2 + f c = As Ac n sWs 1/s. (24) 2pl sc Here l sc is the distance between the skimmer and the collimator. According to the paper, the gain in beam intensity provided by the formation of a beam with hydrodynamic properties compared to simple gas outflow is:
1/ cp G @ p k gM s2. (25) However, the presented gain in intensity is overestimated for real beams. This is due to the fact that there is scattering of beam particles on the residual gas of the vacuum chamber.
23 1.3.4 Evaluation of the source intensity Knowing the density of particles exiting the nozzle is essential for estimating the intensity of a source of polarized atoms. A method that allows in turn to estimate the density is described in. Its idea is that the conical nozzle is replaced by a series of short tubes with a diameter of d in - d out di = i + d out. (26) N and length ln l = li =. (27) N Here l n is the nozzle depth, N is the number of tubes, d in and d out are the nozzle inlet and throat diameters, respectively.
PN N N- N- Pi i Pi P 2. Scheme of splitting the nozzle into elementary tubes.
The flow of gas from one volume to another through an elementary tube (see Fig. 2) is defined as:
Q \u003d C i (Pi 2 - Pi1) (28) where Pi 2 and Pi1 are pressures on both sides of the tube, and to maintain pressure continuity, Pi 2 = Pi +1.1, C i is the conductivity of the tube, for which there is a universal formula for any gas flow regime:
d (P + Pi1) d i3 Tb 1.96 10 - 2 i i 2 l/s.
C i = 1.25 10 -6 + 3.04 10 4 (29) 2h l M - 24 In this formula, all linear dimensions are expressed in mm, pressures are in mbar, h = 8.58 10 -8 mbar s M - molar mass, viscosities at room temperature.
The room temperature viscosity coefficient can be converted to any other temperature using Sutherland's constant C, which for hydrogen is 73:
T 1 + C / T h T = hT0. (30) T0 1 + C / T Tn = 100 K the gas temperature will be For a nozzle with a temperature equal to Tb = 0.290 Tn = 29 K . Therefore, the viscosity coefficient will be h = 9.59 10 -9 mbar·s. (31) The particle density in the nozzle throat is defined as P n=, (32) kTb where k = 1.38·10-19 mbar·cm3/K is the Boltzmann constant. The expression for Pi 2 following from equations (28) and (29) is written as:
Pe Q e e + + Pi1 + i1 + Pi 2 = - (33), 2z 2z u xz 3.04 10 4.
M To estimate the beam density at the exit from the nozzle, it is necessary to make an assumption about the gas pressure distribution inside the dissociator discharge tube. During ABS operation at the accelerator, the inlet flow of molecular hydrogen is planned to be maintained at 1.7 mbar l/s. For such a flow, the pressure measured at the entrance to the discharge tube of the dissociator is 1.53 mbar.
Let us assume that the discharge region is approximately in the middle of the dissociator.
After the process of dissociation and recombination on the surface of the discharge tube, the degree of dissociation at its outlet end is 90%, and, consequently, the number of particles, 25, is 1.9 times greater than at the entrance to the dissociator. It follows from this that the pressure created by the gas at the entrance to the nozzle is PN 2 = 2.81 mbar.
Having carried out the calculation according to the above procedure with the number of partitions N = 90, the pressure in the nozzle throat turns out to be P12 = 2.78 mbar. Then, from expression (32) the particle density is n = 6.95 1017 cm -3. (35) Relation (24) can be rewritten as As n0 a 0 M Ac fc = (3 + gM 2) 2pl sc 3 (36) 1 1 + (g - 1)M 2 where n0 is the particle density in the nozzle throat, a0 is the speed of sound in the nozzle and M = M s.
Since a0 = 4.1376 10 4 cm/s at temperature Tb, the gas flow through the collimator is f c = 2.24 1018 1/s. (37) As already noted, such an estimate gives an overestimated value for the intensity. The reason for this is the process of intensity attenuation due to the scattering of beam particles by the residual gas.
In practice, to determine the parameters of the beam formation system at which its intensity is maximum, empirical methods are used. For this purpose, the intensity of the atomic beam is measured as a function of the geometry of the nozzle, skimmer, and collimator, the inlet gas flow, and the temperature of the nozzle.
In this regard, when creating installations for working with atomic and molecular beams, it is necessary to ensure the possibility of adjusting the fullest possible set of parameters of the beam formation system.
26 Chapter 2
Methods for creating polarization in atomic beams 2.1 Introduction The technique for creating beams of polarized protons and (or) deuterons consists in preparing a beam of neutral atoms in such a way that the spins of nuclei (protons or deuterons) in an atom are oriented predominantly along the direction of the external magnetic field. Upon subsequent ionization of atoms, for example, by electron impact, the nuclear polarization is preserved, which makes it possible to obtain beams of polarized protons (or deuterons).
The technique for creating polarized beams of neutral hydrogen or deuterium atoms is based on the fact that the nuclear and electron spins are interconnected. Therefore, by acting on the magnetic moment of the electron, one can also act on the nuclear spin.
The hydrogen atom in the ground state has an electron spin S = 1/2 with the projection mj = ±1/2 and a proton spin I = 1/2 with the projection mI = ±1/2. That. the total rrr spin of the atom F = S + I (F = 0, 1) has the projections mF = 0 and mF = 0, ±1, respectively.
Energy difference between the levels with F = 0 and F = 1 in the absence of an external magnetic field DW = h1420.4 MHz . As a result of the interaction of the magnetic moment of an atom with an external magnetic field, the level with F = 1 splits, according to the Zeeman effect. The strength of the external field is determined by the relation to the so-called. "critical" field Bc, which is defined as DW Bc = (for hydrogen 507 G), (38) (g I - g j)m B electron in units of the Bohr magneton m B = -0.927 10 -20 erg/G. That. the field strength is defined as c = B/Bc.
Energy splitting is determined by the Breit-Rabi formula:
27 DW DW 4m F + g I m B m F Bc c + (-1) F +1 c + c2.
W =- 1+ (39) 2(2 I + 1) 2I + 3.
2 mF F=1 + 1: mj=+1/2 mI=+1/ W/DW 0 2: mj=+1/2 mI=-1/ 0 - 3: mj=-1/2 mI=-1 / 4: mj=-1/2 mI=+1/ F= - - 0 2 4 6 c=B/Bc 3: Energy level diagram of a hydrogen atom in a magnetic field B. For the ground state Bc = 507 G, for the 2S1/2 state Bc = 63.4 G. The energy W is measured in units of DW = h1420.4 MHz (= 5.9 10-6 eV).
In the region c 1 the slope of the curves is determined by the magnetic moment of the electron.
r r When c 1, S and I are no longer independent vectors; therefore, in the region of weak fields, the curves are denoted by the projections mF of the total spin F.
2 mF 1: mj=+1/2 mI=+ +3/ F=3/2 2: mj=+1/2 mI= +1/ 3: mj=+1/2 mI=- W/DW -1 / 0 -3/2 4: mj=-1/2 mI=- -1/2 5: mj=-1/2 mI= 6: mj=-1/2 mI=- F=1/2 +1/ - -4 0 2 4 6 c=B/Bc 4: Energy level diagram of a deuterium atom in a magnetic field B. For the ground state Bc = 117 G, for the 2S1/2 state Bc = 14.6 G. The energy W is measured in units of DW = h327.4 MHz (= 1.4 10-6 eV).
28 For deuterium, which has a nuclear spin I = 1 (F = 1/2 and F = 3/2), the critical field is Bc = 117 G. The dependence of the energy of hyperfine levels of deuterium on the strength of the external magnetic field is shown in fig. 4.
The polarization of a proton with spin I = 1/2 (mI = ±1/2) is defined as the vector polarization N m I = +1/2 - N mI = -1 / Pz (I = 1/2) =, (40 ) N m I = +1 / 2 + N m I = -1 / where, N mI = +1/ 2 and N mI = -1 / 2, respectively, the number of atoms with a spin parallel and antiparallel to the applied external field.
To describe the polarization of the deuteron, which has a nuclear spin I = 1 (mI = –1, 0, +1), in addition to the vector polarization N m I = +1 - N m I = - Pz (I = 1) = (41) N m I = +1 + N m I = 0 + N m I = -1, the tensor polarization is also used, defined as 1 - 3 N mI = Pzz (I = 1) = (42) N m I = +1 + N m I \u003d 0 + N m I \u003d -1.
On fig. Figure 5 shows the dependences of the vector (I = 1/2 and I = 1) and tensor (I = 1) polarizations of the hyperfine levels of hydrogen and deuterium as a function of the external magnetic field. States 1, 3 for hydrogen and 1, 4 for deuterium are pure and completely polarized regardless of the magnitude of the external magnetic field.
In a strong magnetic field in the hydrogen states 2 and 4, the proton and electron are polarized in opposite directions. As the field decreases, the magnetic moments of the proton and the electron begin to precess with respect to each other, as a result of which the proton polarization decreases, as shown in Fig. 5. In the absence of an external field, the proton and electron polarizations change sinusoidally with time (with the Larmor frequency), on average creating a zero polarization. Similar reasoning can be carried out for the deuterium states 2, 3, 5, and 6.
29 Hydrogen Vector polarization Pz 0. -0. - 0.01 0.1 c = B/Bc 5. Nuclear polarization of the levels of hyperfine splitting of the hydrogen atom as a function of the external magnetic field.
Deuterium Vector polarization Tensor polarization Pz Pzz 1 + 1 0. 0. 2 0 -0. thirty. -one. -1 - 0.01 0.1 1 10 0.01 0.1 1 c = B/Bc c = B/Bc 6. Nuclear polarization of the levels of hyperfine splitting of the deuterium atom as a function of the external magnetic field.
In a strong field of a separating magnet, atoms with mj = +1/2 have zero nuclear polarization. For equally populated hydrogen levels 1, 2, i.e.
N mI \u003d + 1 / 2 \u003d N mI \u003d -1 / 2 and deuterium 1, 2 and 3, i.e. N mI = +1 = N mI = 0 = N mI = -1, from fig. It can be seen from Fig. 6 that Pz = 0 and Pzz = 0 at c 1. During the adiabatic transition to the c 1 region, Pz = +1/2 for hydrogen, Pz = +1/3 for deuterium, and Pzz = –1/3.
Thus, to create a polarization of an atomic beam, it is necessary to select atoms in one or several, in the case of tensor polarization of deuterium, hyperfine states.
30 At present, installations for creating polarized beams are widely used in various physical experiments both as sources of polarized protons and deuterons for charged particle accelerators and as polarized gas targets. The most common types of such installations today are:
sources using the Lamb shift (LSS6);
sources with optical pumping (OPPIS7);
· polarized sources of atomic beams (PABS8).
2.2 Sources using the Lamb shift (LSS) As already noted, in order to create polarization in a beam, it is necessary to select the “required” hyperfine states. This is achieved both by spatial separation of the beam components (Stern-Gerlach-type sources) and by using the technique of discharging the 2S1/2-metastable state into the short-lived 2P1/2-state.
E mS +1/ 2S1/2 mI +1/2 -1/ (t = 0.14 s) F=1 1609 MHz 0 -1/ 4.410-6 eV DELamb +1/ DEhyperfine -1/ 2P1/2 1.610-7 eV (t ~ 10-9 s) External magnetic field, G 535 Fig. 7. Diagram of energy levels of hyperfine splitting for 2S1 / 2 and 2P1 / 2 states of the hydrogen atom.
Lamb-Shift Source Optically Pumped Polarized Ion Source Polarized Atomic Beam Source - 31 Figure 7 shows the energy level diagram of the hyperfine splitting for the 2S1 / 2 and 2P1 / 2 states of the hydrogen atom. In the absence of an external magnetic field, the energy difference between these levels (the Lamb shift) is 1058 MHz. The main characteristic of the 2S1 / 2 level is that it is a metastable level with a lifetime t 2 S1 / 2 » 0.1 s. Level 2P1 / 2, in turn, is short-lived, with a lifetime t 2 P1 / 2 ~ 10 -9 s.
a Following the notation adopted in the work, we denote through the components of the 2S states with mj = +1/2, through b, respectively, the components with mj = –1/2. The corresponding components of the 2P state will be denoted by e and f. As can be seen from fig. 7, when the magnetic field reaches 535 and 605 G, the b states mix with the e states in the presence of an external electric field due to the Stark effect. This process is often referred to as the discharge of the 2S1 / 2 metastable state. Thus, only the a states with mj = +1/2 and mI = ±1/2 remain in the beam.
The difference between the energies of the levels a+ and e+, and a– and e–, where the signs “+” and “–” denote the sign of the projection of the proton spin (mI), is ~1600 MHz at a magnetic field of 535 and 605 G, respectively. Thus, by applying, in addition to the magnetic and electric fields, a high-frequency field with a frequency of ~1600 MHz and setting one or another magnetic field value, it is possible to discharge the a+ or a– level. Those.
create positive or negative vector beam polarization.
1 2 Alkali metal vapor chamber Proton source for formation Spin filter (ionizer) of metastable atoms in (2S1/2) 8. Main elements of a polarized source at the Lamb shift.
On fig. Figure 8 shows the main elements of a polarized source at the Lamb shift. To create metastable atoms, a proton beam from an ionizer (1) is passed through a chamber filled with alkali metal vapors (2), where, as a result of charge-exchange interaction, atoms are formed in the 2S1 / metastable state. Next, the beam of metastable atoms enters the spin filter (3), where the b-states are discharged and one of the two a - 32 states is selected. Thus, at the output of the source, a beam with one or another vector polarization is obtained.
Sources using the Lamb shift are mainly used as sources of polarized protons for charged particle accelerators.
However, the principle of operation of sources of this kind has found wide application in the field of polarization measurements. Such devices are called polarimeters using the Lamb shift, and make it possible to measure the polarization of beams of neutral atoms and ions with an energy of several hundred electron volts with an accuracy of about 1%. The setup described in , in particular, was used in the course of measurements of the polarization of the hydrogen and deuterium beams of ANKE ABS.
The advantages of sources using the Lamb shift include a relatively simple design, reliability, and low cost. They also make it possible to obtain proton and deuteron beams with a fairly high (7080%) degree of polarization. However, the main disadvantage of sources of this type is the low intensity rarely exceeding 0.5 mA. It is the low beam intensity that limits the use of LSSs as polarized targets, since the effective density of such a target is ~105 atoms/cm2.
2.3 Optical pumped sources (OPPIS) Optical pumped sources operate as follows.
The proton beam from the ECR9 ionizer (1, Fig. 9) is accelerated to an energy of several kiloelectronvolts and enters the neutralizer chamber filled with alkali metal vapors (2). The use of circularly polarized laser radiation makes it possible to create polarization along the electron spin in alkali metal atoms (optical pumping). Further, as a result of the charge-exchange reaction, the beam protons capture the polarized electrons of the alkali metal atoms and form neutral atoms in the metastable 2S1/2 state.
To maintain the electronic polarization of metastable atoms, chamber (2) is placed in a strong longitudinal magnetic field. Thus, a beam of neutral atoms polarized along the electron spin is formed at the output of the neutralizer.
Electron Cyclotron Resonance - 33 Laser for optical pumping of alkali metal vapors Polarization transfer Capture of polarized Proton source from electron to proton Alkali atom electron ionizer (ECR ionizer) by means of Sohn metal effect 1 2 3 Fig. 9. Operating principle of an optically pumped source.
The creation of nuclear polarization is based on the transfer of electron polarization to a proton, or the so-called Son effect. Its essence is as follows.
Since the beam of metastable atoms is polarized along the electron spin, the beam contains atoms only in states 1 and 2, which have an antiparallel nuclear spin. With an adiabatic decrease in the external magnetic field, states 1 and 2 will go over to states 1' and 2' (see Fig. 10), the nuclear spins of which are parallel. Thus, at the exit of the chamber (3, Fig. 9), the beam of metastable atoms acquires nuclear polarization.
Next, the beam of polarized metastable atoms enters the ionizer (4) or the second chamber containing alkali metal vapors, where H - ions are formed as a result of charge exchange interaction. The nuclear polarization possessed by a beam of neutral metastable atoms is preserved in this case.
E 3’ 2’ 1’ 4’ B negative B positive 10. Energy levels of the hyperfine splitting of the hydrogen atom in the 2S1 / 2 state as a function of the external magnetic field.
Thus, at the output of OPPIS there is a beam of polarized protons or H - -ions with an energy of several kiloelectronvolts.
34 Optically pumped sources have found their main application as sources of polarized protons for various accelerators. Typical, today, OPPIS parameters are: beam current ~1 mA (for DC sources) and polarization ~75%. However, despite the rather high intensity and polarization of the beam, sources of this type are rarely used as polarized targets, because the beam they create has a rather high velocity (~105 m/s), which leads to a decrease in the effective target density to 109 atoms/cm2.
2.4 Polarized Atomic Beam Sources (PABS) The idea of creating a source of polarized atoms was put forward by Norman F. Ramsey in . Its essence lies in the spatial separation of hyperfine beam components in a nonuniform magnetic field and subsequent induction of transitions between hyperfine splitting levels.
vacuum pumps vacuum pumps H2, D2 4 5 6 accelerator beam vacuum pumps vacuum pumps Pic. 11: Block diagram of a source of polarized atomic hydrogen/deuterium. 1 gas flow regulator;
2 - radiofrequency dissociator;
3 - gas jet formation system (nozzle, skimmer, collimator);
4 - the first group of spin-separating magnets;
5 - the first group of blocks of hyperfine transitions;
6 - the second group of spin-separating magnets;
7 - the second group of blocks of hyperfine transitions;
8 storage cell (target).
The main elements of PABS are (see Figure 11):
· a device for supplying and controlling the flow of molecular hydrogen (H2) or deuterium (D2);
dissociator, where H2 or D2 molecules dissociate into neutral atoms;
· gas jet formation system (nozzle, skimmer, collimator);
· a system for creating polarization (spin-separating magnets and blocks of hyperfine transitions).
35 An RF dissociator is usually used to create a hydrogen or deuterium atomic beam. Free electrons are accelerated in a high frequency electromagnetic field and excite vibrational levels of hydrogen molecules. This process can be represented as follows:
H 2 + e - + DE ® H 2 + e - ® H + H + e -, * where DE = 8.8 eV is the excitation energy of the vibrational levels of a hydrogen and deuterium molecule.
The flux of molecular hydrogen (deuterium) usually ranges from 0.5 to 2 mbar l/s. The upper limit is due to a decrease in the degree of dissociation at higher fluxes. Thus, it is necessary to find the optimal operating conditions under which both the degree of dissociation and the gas flow are maximum.
The beam dissociated into atoms passes through the gas jet formation system, namely, a nozzle, a skimmer, and a collimator. The nozzle temperature stabilizes around 80 K, which makes it possible to obtain the velocity distribution of the beam atomic component necessary for the maximum throughput of spin-separating magnets.
After the beam has been formed, it enters the system of spin-separating sextupole magnets, where the atomic component is separated by the orientation of the electron spin. Thus, states with electron spin projections mj = +1/2 and mj = –1/2 are spatially separated in a strong inhomogeneous magnetic field. As a result, the atomic component with mj = –1/2 leaves the beam and is removed by pumps that provide pumping out of the vacuum chamber.
To create a given vector or tensor polarization, i.e. creating a certain population of levels of hyperfine splitting, the technique of excitation of transitions in radio frequency fields is used.
The essence of this technique is as follows. With the passage of an atomic beam through the region of the magnetic field B and the radio frequency field with a frequency corresponding to the energy difference between the hyperfine splitting levels for a given B, transitions between the given levels are excited. Since the transitions between hyperfine splitting levels are bidirectional, it is necessary to exclude the possibility of reverse transitions leading to beam depolarization. This goal is achieved by inducing transitions in a gradient magnetic field. In this case, for an atom moving in such a field, the conditions for the transition are formed only in a limited region of space, where the frequency corresponds to the magnitude of the field. It is important that when the atom moved in this region, the interaction with the photon was single. This is achieved by choosing the HF field amplitude, which determines the photon density.Sources of polarized atomic beams are widely used both for injection of polarized protons and deuterons into accelerators and as an internal gas target. Typical parameters of PABS today are: beam intensity ~5·1016 atoms/s and polarization 8595%. When using PABS as a jet target, the effective density of such a target will be ~5·1011 atoms/cm2. In the case of injection of a beam of polarized atoms into the storage cell, this makes it possible to increase the target density by one or two orders of magnitude compared to a simple gas jet.
Thus, when creating a polarized gas target for nuclear physics experiments, the source of a polarized atomic beam is the most optimal choice, among those considered above, since it provides both high density and high polarization of the target.
37 Chapter 3
Source of polarized atomic hydrogen and deuterium for the internal gas target of the ANKE spectrometer 3.1 Brief description of the design In fig. 12 shows the position of ANKE ABS on the COZY storage ring between the deflection magnet D1 and the central magnet of the ANKE spectrometer D , and also shows a special vacuum chamber designed to install various types of targets (accumulation cell, solid-state, cluster and pellet targets). Since the space in the storage ring tunnel is limited, the source will be installed vertically. Such setup scheme is also Source of polarized ANKE central magnet (D2) atomic hydrogen and deuterium ANKE ABS Deflecting magnet (D1) Target chamber Fig. 12. ANKE ABS and a special vacuum chamber for mounting various types of targets on the COZY storage ring. The source of polarized atomic hydrogen and deuterium is located between the deflecting magnet D1 and the central magnet of the spectrometer D2. COZY beam direction from left to right.
38 will make it possible to place the source closest to the central magnet of the spectrometer, which, in turn, is one of the main factors determining the angular capture of the spectrometer.
A detailed drawing of ABS is shown in fig. 13. The created design takes into account the experience of creating and operating similar sources in IUCF and HERMES / DESY, however, it has a number of advantages over them.
The intermediate flange (7) between the upper and lower vacuum chambers is attached to the bearing bridge connecting the yoke of magnets D1 and D2 (see Fig. 12). This fastening ensures the movement of the ABS and the vacuum chamber of the storage cell as a whole, when the central magnet D2 is shifted, and also allows for quick dismantling of the source and the carrier bridge as a whole.
To create a hydrogen or deuterium atomic beam, a radio frequency dissociator is used (1, Fig. 13). RF power is supplied to the parallel LC circuit from a 13.56 MHz generator. Cooling of the discharge tube is provided by the flow of an alcohol-water mixture between two outer coaxial tubes of larger diameter. To stabilize the nozzle temperature in the range of 40100 K, a cryogenerator (2) was used, connected to the nozzle via a flexible copper thermal bridge (3). The upper vacuum chamber is divided by two movable aluminum partitions (4) into three stages of differential pumping (I, II, III). The skimmer, which serves to form the gas jet, is fixed on the partition separating chambers I and II. The design of the upper flange allows movement of the nozzle axis relative to the skimmer axis in all directions. The use of a flexible vacuum connection between the dissociator flange and the upper flange of the vacuum chamber makes it possible to vary the distance between the nozzle and the skimmer without disturbing the vacuum. A collimator is installed on the partition separating chambers II and III, which finally forms the gas jet.
The first group of spin-separating sextupole magnets (5) provides, as in the classical Stern-Gerlach experiment, the spatial separation of the beam along the electron spin. In this case, the component with mj = +1/2 is focused in the strong inhomogeneous magnetic field of the sextupole and enters the hyperfine transition block (6), while the component with mj = –1/2 is defocused and removed by pumps that provide pumping out of the vacuum chamber. The block of ultrafine transitions (6), like the magnets (5), is rigidly fixed on the ABS central flange (7), which determines the entire geometry of the source.
39 I II III IV p Fig. 13. ANKE ABS drawing. Explanations are given in the text.
40 Chamber IV houses the second group of spin-separating sextupole magnets (8) and additional blocks of hyperfine transitions (9), which are responsible for creating the tensor polarization of the deuterium beam.
Finally, at the very bottom is shown a prototype storage cell (10) planned for use on the COZY storage ring.
On fig. 14 is a photograph of ANKE ABS and a Lamb shift polarimeter in the IKP10 laboratory.
Rice. 14. Photo of ANKE ABS in the laboratory. The height of the upper vacuum chamber is 80 cm.
Institut fr Kernphysik, Forschungszentrum Jlich, D-52428 Jlich, Germany - 41 Summing up, we can say that the specifics of the design, dictated by the use of the source under the conditions of the experiment at the accelerator (limited access for maintenance, severe limitations in volumes for experimental equipment, etc. .) composed:
· in compactness, which allows to install the source in the limited space of the COZY storage ring tunnel and at the same time provide the necessary space for the detector system of the ANKE spectrometer.
· in the mobility of the source for quick mounting and dismounting on the storage ring, which makes it possible to drastically reduce the loss of acceleration time when replacing the source with one of the non-polarized targets (solid-state, cluster, pellet target) used in other physical experiments on the ANKE spectrometer.
3.2 Vacuum system One of the main factors determining the intensity of an atomic beam, and, consequently, the target density, is the pumping speed of scattered atoms and molecules in the first and second chambers of the source (I, II, see Fig. 13). The interaction of the residual gas with the beam particles destroys the directed flow of atoms and ultimately leads to a decrease in the target density. To minimize the effects of scattering and attenuation of the beam on the residual gas in the sources of atomic beams, a powerful differential pumping system is used, which provides a vacuum in the first and second chambers at a level of 10-410-5 mbar.
3.2.1 Construction of the vacuum chamber The ABS vacuum chamber consists of two cylindrical vacuum chambers fixed above and below the central bearing flange (7, Fig. 13), with dimensions of 40050050 mm3. The wall thicknesses of the upper and lower vacuum chambers made of stainless steel are 8 and 2.5 mm, respectively. To ensure differential pumping, the upper vacuum chamber, having an inner diameter of 390 mm, is divided into three parts by two dividing partitions. Unlike other sources, the dividing baffles are made movable, which greatly simplifies the procedure for optimizing the gas jet formation system.
The complex shape of the baffles is caused by the desire to improve the vacuum conditions near the nozzle, skimmer and collimator and to provide the maximum open space for turbomolecular pumps pumping out the first and second vacuum chambers. The upper partition separating chambers I and II has a diagnostic glass window for observation and nozzle change through a special flange in chamber II. Both baffles with a diameter of 389 mm and a height of 200 mm are made of aluminum by precision casting. Despite the fact that the aluminum casting has a porous surface, during operation there were no problems associated with the deterioration of the vacuum in the upper vacuum chamber. The partitions are processed in such a way that the conductivity of the gap, which is less than 0.5 mm, between the inner surface of the vacuum chamber and the surface of the partition is negligible. This made it possible to avoid additional compaction and significantly simplified the design of the upper vacuum chamber.
Rice. 15. Upper movable partition.
Ball guides fixed on the baffle and sliding along the inner surface of the vacuum chamber make it easy to move the baffles along the beam axis. The position of the lower baffle, on which the collimator is fixed, can be changed with the help of two micrometric vacuum inlets fixed on the central bearing flange without breaking the vacuum.
Thus, it should be noted that the use of movable partitions of complex shape made it possible to:
· for the first time it was possible to combine three stages of the source in one vacuum chamber, which significantly reduced its linear dimensions and minimized the number of seals;
· to reduce the distance from the gas source to the vacuum pump and the ratio of the "passive" surface of the chambers to the "pumping out", which led to a significant improvement in pumping conditions;
A deuteron is a nucleus consisting of one proton and one neutron. By studying the properties of this simplest nuclear system (deuteron binding energy, spin, magnetic and quadrupole moments), one can choose a potential that describes the properties of the nucleon-nucleon interaction.
The deuteron wave function ψ(r) has the form
is a good approximation for the entire range of r. 
Since the spin and parity of the deuteron are 1 + , the nucleons can be in the s-state (L = 0 + 0), and their spins must be parallel. The absence of a bound state with spin 0 in the deuteron says that the nuclear forces depend on the spin.
The magnetic moment of the deuteron in the S state (see. Magnetic moment of the nucleus) μ(S) = 0.8796μ N , is close to the experimental value. The difference can be explained by a small admixture of the D state (L = 1 + 1) in the deuteron wave function. Magnetic moment in the D-state
μ(D) = 0.1204μ N . The D-state impurity is 0.03.
The presence of an admixture of the D-state and a quadrupole moment in the deuteron testify to the non-central character of nuclear forces. Such forces are called tensor forces. They depend on the magnitude of the projections of spins s 1 and s 2 , nucleons on the direction of the unit vector , directed from one deuteron nucleon to another. The positive quadrupole moment of the deuteron (prolonged ellipsoid) corresponds to the attraction of nucleons, the flattened ellipsoid corresponds to repulsion.
The spin-orbit interaction manifests itself in the features of the scattering of particles with nonzero spin on non-polarized and polarized targets and in the scattering of polarized particles. The dependence of nuclear interactions on how the orbital and spin moments of the nucleon are directed relative to each other can be found in the following experiment. A beam of unpolarized protons (spins with the same probability are directed conventionally "up" (blue circles in Fig. 3) and "down" (red circles)) falls on the 4 He target. Spin 4 He J = 0. Since the nuclear forces depend on the relative orientation of the vectors of the orbital momentum and spin , protons are polarized during scattering, i.e. protons with spin "up" (blue circles), for which ls, are more likely to scatter to the left, and protons with "down" spin (red circles), for which ls, are more likely to scatter to the right. The number of protons scattered to the right and to the left is the same, however, upon scattering at the first target, beam polarization occurs - the predominance of particles with a certain spin direction in the beam. Further, the right beam, in which protons with spin "down" predominate, falls on the second target (4 He). Just as in the first scattering, protons with spin "up" mostly scatter to the left, and those with spin "down" mostly scatter to the right. But since in the secondary beam, protons with spin "down" predominate; upon scattering on the second target, the angular asymmetry of the scattered protons relative to the direction of the beam incident on the second target will be observed. The number of protons that are registered by the left detector will be less than the number of protons that are registered by the right detector.
The exchange nature of the nucleon-nucleon interaction manifests itself in the scattering of high-energy neutrons (several hundreds of MeV) by protons. The differential neutron scattering cross section has a maximum for backscattering in the cm, which is explained by the charge exchange between a proton and a neutron.
Properties of nuclear forces
- Short range of nuclear forces (a ~ 1 fm).
- Large value of the nuclear potential V ~ 50 MeV.
- Dependence of nuclear forces on spins of interacting particles.
- Tensor character of interaction of nucleons.
- Nuclear forces depend on the mutual orientation of the spin and orbital moments of the nucleon (spin-orbit forces).
- Nuclear interaction has the property of saturation.
- Charge independence of nuclear forces.
- Exchange character of nuclear interaction.
- Attraction between nucleons at large distances (r > 1 fm) is replaced by repulsion at short distances (r< 0.5 Фм).
The nucleon-nucleon potential has the form (without exchange terms)