The idea of a nonrelativistic hydrogen isotope ion storage ring is proposed. The influence of different factors on the main parameters of circulating beam is considered. The principal possibility for construction of such installation is shown

Guk, I.S.

Paschenko, A.V.

Shapoval, I.N.

Tarasenko, A.S.

Наукова електронна бібліотека періодичних видань НАН України (Vernadsky National Library of Ukraine)

THE PHYSICAL BASESOF LOW-ENERGY HYDROGEN ISOTOPE IONS STORAGE RINGI.S. Guk, A.V. Paschenko, A.S. Tarasenko, I.N. Shapoval National Science Center “Kharkov Institute of Physics and Technology”, Kharkov, Ukrainee-mail: guk@kipt.kharkov.uaThe idea of a nonrelativistic hydrogen isotope ion storage ring is proposed. The influence of different factors on the main parameters of circulating beam is considered. The principal possibility for construction of such installation is shown.PACS: 12.20.-m, 13.40.-f, 13.60-Hb, 13.88.+e1. INTRODUCTION The main factor, which for a long time prevented the proton storage ring construction, was lack of  betatron and synchrotron oscillations damping that is caused by negligible  quantity  of  proton  energy  losses  for synchrotron radiation.The  offer  an  electron  [1],  and  then  stochastic  [2] method of oscillation damping has allowed to construct proton storage rings with energies from several tens to several thousands of MeV [3,4].Rather earlier it was offered to use the proton energy losses for internal target ionization as a braking force for ensure the oscillation damping [5]. However, as it was shown in [6], it is impossible to ensure the damping of all oscillation modes in this case.In paper [7] it was shown that the use of the non-elastic  energy  losses  of  charged  particles  passing through the  substance  allows one  to  provide  in  some range of velocities (υp≤4∗108 cm/s) the damping of all oscillation  modes.  This  fact  was  put  as  a  base  of proposals  on  designing  the  hydrogen  isotope  storage ring, which were suggested in papers [8,9].This  work  is  dedicated  to  investigation  in  single particle  approximation  the  influence  of  neutral  and plasma  target  on  the  main  parameters  of  circulating beam.2. THE MAIN PARAMETERS OF CIRCULATING BEAM1. The energy. The following factors were taken into account for choice the energy of accumulating particles:a) close by the operating energy value the necessary and  sufficient  condition  of  all  modes  of  oscillations damping must be satisfied [6,7]:dea/dEP>0,here  еа is  the  atomic  stopping  ability  of  a  target substance for protons; Ep is the proton kinetic energy;b) the energy of hydrogen isotope ions must be close to 53 keV/a.m.u. This condition is connected with that the maximum cross-section of T(d,n)4He reaction takes place at the energy range ~53 keV/a.m.u.The measurement data of the atomic stopping ability of different elements for protons, that were obtained in many experiments and are adduced in [10a], points that the condition dea/dEP>0 is valid for energies ЕР≤50 keV. This corresponds to the proton velocity υp=3.1∗∗108 cm/s.  The  energy  ЕР=46.97 keV  corresponds  to  υp=3*108 cm/s (β=10-2).2. The time of oscillation damping. For the case the stopping  target  is  installed  in  achromatic  straight section, the expressions for the damping time (refer to. [6]) may be transformed to the form1, )2( −Π∗ΕΕ=ldxdctzx βτ1))(2( −Π∗∂Ε∂∗Ε=ldxdcts γβ γτ .Here dE/dx is the particle energy losses on the path unit  in  the  target;  Ns are  the  target  atomic  surface density; Et is the total particle energy; П is the perimeter of the installation; γ is the particle relativistic factor; l is the target thickness.After  substitution of  numerical  values,  with taking into  account  if  Ep≈50 KeV,  dE/dx  for  protons  in hydrogen [11] is equal to ~6.4*10-15∗N eV/cm (N is the volume density of the target), one obtains:sстаtNсmszx ,)(10211,Π≈τ(1)scmatNcmss ,.)(104211Π∗≈τ(2)3. The settled energy spread. This value is defined by the expression [12a]:2122124  Ν=∆ sЕ τε(3)here:  2ε  is  the  mean square  of  the  energy  that  the particle loses in a single act of scattering, N is the mean number of collisions, which the particle subjects at one pass through the target.86 PROBLEMS OF ATOMIC SCIENCE AND TECHNOLOGY. 2002, № 2.Series: Nuclear Physics Investigations (40), p. 86-89.So  far  as  we  do  not  dispose  the  data  about  the spectral  density of  non-elastic  energy losses,  we shall evaluate  the  settled  energy  spread  in  suggestion  that dispersion  of  energy  losses  spectrum is  equal  to  the mean value of losses i.e. ( ) 22 εεε =−  or 22 2εε = .2int2int ReNRNenassacol pipiε ==∆ Ε= . (4)Here ∆ Ε  is the mean energy, that the particle loses of one pass through the target; coln  is the mean number of  collisions,  subjected  by  the  particle  at  one  pass through the target; Rint is the maximum distance between the particle and the target atom nucleus, beginning from which the particles are non-elastically scattered.Rint value is defined from the expression:)()( 21 rr ai ϕϕ = ; Rint = r1+r2where 1)( −= erriϕ  is the potential of the particle field;)2exp()()( 10101 −−−−+= raarerаϕ  is  the  potential, which is created by the hydrogen atom [10a];а0 is Bohr orbit radius of hydrogen atom.After  substitution  the  corresponding  values  in  (3), taking into account expressions (2) and (4), we obtain:eVcmsсаеа 1183),1011.1(7.42 311021212=∗∗∗=∆ Ε −βpipi .(5)Thus, the settled energy spread in the storage ring depends only from the braking target substance (ea) and is  independent  neither  from its  density,  nor  from the perimeter of the installation.4. The particle lifetime due to fast processes. The fast processes, that quit the particles out during one turn, are: a) the particle scattering on the angle that is greater than the permissible one for a given magnetic structure; b)  the  circulating  particle  neutralization  (the  charge exchange) on the target atoms.We  shall  consider  both  these  factors  one  after another.a) The lifetime due to particle scattering through an  angle  that  is  greater  than  the  most  permissible.  The numerous experimental studies [10a] have showed that in  the  energy  range  from  60 keV/a.m.u.  up  to 0.1 MeV/a.m.u.  the  interaction  of  hydrogen  isotope nuclei  with a  substance  is  defined  by  the  non-elastic scattering.  Since  the  number  of  collisions  during  one particle pass through the target is much greater than one, it is necessary to consider the process of multiple non-elastic  scattering.  The  comparisons  with  experimental study  results  have  shown  that  multiple  scattering  is described  the  best  by  the  distribution  function  of following type [10a]:[ ] 3 21 1 exp( 2 )( , , )4 1 exp( 2 ) 2exp( )cospf d Ep pθpi θ− −= ∗+ − − −(6)Here∫ ∗+=−−01112210221 )(05.2 EEdEdSdEENMMMaeZZp  ,M1,2 is  the  mass  of  bombarding  and  rest  particle respectively;E0,1 is the particle energy before and after passing the target, respectively; N is the target volume density.For the case of protons (or deuterons) on hydrogen scattering  192.35(3.8) 10 sp N−≈ ∗ .  From  Fig.1  one can  see  that  in  the  region  where  1p < <  2sin 0.2 pθ ≈ .  Here  θ is  the  deflection  angle  of  a bombarding particle in the coordinate system, where the scattering particle rests. θ2sin  p Fig. 1.  The mean-square scattering angle vs parameter p  in the region 1< <pIn the laboratory coordinate system the mean-square angle of proton on hydrogen atoms scattering is equal to 1.2*10-2 rad.  and  3.5*10-2 rad.  for  the  target  surface density 1016 cm-2 and  1017 cm-2  respectively.  The  same value  in  the  case  deuterium  scattering  on  hydrogen under  the  same  target  surface  densities  is  equal  to 8.3*10-3 rad and 2.6*10-2 rad respectively.The  angular  particle  distribution  after  the  target passing  is  close  to  Gaussian  with  the  dispersion 212sin θ=D .  For  ensuring  the  lifetime  due  to scattering  on  the  internal  target  be  more  than  the damping time by a factor of one hundred (not less), the magnetic  system of  the  storage  ring must  provide  the capture of particles scattered through an angle  ϑ~5∗D into the circulating mode. This angle is equal ~0.15 rad. (for  protons)  and  ~0.12 rad.  (for  deuterons)  at Ns=1017 cm-2 and, 0.06 rad and 0.04 rad at Ns=1016 cm-2 respectively.The atomic hydrogen as a target is proposed.b) The lifetime due to ion neutralization (the charge  exchange) during passing through the atomic target. In case of heavy charged particles interaction (for instance, protons with an energy Ep~47 keV) with the atomic or molecular target, two types of reactions can exist: a) the reactions with nuclei redistribution between interacting particles (nucleus conversions); b) the reactions with the excitation  of  electron  levels  in  atom  or  the  electron redistribution  between  interacting  particles  (the reactions  of  ionization,  neutralization,  the  charge exchange).At a mentioned energy the first type reaction cross sections do not exceed 10-24 cm2 while cross section of the second type reactions  can reach to  10-16-10-15 cm2. 87Since  these  reactions  are  determining  for  low energy protons let us consider them in detail.The proton interaction with atomic target can occur by the following channels:р+А→Н+А+ (7)р+А→р+А++е (8)р+А→Н*+А+ (9)р+А→р+А* (10)р+А*→р+А++е (11)р+А*→Н+А+ (12)The  reactions  (7),  (9),  (12),  which  describe  the neutralization of bombarding protons, are characterized by  the  cross  section  σ10.  The  reactions  (8)  and  (11) describe  inverse  ionization  and  are  characterized  by cross  section  σ01.  In the reactions (8)  (10)  the charge beam composition does not change.The equations, which describe the time evolution of charged  and  neutral  beam  components,  have  the following form:000 nndxdn++ −= λλ+++−= nndxdn00 λλ . (13)Hereλ0=σ10nm;λ+=σ01nm  nm  is the target volume density;n0 and n+ are respectively the number of neutral and charged particles in the beam, n++n0=const.Solution of system (13) gives:1)](exp[ 0000−+−++=++++ λλλλλλlnn. (14)Finally one obtains:)](exp[)])(exp[1(100110010110100σσσσσσσ+−++−−=+ smsmnnnn. (15)For a  "thick"  target  (nsm(σ01+σ10)>>1,  where nsm is the surface target density) we obtain:01100σσ≈+nn. (16)For σ10≈σ01=σ and nsm(σ01+σ10)<<1 ("thin" target):σκ smnnn≅=+0 . (17)From expression (17) one can see the inefficiency of the  target  thickness  reduction  for  decrease  the  beam neutralization degree,  since as neutral  target  thickness decreases the beam damping time increases. The ratio of the  lifetime due  to  the  beam  neutralization  to  the oscillation damping time remains constant.In  the  table  are  presented  interaction  reactions  of 50 keV protons with hydrogen and their cross sections according to [13]. These reactions can be divided into four groups: i) (4) - direct ionization reaction; ii) (1)→(5), (6)→(4), (2)→(5) - reactions of ionizing through the intermediate state; iii) (6), (7), (8) - reactions of direct charge exchange, iv) (1,2)→(9,10) - reactions of charge exchange through the intermediate state.The reactions of groups i) and ii) are characterized by the general cross section σ01; the reactions of groups iii) and iv) are characterized by the general section σ10. At Ep=50 keV σ10≈σ01≈10-16 cm2 and n+/n≈n0/n=0.5 [14] that means practically complete beam loss after several the target passing.№ ReactionCross-section σ, cm21 p+Н(1s)→p+H*(2p) ~4∗10-172 p+H(1s)→p+H*(2s) ~2∗10-173 p+H*(2s)→p+H*(2p) ~2∗10-144 p+H(1s)→p+H++e ~3∗10-165 p+H*(n)→p+H++e ~3∗10-166 p+H(1s)→H(1s)+p   4∗10-167 p+H(1s)→H*(2s)+p ~10-178 p+H(1s)→H*(2s)+p ~10-179 p+H*(n)→H*(n)+p (n=2,3) ~10-1610 p+H*(n)→H*(n)+p (n≥4)    5∗10-15In this connection we have considered possibility of ionization  the  neutral  beam  component  immediately after the braking target passing.Since the potential of hydrogen ionization is equal to ~14 eV, its photoionization in laser field can occur by to multiphoton  absorption.  The  velocity  of  multiphoton ionization w is connected with the electromagnetic field strength F by expression [15]:kFw 2∝ ,where k=〈Ei/hν+1〉 is the number of absorbed photons; E is the potential of ionization.From this expression it is clear that for efficiency of multiphoton ionization the large values of the laser field strength  are  required  that,  in  one′s  turn,  causes significant technical difficulties.Therefore  we have  considered  a  possibility of  the hydrogen atoms ionization by means of plasma target.c) Ionization  in  plasma  jet.  The  passing  of  two-component  (neutral  atoms and  protons)  beam through the  quasi-neutral  plasma  is  accompanied  by  the following conversions:H+p→H++p+e (18)H+p→p+H (19)H+e→H++2e (20)p+e→H*+hν (21)Here  the  velocity  of  hydrogen  atom  in  reactions (18)-(20) is approximately equal to the proton velocity in reaction (21)  and formers ~3*108 cm/s. In reactions (21)  one  can  shifts  to  proton  rests.  In  this  case  the electron energy equals  Ее≈25 eV (vе~3∗108 cm/s). The reactions (18)  and (19),  describe the atomic hydrogen beam ionization when it passes through the plasma. The  complete  cross  sections  of  ionization  σi and neutralization σ0, according to the data of [13], are 7.5∗10-16 cm2 and ~6.7∗10-23 cm2, respectively. Since σi>>σ0, then  in  the  subsequent  calculations  the  proton neutralization  was  not  taken  into  account.  From  the adduced values it is seen that the plasma target with a surface density of ~1.7*1016 cm-2 is "thick" and provides almost full ionization of the neutral beam component.88The  energy  loss  of  the  particle  passing  through plasma is described by expression [10e]: nLvMMMeZZvdtdEdxdE221142221)(41+=∗−=−µpi. (22)Here М1  and М2 are the masses of the test and field particles,  respectively;  v is  the  velocity  of  the  test particle; n is the volume atomic density of the target; L is the Coulomb logarithm (for proton-electron collisions under n~1016 L≈5).For protons with an energy of ~47 keVcmeVndxdE ,105.2 14 ∗∗≈− − .From this relation and expression (22) one can see that, firstly, the main particle energy losses occur by the particle  collisions  with  plasma  electrons,  secondly, specific energy losses in the plasma target are approxi-mately by a factor four higher than the similar value for atomic hydrogen target and, thirdly, the value of specific losses decreases with test particle energy increasing.The  plasma  target  density  must  be  sufficient  to provide full beam ionization and, at the same time, such that the synchrotron oscillation increment is not higher than the decrement that is caused by the neutral target.These requirements both may be satisfied if the neu-tral target density nsа=1.7∗1017 cm-2 and the plasma one nsp=1.7∗1016 cm-2. Under these conditions τs =1.6∗10-2 s. For the case without plasma target τs≈4∗10-3 s.3. CONCLUSIONSThe  given  above  considerations  and  results  of numerical  estimations  allow  one  to  do  the  following conclusions:it  is  possible  to  realize  the  installation  for nonrelativistic (β≅10-2) proton (deuteron) accumulation;preliminary parameters of such installation may be following:  П≅15 m,  Ns  ~  1016–1017 cm2,  the  capture angle ~0.15 rad;for  particle  accumulation  one  must  provide  the device for ionization of neutral atoms, which are formed after the beam passing through the braking target.To construct such installation it seems to be expedi-ent with the following considerations:as far as in none of the installation the energy loss of nonrelativistic particles in the neutral target is not used for damping of all oscillation modes it would be useful to investigate in detail such principle of damping ensuring;such installation may be used for perfection of some units and systems necessary for applying the installation in  other  fields  of  investigations,  in  particular,  as  a neutron  source  or  in  studies  on  plasma  physics  and controlled fusion.REFERENCES1. G.I. Budker. An efficient method of particle oscillation  damping  in  proton  and  antiproton storage rings // Atomic energy. 1967, v. 22, p. 346-351 (in Russian).2. S.  Van  der  Meer.  Stochastic  damping  of  betatron oscillation in the ISR. CERN/ISR-PO/72-31 1972.3. G.I. Budker  et  al.  Experimental  studies  of electron cooling // Part. Accel. 1976, v. 7(4), p. 197-211.4. M. Bregman  et  al.  Measurement  of antiproton lifetime using the ISR Storage Ring // Phys. Lett. 1978, v. 78B, p. 174.5.  A.A. Kolomensky.  About  oscillation decrements in accelerators in presence of arbitrary energy  losses  //  Atomic  Energy.  1965,  v. 19, p. 534-535 (in Russian)6.  Yu.M. Ado,  V.I. Balbekov.  About possibility to use an ionization friction for heavy particles  storing  //  Atomic  Energy. 1970,  v. 31, p. 40-44 (in Russian).7. E.V. Inopin,  O.S. Tarasenko.  The nonrelativistic  tritium  ions  storage  ring  like  the neutrons source //  Ukr Fiz. Zhurn. 2000, v 45(11), p. 1301-1305 (in Ukrainian).8. Yu.N. Grigor′ev et al. Storing nonrelativistic nuclei  of hirogen isotopes //  Problems of  Atomic  Science  and  Technology,  Ser.:  Nuclear-Physical  Research (36). 2000, №2, p. 80-82.9. Yu.N. Grigor’ev et al.  The storage ring for  nonrelativistic  protons,  deuterons  and  tritons.  Proc.  of  XVII  Conference  on  Charged  Particle Accelerators. Protvino, October 17-20, 2000, p. 80-83.10. Yu.V. Gott.  Interaction  of  particles  with  the  material  in  plasma  studies. M.:  Atomizdat, 1978;  а) p. 94-130;  b) p. 11;  c) p. 83;  d) p. 156; e) p. 63 (in Russian).11. H.K. Reynolds,  D.N.F. Dunbar, W. Wenzel,  W. Whaling.  The  stopping  cross section of gases for protons, 30-600 keV //  Phys.  Rev. 1955, v. 92 (3), p. 742-748.12. G. Bruk.  Cyclic  accelerators  of  charged particles. M.: Atomizdat, 1970; а) p. 205; b) p .228 (in Russian).13. R.K. Janev,  W.D. Langer,  K. Evans,  Jr., D.E. Post.  Atomic  and  Molecular  Processes  in  Hydrogen-Helium  Plasmas  PPPL-TM-368, June 1985, p. 156-160.14. I. Mac-Daniel’.  Collision  processes  in ionized gases. M.: “Mir”, 1967, p. 40 (in Russian).15. N.B. Delone,  V.P. Krajnov.  Tunnel  and above-barrier atom ionization of atoms and ions in the field of laser radiation //  Uspekhy Phis. Nauk. 1998, v. 168(5), p. 531-549 (in Russian).89

The physical bases of low-energy hydrogen isotope ions storage ring

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The physical bases of low-energy hydrogen isotope ions storage ring

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Наукова електронна бібліотека періодичних видань НАН України (Vernadsky National Library of Ukraine)