The research of inertial controlled fusion (ICF) on high-current heavy-ion beams is one of the main trends in ICF. Modern techniques of a heavy-ion beam production and acceleration make it possible to obtain high-current beams with high intensity using linear induction accelerators (linacs). ICF purposes require the increasing of the beam intensity and the beam brightness by several orders. The main process that restricts the high-current ion beam intensity is the beam spreading caused by the influence of self-fields of charged particle beam. Self-fields are several orders greater than the external fields used for beam control, acceleration and focusing. Under these conditions, it is impossible to obtain high-current heavy-ion beams of quality necessary for ICF without charge and current compensation of beams

Karas', V.I.

Kornilov, E.A.

Shulika, O.N.

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

LINEAR INDUCTION ACCELERATOR WITH CHARGE AND CURRENT COMPENSATIONV.I. Karas', E.A. Kornilov, O.N. ShulikaNational Science Center "Kharkov Institute of Physics & Technology"61108, Kharkov, Academicheskaya St., 1unicorn@kipt.kharkov.uaThe research of inertial controlled fusion (ICF) on high-current heavy-ion beams is one of the main trends in ICF. Modern techniques of a heavy-ion beam production and acceleration make it possible to obtain high-current beams with high intensity using linear induction accelerators (linacs). ICF purposes require the increasing of the beam in-tensity and the beam brightness by several orders. The main process that restricts the high-current ion beam intensity is the beam spreading caused by the influence of self-fields of charged particle beam. Self-fields are several orders greater than the external fields used for beam control, acceleration and focusing. Under these conditions, it is impos-sible to obtain high-current heavy-ion beams of quality necessary for ICF without charge and current compensation of beams.PACS numbers: 52.58.Hm; 29.27.-a; 41.75.-i; 29.17.+w; 96.50.Pw1  INTRODUCTIONHigh-current  induction  linacs  present  the  most prospective trend of elaboration of a driver for inertial controlled heavy-ion fusion. The driver on the basis of an induction linac is alternative to the drive on the basis of a vacuum resonance accelerator. A high-current lin-ear  induction  ion  accelerator  with  charge  and  current compensation has  been proposed and studied at  NSC KIPT [1, 2]. The compensation within accelerating gaps of such linac is provided by injection of an additional electron beam with specially chosen parameters (dimen-sions, beam energy, etc.) The compensation of positive space charge within drift gaps is provided by injection of thermal electrons into these gaps.During the last years, we carried out systematic in-vestigations of the dynamics of relativistic electron and non-relativistic ion beam propagation in both an electric field and an axisymmetric non-uniform magnetic field. Thus, in [3 – 8] the results of investigation into both the acceleration processes and the charge and current com-pensation in one and two accelerating sections of the in-duction linac were presented. It was demonstrated that the injection of the electron beam into the magnetoiso-lated accelerating gaps and the injection of the thermal electrons into drift gaps provided the charge and current compensation. With the aim of increasing the ion beam acceleration rate in the two-cusps linac we have studied the optimal correlation between an accelerating electric field and an electron beam energy [9 – 10].  Also we have obtained the restriction on the wall thickness of an-nular high-current ion beam, which ensure the uniformi-ty of charge and current compensation in the ion beam cross-section and acceleration stability (in radial direc-tion). These processes occur due to the fact that penetra-tion depth of the accelerating electric field is consider-ably greater than the beam wall thickness.This  paper  presents  the  results  of  the  distribution function studying of both the accelerated ion beam and the compensating electron beam in the cases of different accelerating electric field values.2  MATHEMATICAL AND DISCRETE MOD-ELHollow magnetized relativistic electron beam (Lar-mor radius  rLe  is substantially smaller than the size of the cusp Lz  and the chamber radius rL ) and high-cur-rent unmagnetized ion beam (Larmor radius rLi  is more greater than Lz  and  rL ) were injected along z-axis of the system consisted of  one (or  two) magnetoisolated accelerating gaps and a drift one (see. Fig. 1).rLeiz,(cm)r,(cm)B0∆ Φ (z,rL)Fig. 1. View of the modeling region.The  beam current  densities  at  z = 0  were  equal. The ion beam velocity was v ci = 0 285.  and the elec-tron beam velocity was  v ce = 085. .  The preliminary injection of the thermal electrons with the Maxwellian distribution  function  with  the  temperature T m cce = 0 002 02.  into drift gap was used to suppress the positive space charge within this gap.Numerical simulation of above-described problem is based on the solving of Vlasov equations set for the dis-tribution functions (DF) of particles ( )f P R ts  , ,  in the axisymmetric  cylindrical  geometry ( )( )∂ ∂ θ = =0, ,R r z .  The  self-consistent  electric ( ) E R t,  and  magnetic  ( ) B R t,  fields  including  in ВОПРОСЫ АТОМНОЙ НАУКИ И ТЕХНИКИ. 2001. №5.Серия: Ядерно-физические исследования (39), с. 21-23.21Vlasov's  equations  are  determined  by  the  Maxwell's equations that can be written as the wave equations for the scalar ( )Φ R t,  and vector ( ) A R t,  potentials.The boundary conditions for the DF of particles of a given sort (s= e, i - electrons and ion correspondingly) at  z = 0  is  defined  by ( ) ( ) ( ) ( )f m u R t u u u us s r z s , , = −δ δ δ θ0  for r r rmin max≤ ≤  and  uz > 0 .  Here  rmin  and  rmax  are the minimum and maximum beams radii respectively.The configuration of the external magnetic field is defined  by  the  expression ( ) ( )A B k I kr kzθ = − 0 1 cos ,  where  ( )I kr1  is  the first order modified Bessel function,  B0  is the ampli-tude of magnetic field, and  k K zL= pi ,  K  is total number of cusps.The set  of  equations  and the  initial  and boundary conditions for the potentials and DF are described in de-tail in [7].The units of measurement using in the treatment are determined  by  relations:  [ ]v c= ,  [ ]r z c pe, = ω , [ ]t pe= −ω 1 ,  [ ]n n e= 0 ,  [ ]q e= ,  [ ]m m= 0 , [ ]J en e= 0 ,  [ ]Φ , A m c e= 0 2 , [ ] ( )E B n e ch, = 4 0 1 2pi ε ,  [ ]T m cce = 0 2 ,  [ ] [ ]P c pe0 2= =ψ ω ,  where   u v= γ , { }v r r z= , , θ ,  ψ γ θ θ θ= = −r P qm rA2   ( Pθ  is the dimensionless  generalized  particle  momentum), ( )( )γ ψ= + + +1 2 2 2 1 2u r ur z  is the relativistic fac-tor,  ω pipe en e m= 4 020  is the electron plasma fre-quency, n m ee0 0, ,  are the initial density, rest mass and charge of the electrons respectively, Tce  is the tempera-ture of cold electrons.The  mass ratio  was  m mi e = 100 ,  m me = 20 0 . The number of particles in the cell was 6000. The num-ber of the nodes was equal to  J Jz r× = ×64 64 .  The time step was varied within the range 0 025 0 05 1, ,− −ω pe  for  solving  the  equations  of  motion  and 0 0125 0 025 1, ,− −ω pe  when solving the wave equations.The  discrete  model  is  realized  as  2.5-dimensional electromagnetic  relativistic  axisymmetric  numerical code. The calculations were carried out using computer of the Pentium-class.3  RESULTS OF NUMERICAL SIMULATIONA series  of  2.5-D simulation  has  been  performed. The distributions of DF of the electron and ion beams are presented in Fig. 2-Fig. 4 for different values of the initial accelerating electric field.As one can see, the large spread in both the radial and longitudinal velocities is observed for the electron beam. As for the ion beam, it spreads only by 10-15%.Fig. 2. Distribution function ( )f V  of electrons (1) and ions (2). The initial potential difference is ∆ Φ = 30 0 02. m c e .Fig. 3. Distribution function ( )f V  of electrons (1) and ions (2). The initial potential difference is ∆ Φ = 15 0 02. m c e .It should been noticed that the total initial potential difference is the same ( ∆ Φ = 30 0 02. m c e ) for cases presented in Fig. 2 and Fig. 3. In the first case this po-tential difference is applied to one accelerating gap (see Fig. 1) and in the second case there are two accelerating gaps in the system. Having compared these two vari-ants, one can draw the conclusion that the number of ion beam particles with low energy is greater for the case of one-cusp system. In this case the charge compensation of ion beam is weaker. While the ion beam propagates through the system with two accelerating gaps and one drift gap under the same potential difference, the charge compensation is  increased due to the thermal electron injection into the drift gap to neutralized the essential positive space charge of ion beam there.22Fig. 4. Distribution function ( )f V  of electrons (1) and ions (2). The initial potential difference is ∆ Φ = 0 8 02. m c e .If  the  initial  potential  difference  is  rather  small  (∆ Φ = 0 8 02. m c e ),  the  kinetic  energy  of  electron beam is sufficient to overcome it. As the result the space charge overcompensation and radial focusing of the ion beam is occur as one can see in Fig. 4.4  CONCLUSIONIn this paper it has been shown that the process of compensation of high-current ion beam as this beam, to-gether  with  the  additional  electron  beam,  propagates through two-sectioned  induction  linac,  is  followed by the increase of beam spreading in the radial and longitu-dinal velocities. Although the electron beam spread is about 100%, it does not impede the charge compensa-tion of the high-current ion beam by electrons. At that time the ion beam spread in the velocities does not ex-ceed 10%.REFERENCES1. V.I.Karas', V.V.Mukhin, V.E.Novikov, A.M.Nabo-ka. On Ion Beam Acceleration in Magneto-Isolated Systems  //  Plasma  Physics  Reports. 1987,  v.  1, № 4, p. 494-496.2. V.I.Karas',  V.A.Kiyashko,  E.A.Kornilov,  Ya.B.-Fainberg. Theoretical  and Experimental  Investiga-tions of Neutralized Ion Induction Linac for Inertial Confinement  Fusion.  //  Nuclear  Instruments  and Methods  in  Phys.  Res. 1989,  A278,  №  1, p. 245-246.3. N.G.Belova,  V.I.Karas',  Yu.S.Sigov.  Numerical Simulation of Charged Particle Beams Dynamics in Axisymmetric Nonuniform Magnetic Filed //  Plas-ma Physics Reports. 1990, v. 16, № 2, p. 209-215.4. N.G.Belova,  V.I.Karas'.  Numerical  Simulation  of High-Current  Ion  Beam Acceleration  and  Charge Compensation  in  Magneto-Isolated  Systems.  // Part. Accel. 1992, v. 37-38, p. 225-234.5. N.G.Belova, V.I.Karas'. Numerical Investigation of High-Current  Ion Beam Acceleration in  Two-Ac-celerating Gaps of Induction Linac // Proc of 1993 IEEE Part. Accel. Conf.,  Washington DC, v. 1, p. 664-666.6. N.G.Belova, V.I.Karas'. Optimization of High-Cur-rent Ion Beam Acceleration and Charge Compensa-tion in Two-Cusps of Induction Linac // Proc of 10-th  Int.  Conf.  on  High  Power  Particle  Beams.  BEAMS'94, San Diego. v. 2. p. 563-566.7. N.G.Belova, V.I.Karas'. Optimization of High-Cur-rent Ion Beam Acceleration and Charge Compensa-tion  in  Two-Cusps  of  Induction  Linac  //  Plasma Physics Reports. 1995, v. 21, № 12, p. 1065-1074.8. N.G.Belova, V.I.Karas'. Acceleration and Stability of  High-Current  Ion  Beam  in  Two  Accelerating Gaps of Induction Linac // Plasma Physics Reports. 1997, v. 23, № 4, p. 355-358.9. N.G.Belova, V.I.Karas', O.N.Shulika. Charge Com-pensation  and  Acceleration  of  a  Thick-Walled High-Current  Ion  Beam  in  Induction  Linac  // Dopovidi  NAN  Ukrainy  (Reports  of  National  Academy  of  Sciences  in  Ukraine), 1999,  v.  1, p. 70-74. (in Ukrainian).10. N.G.Belova, V.I.Karas', O.N.Shulika. Charge Com-pensation  and  Acceleration  of  a  Thick-Walled High-Current Ion Beam in Induction Linac // Prob-lems of Atomic Science and Technology. Issue: Nu-clear-Physics Research (34), 1999, v. 3, p. 77-78.11. V.I.Karas',  E.A.Kornilov,  V.D.Levchenko, Yu.S.Sigov, Ya.B.Fainberg, and O.N.Shulika. High Current Linac for Inertial Confinement Fusion on Heavy Ion Beams // Abstracts of XXVII Conference on  Plasma Physics  and ICF (Zvenigirod,  Russia, February 2000). p. 165.ВОПРОСЫ АТОМНОЙ НАУКИ И ТЕХНИКИ. 2001. №5.Серия: Ядерно-физические исследования (39), с. 23-23.23

Linear induction accelerator with charge and current compensation

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Linear induction accelerator with charge and current compensation

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