At present, several methods of obtaining highcurrent ion beam, which are based on the use of induction accelerators and are applied to inertial controlled fusion (ICF) research, are being considered

Belova, N.G.

Karas, V.I.

Shulika, O.N.

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

CHARGE COMPENSATION AND ACCELERATION OF A THICK-WALLED HIGH-CURRENT ION BEAM IN INDUCTION LINACN.G.Belova, V.I.Karas’*, O.N.Shulika*Institute of Physics & Technology Russian Academy of Sciences, Moscow, Russia* NSC KIPT, Kharkov, UkraineINTRODUCTIONAt present,  several  methods of  obtaining high-current  ion  beam,  which  are  based  on  the  use  of induction  accelerators  and  are  applied  to  inertial controlled fusion (ICF) research, are being considered [1-3]. To date, kiloampere ion beams with energies of several  hundred  keV  have  been  produced  in  high-current  linear  induction  accelerators  (linac)  with collective focusing [4-6]. The power of the hollow high-current  ion beam (HHCIB) for ICF purposes must  be several  orders  greater,  with  rather  stringent requirements  on  beam  brightness.  Therefore,  when developing  a  driver  for  ICF  on  the  basis  of  a  high-current linac, it is necessary to investigate a number of important physical problems: (1) the formation of high-current beams in injector;  (2) the provision of efficient magnetic  insulation  for  accelerating  gaps;  (3) charge compensation of the ion beam in the transport channel and  in  the  magneto-insulated  accelerating  gaps;  (4) effective acceleration and stability of the ion beam in accelerating  channel;  and  (5) transport,  focusing,  and space-time compression of HHCIBs.In  linac,  the  conventional  way  of  charge  and current compensation [7, 8] is inefficient. In [9, 10], a new mechanism for  the  neutralization  of  HHCIBs  in axially  symmetric  magneto-insulated  gaps  was proposed.  Its  physical  meaning  is  that  a  specially injected compensating electron beam drifts through the cusp due to self-consistent azimuthal magnetic field and an electric field caused by a small radial separation of ion and electron beams.In  [11-13],  the  investigation  results  of  the acceleration, and the charge and current compensation of  HHCIBs  in  one  and  two linac  cusps  are  reported. These results have shown that both in the presence and in  the  absence  of  an  accelerating  electric  field,  the following  effects  take  place:  (1) charge  and  current compensation of  HHCIB in the accelerating gaps;  (2) stability of the ion beam during times that substantially exceed  the  inverse  ion  Langmuir  and  Larmor frequencies. The performed numerical simulations have also  shown  that  in  the  drift  space  between  two accelerating gaps the current and charge compensation of the ion beam proved to be insufficient because of a substantial difference in the electron and ion velocities acquired  up  to  the  time  of  the  transit  of  the  beams through the drift gap. As a result, the positive potential of the self-consistent field in the drift space leads to the spread  and  deceleration  of  the  ion  beam  and, consequently, to the degradation of the beam brightness. The  positive  space  charge  in  the  drift  gap  can  be compensated  by  injecting  thermal  electrons  into  it.  It was shown that a preliminary injection of cold electrons permits to eliminate broadening and decelerating an ion beam  in  the  drift  gap  and  to  provide  its  additional focusing.In  this  work,  the  investigation  directed  to:  (1) reaching  of  the  optimal  relation  between the  external electric field parameters and the compensating electron beam parameters;  (2) defining of the optimal thickness of  annular  beam at which the ion beam is effectively accelerated and at a time is remaining compensated and not losing a stability.MATHEMATICAL AND DISCRETE MODELTo describe the collisionless plasma dynamics of beams the set of relativistic Vlasov's equations for the distribution functions of particles  ( )f P R ts  , , ) in the axisymmetric  ( )∂ ∂ θ = 0  cylindrical  geometry ( )R r z= ,  has been used for the investigation of the transient  and  stationary  processes  in  linac  (here  P  momentum).  The  self-consistent  electric  ( )E r z,  and magnetic  ( )B r z,  fields  including  in  Vlasov's equations  are  determined by the  Maxwell's  equations, the right hands of which are defined as the zeroth and first moments of the distribution functions. From the set of  Vlasov's  equations  can  be  obtained  the  set  of  the dynamic  equations  for  the  particles.  The  Maxwell's equations  using  the  Lorentz  gauge ( )div A c t+ =− 1 0∂ ∂Φ  can be reduced to the wave equations for  the scalar  ( )Φ r z,  and vector  ( )A r z,  potentials.The initial velocity of a given sort (s) of particles is  defined  by  the  boundary  conditions  for  the distribution  functions  at  z = 0 : ( ) ( )f m u R t us s r , , = δ ( ) ( )× −δ δ θu u uz s0  for r r rmin max≤ ≤  and  uz > 0 .  Here  rmin and  rmax  are the  minimum and maximum beams radii  respectively which  define  the  initial  r-coordinates  of  particles, u v vs s s021= − ,  vs  is  a  beam  velocity.  At  (r = 0 ,  r rL= )  the  reflection  regime  is  set.  The particles exit free from the simulation region at z zL= . At  the initial time the particles are absent in modeling region.The set of equations and the initial and boundary conditions for the potentials and distribution functions are described in detail in [15].The configuration of the external magnetic field is defined by the expression  ( )A B k I krθ = − ×0 1  ( )× cos kz ,  where  ( )I kr1  is the first order modified Bessel function, B0  is the amplitude of magnetic field, and k K zL= pi , K  is total number of cusps.The discrete model, which is developed for the ВОПРОСЫ АТОМНОЙ НАУКИ И ТЕХНИКИ. 1999. №3.Серия: Ядерно-физические исследования. (34), с. 77-78.77study  of  both  relativistic  and  nonrelativistic axisymmetric plasma configuration, is realized as 2.5-dimensional  axisymmetric  numerical  code.  The calculations were carried out using Pentium-133.Hollow  magnetized  relativistic  electron  beam (Larmor radius rLe  is substantially smaller than the size of the cusp  Lz  and the chamber radius  rL ) and high-current unmagnetized ion beam (Larmor radius  rLi  is more greater Lz  and rL ) were injected along z-axis. In all  cases  the  beam  current  densities  were  equal  to q n V q n Ve e e i i i0 0= .  The  ion  beam  velocity  was Vi = 0 285. . The minimum and maximum beams radii were rmin =30 and rmax =37.5. The size of one cusp and radius  of  the  chamber  were  Lz =78.5  and  rL =157.5 respectively.  The  amplitude  of  the  external  field  was B0 176= . .  The mass ratio was  mi/me=100,  me=20m0. The  number  of  particles  in  the  cell  was  N e = 64 , N i = 180 . The number of the nodes was equal to (Jz×Jr)=(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 parameters of the electron and ion beams have  satisfied  the  condition  of  the  electron  beam transport  together the ion beam through the magneto-insulated  accelerating  gap  ( ve = ÷08 085. . ).  The preliminary injection of the thermal electrons with the Maxwellian distribution function with the temperature Tce = 0 002.  into drift gap was used.RESULTS OF SIMULATIONFurther  (below)  the  results  of  three  cases distinguished by the potential difference across one cusp are discussed. The distributions presented in Fig.1 show that the applied external electric field, which accelerates ions and retards electrons, does not prevent the electron beam drift  through the accelerating gaps.  It  is  clearly seen  that  not  only  the  charge  but  also  the  current compensation  of  the  ion  beam  occur.  The  ion  beam generally  retains  monoenergetic  shape,  because  its spread in vz  and vr  does not exceed 10%.Fig. 1. Distribution of the total charge density ρ(r,z), the scalar potential Φ(r,z) and the total axial current densities jz(r,z) at t pe=−440 1ω  for the case with additional electron injection into drift gap and thick-wall ion beam.More  optimal  relation  between  the  potential difference  ∆ Φ = 15 0.  and the electron beam energy was at the parameters ve = 085. , γ ≈ 19. . The kinetic energy of electron beam  ε eb ≈ 18 0.  was sufficient to overcome the potential difference. As a results the ion beam is accelerated and then its velocity is a constant in all  time of  simulation.  Fig.  1  illustrates  that  the self-consistent field of the positive charge is suppressed, and an  additional  focusing  of  ion  beam  by  the  negative space charge of the thermal electrons occur also. As a result the better characteristics of the ion beam can be produced in linac.The  preliminary  injection  of  the  thermal electrons into the drift gap upgrades the characteristics of HHCIB. At Fig. 2 the time dependences of the mean ion beam velocities for three cases are presented.+++++++++++++++++++++++++∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗1000.750.500.250.0.0.250.3<Vi>,(c)t,(ω pe-1)Fig. 2. Distribution of the mean ion velocity <Vi(t)>: (*)  - without thermal injection into accelerating gap; (+) - with injection and without accelerating field; (◊) - with injection and accelerating field.CONCLUSIONResults of the 2.5-dimensional numerical simulation of HHCIB dynamics in two magnet-isolated accelerating gaps separated by the drift gap are presented. 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. We obtained the restriction on the wall thickness of annular HHCIB which ensure the following: (1) charge- and current compensation is homogeneous on the ion beam cross-section; (2) a penetration depth of the accelerating electric field is considerably greater than the beam wall thickness.This  work  was  partly  suppoted  by  State Foundation  for  Fundamental  Researches  (grant 1/2.52/38).REFERENCES1. A.I. Fattens, and D. Keeffe, Proc. Lin. Accel. Conf., Santa Fe, LA-9234c, 205 (1981).2. R.O. Bangerter, Part. Accel. 37-38, 3 (1992).3. S.A. Slutz, P. Primm, T. Renk et.al. Final Report, SAND97-0344 UC-414, March 1997.4. V.A. Kiyashko, Yu.E. Kolyada, E.A. Kornilov, Ya.B. Fainberg, Pis'ma Zh. Tekhn. Fiz. 3, 1257 (1977).5. S.Jr. Humphries, Nucl. Fusion 20, 1549 (1980).6. I.S. Roth, J.D. Ivers, J.A. Nation Proc. VI Int. conf. on high power particle beams, Kobe, 1986.7. W. Peter, N. Rostoker, Phys. Fluids 25, 730 (1982);8. W. Peter, A. Ron, N. Rostoker, Phys. Fluids 22, 1471 (1979).9. V.I. Karas', V.V. Mukhin, V.E. Novikov, A.M. Naboka, Fiz. Plazmy 13, 494 (1987).10. V.I. Karas', V.A. Kiyashko, E.A. Kornilov, Ya.B. Fainberg, Nuclear Instruments and Methods in Physics Research A278, 245 (1989).11. N.G. Belova, V.I. Karas', Yu.S. Sigov, Fiz. Plazmy 16, 209 (1990).12. N.G. Belova, V.I. Karas', Part. Accel. 37-38, 225 (1992).13. N.G. Belova, V.I. Karas', Proc.IEEE Part.Accel. Conf. (Washington DC, V.I, 1993).14. V.I. Karas', N.G. Belova, Proc. X Int. Conf. on High Power Particle Beams BEAMS'94 (San Diego, 1994).15. N.G. Belova, V.I. Karas', Plasma Physics Reports 21, 1005 (1995).16. N.G. Belova, V.I. Karas', Plasma Physics Reports 23, 328 (1997).78

Charge compensation and acceleration of a thick-walled high-current ion beam in induction linac

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Charge compensation and acceleration of a thick-walled high-current ion beam in induction linac

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