Charge compensation and acceleration of a thick-walled high-current ion beam in induction linac
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.
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Національний науковий центр «Харківський фізико-технічний інститут» НАН України
1999
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| Zitieren: | Charge compensation and acceleration of a thick-walled high-current ion beam in induction linac / N.G. Belova, V.I. Karas’, O.N. Shulika // Вопросы атомной науки и техники. — 1999. — № 3. — С. 77-78. — Бібліогр.: 16 назв. — англ. |
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irk-123456789-813612015-05-15T03:02:19Z Charge compensation and acceleration of a thick-walled high-current ion beam in induction linac Belova, N.G. Karas, V.I. Shulika, O.N. 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. 1999 Article Charge compensation and acceleration of a thick-walled high-current ion beam in induction linac / N.G. Belova, V.I. Karas’, O.N. Shulika // Вопросы атомной науки и техники. — 1999. — № 3. — С. 77-78. — Бібліогр.: 16 назв. — англ. 1562-6016 http://dspace.nbuv.gov.ua/handle/123456789/81361 en Вопросы атомной науки и техники Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
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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. |
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Article |
| author |
Belova, N.G. Karas, V.I. Shulika, O.N. |
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Belova, N.G. Karas, V.I. Shulika, O.N. Charge compensation and acceleration of a thick-walled high-current ion beam in induction linac Вопросы атомной науки и техники |
| author_facet |
Belova, N.G. Karas, V.I. Shulika, O.N. |
| author_sort |
Belova, N.G. |
| title |
Charge compensation and acceleration of a thick-walled high-current ion beam in induction linac |
| title_short |
Charge compensation and acceleration of a thick-walled high-current ion beam in induction linac |
| title_full |
Charge compensation and acceleration of a thick-walled high-current ion beam in induction linac |
| title_fullStr |
Charge compensation and acceleration of a thick-walled high-current ion beam in induction linac |
| title_full_unstemmed |
Charge compensation and acceleration of a thick-walled high-current ion beam in induction linac |
| title_sort |
charge compensation and acceleration of a thick-walled high-current ion beam in induction linac |
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Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
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1999 |
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http://dspace.nbuv.gov.ua/handle/123456789/81361 |
| citation_txt |
Charge compensation and acceleration of a thick-walled high-current ion beam in induction linac / N.G. Belova, V.I. Karas’, O.N. Shulika // Вопросы атомной науки и техники. — 1999. — № 3. — С. 77-78. — Бібліогр.: 16 назв. — англ. |
| series |
Вопросы атомной науки и техники |
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AT belovang chargecompensationandaccelerationofathickwalledhighcurrentionbeamininductionlinac AT karasvi chargecompensationandaccelerationofathickwalledhighcurrentionbeamininductionlinac AT shulikaon chargecompensationandaccelerationofathickwalledhighcurrentionbeamininductionlinac |
| first_indexed |
2025-07-06T06:05:42Z |
| last_indexed |
2025-07-06T06:05:42Z |
| _version_ |
1836876507378614272 |
| fulltext |
CHARGE COMPENSATION AND ACCELERATION OF A THICK-
WALLED HIGH-CURRENT ION BEAM IN INDUCTION LINAC
N.G.Belova, V.I.Karas’*, O.N.Shulika*
Institute of Physics & Technology Russian Academy of Sciences, Moscow, Russia
* NSC KIPT, Kharkov, Ukraine
INTRODUCTION
At 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 MODEL
To 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 s0
21= − , 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= π , 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.
77
study 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 SIMULATION
Further (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.
0.25
0.3
<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.
CONCLUSION
Results 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).
REFERENCES
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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);
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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).
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(Washington DC, V.I, 1993).
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Particle Beams BEAMS'94 (San Diego, 1994).
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78
INTRODUCTION
MATHEMATICAL AND DISCRETE MODEL
RESULTS OF SIMULATION
CONCLUSION
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