Computer simulation of high-current ion bunches transport and acceleration with additional space charge compensation by thermal electrons
The particle in cell simulation results, within the limits of the complete set of the Maxwell-Vlasov equations, of the short (the ion bunch length is much smaller than the cusp length) and long (the ion bunch length is much longer than the cusp length) high-current compensated tubular ion bunches tr...
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Національний науковий центр «Харківський фізико-технічний інститут» НАН України
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irk-123456789-801372015-04-13T03:02:14Z Computer simulation of high-current ion bunches transport and acceleration with additional space charge compensation by thermal electrons Manuilenko, O.V. Karas, V.I. Новые и нестандартные ускорительные технологии The particle in cell simulation results, within the limits of the complete set of the Maxwell-Vlasov equations, of the short (the ion bunch length is much smaller than the cusp length) and long (the ion bunch length is much longer than the cusp length) high-current compensated tubular ion bunches transportation and acceleration in the peaked fence magnetic field are presented. The ion bunch current, at injection in the cusp, is compensated by an accompanying electron bunch. Additional compensation of the ion bunch space charge by means of thermal electrons generated in the drift space has been studied. It is shown that both for short and for long ion bunches, the optimized additional space charge compensation by thermal electrons leads to a reduction of the energy spread of the accelerated ion beam at the output of the cusp. Приведены результаты численного моделирования методом макрочастиц в рамках полной системы уравнений Власова-Максвелла, транспортировки и ускорения коротких (длина ионного сгустка значительно меньше длины каспа) и длинных (длина ионного сгустка значительно больше длины каспа) сильноточных трубчатых ионных сгустков в магнитном поле остроугольной геометрии. Ток ионного сгустка при инжекции в касп скомпенсирован сопровождающим электронным сгустком. Изучена дополнительная компенсация объемного заряда ионного сгустка тепловыми электронами. Показано, что как в случае коротких, так и в случае длинных ионных сгустков оптимизированная дополнительная компенсация объемного заряда тепловыми электронами приводит к уменьшению энергетического разброса ускоряемого ионного пучка на выходе из каспа. Наведено результати числового моделювання методом макрочасток у рамках повної системи рівнянь Власова-Максвелла, транспортування та прискорення коротких (довжина іонного згустка значно менше довжини каспа) та довгих (довжина іонного згустка значно більша за довжину каспа) сильнострумових трубчастих іонних згустків у магнітному полі гострокутової геометрії. Струм іонного згустка при інжекції в касп, скомпенсовано електронним згустком. Досліджено додаткову компенсацію об'ємного заряду іонного згустка за допомогою теплових електронів. Показано, що як у випадку коротких, так і у випадку довгих іонних згустків додаткова оптимізована компенсація об'ємного заряду тепловими електронами призводить до зменшення енергетичного розкиду іонного пучка, який прискорюється на виході з каспа. 2014 Article Computer simulation of high-current ion bunches transport and acceleration with additional space charge compensation by thermal electrons / O.V. Manuilenko, V.I. Karas // Вопросы атомной науки и техники. — 2014. — № 3. — С. 107-111. — Бібліогр.: 16 назв. — англ. 1562-6016 PACS: 41.75.-i, 52.40.Mj, 52.58.Hm, 52.59.-f, 52.65.Rr http://dspace.nbuv.gov.ua/handle/123456789/80137 en Вопросы атомной науки и техники Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine |
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Новые и нестандартные ускорительные технологии Новые и нестандартные ускорительные технологии |
| spellingShingle |
Новые и нестандартные ускорительные технологии Новые и нестандартные ускорительные технологии Manuilenko, O.V. Karas, V.I. Computer simulation of high-current ion bunches transport and acceleration with additional space charge compensation by thermal electrons Вопросы атомной науки и техники |
| description |
The particle in cell simulation results, within the limits of the complete set of the Maxwell-Vlasov equations, of the short (the ion bunch length is much smaller than the cusp length) and long (the ion bunch length is much longer than the cusp length) high-current compensated tubular ion bunches transportation and acceleration in the peaked fence magnetic field are presented. The ion bunch current, at injection in the cusp, is compensated by an accompanying electron bunch. Additional compensation of the ion bunch space charge by means of thermal electrons generated in the drift space has been studied. It is shown that both for short and for long ion bunches, the optimized additional space charge compensation by thermal electrons leads to a reduction of the energy spread of the accelerated ion beam at the output of the cusp. |
| format |
Article |
| author |
Manuilenko, O.V. Karas, V.I. |
| author_facet |
Manuilenko, O.V. Karas, V.I. |
| author_sort |
Manuilenko, O.V. |
| title |
Computer simulation of high-current ion bunches transport and acceleration with additional space charge compensation by thermal electrons |
| title_short |
Computer simulation of high-current ion bunches transport and acceleration with additional space charge compensation by thermal electrons |
| title_full |
Computer simulation of high-current ion bunches transport and acceleration with additional space charge compensation by thermal electrons |
| title_fullStr |
Computer simulation of high-current ion bunches transport and acceleration with additional space charge compensation by thermal electrons |
| title_full_unstemmed |
Computer simulation of high-current ion bunches transport and acceleration with additional space charge compensation by thermal electrons |
| title_sort |
computer simulation of high-current ion bunches transport and acceleration with additional space charge compensation by thermal electrons |
| publisher |
Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
| publishDate |
2014 |
| topic_facet |
Новые и нестандартные ускорительные технологии |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/80137 |
| citation_txt |
Computer simulation of high-current ion bunches transport and acceleration with additional space charge compensation by thermal electrons / O.V. Manuilenko, V.I. Karas // Вопросы атомной науки и техники. — 2014. — № 3. — С. 107-111. — Бібліогр.: 16 назв. — англ. |
| series |
Вопросы атомной науки и техники |
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2025-07-06T04:03:36Z |
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| fulltext |
ISSN 1562-6016. ВАНТ. 2014. №3(91) 107
COMPUTER SIMULATION OF HIGH-CURRENT ION BUNCHES
TRANSPORT AND ACCELERATION WITH ADDITIONAL SPACE
CHARGE COMPENSATION BY THERMAL ELECTRONS
O.V. Manuilenko*, V.I. Karas’
National Science Center “Kharkov Institute of Physics and Technology”, Kharkov, Ukraine
*E-mail: ovm@kipt.kharkov.ua
The particle in cell simulation results, within the limits of the complete set of the Maxwell-Vlasov equations, of
the short (the ion bunch length is much smaller than the cusp length) and long (the ion bunch length is much longer
than the cusp length) high-current compensated tubular ion bunches transportation and acceleration in the peaked
fence magnetic field are presented. The ion bunch current, at injection in the cusp, is compensated by an accompa-
nying electron bunch. Additional compensation of the ion bunch space charge by means of thermal electrons gener-
ated in the drift space has been studied. It is shown that both for short and for long ion bunches, the optimized addi-
tional space charge compensation by thermal electrons leads to a reduction of the energy spread of the accelerated
ion beam at the output of the cusp.
PACS: 41.75.-i, 52.40.Mj, 52.58.Hm, 52.59.-f, 52.65.Rr
INTRODUCTION
The usage of linear induction accelerators (LIA) for
obtaining high-current ion beams (HCIB) with the pa-
rameters required for inertial confinement fusion is per-
spective, as LIA can operate at high pulse frequency,
and can accelerate, with efficiency of 30%, high-current
beams of virtually any ions, and perform time compres-
sion of current pulse in the acceleration process, which
eliminates the operations related to the increase of cur-
rent due to compression rings. The classical vacuum
LIAs are discussed in [1]. The final ions energy at the
target should be approximately 10 GeV with energy
content of 10 MJ and a pulse duration of a few tens of
nanoseconds. The usage of collective focusing methods
in the LIA allows significantly increase the ion beam
current and decrease its energy while maintaining the
required energy content of the beam on the target. In
such kind of LIA the ion beam space charge is compen-
sated by electrons [2 - 4], and the electron current is
suppressed by magnetic insulation of accelerating gaps
[5]. The nature of charge and current neutralization of
an HCIB by an electron beam in an axisymmetric accel-
erating gap was investigated in [5 - 8], where the dy-
namics of electrons and ions in the cusp magnetic fields
in the presence of an accelerating field in the single-
particle approximation, and the influence of own elec-
tric and magnetic fields of electron and ion beams on
the magnetic isolation, and their passage through the
cusp have been studied. The transport and acceleration
of compensated ion beam in the 1 - 6 cusps was investi-
gated in [9 - 13]. It was shown that the ion energy dis-
tribution function of the HCIB at the exit of the acceler-
ator improves with increasing energy of the accompany-
ing electron beam, and that the additional injection of
electron beams in the cusps decreases HCIB energy
spread and reduces its divergence in space. The
transport and acceleration of the short, compared to the
cusp length, high-current electron and ion bunches (IB)
was studied in [14, 15]. It was shown that additional
compensation of the accelerated ion bunch space charge
by thermal electrons leads to reduction of its energy
dispersion and divergence on an exit from the cusp. It
was shown also that overcompensation of the ion bunch
space charge by thermal electrons leads not only to in-
crease of energy spread and divergence of an ion bunch
on an exit from the cusp, but also to deceleration of an
ion bunch.
In this paper we study the acceleration and transport
of short and long high-current tubular IBs in the picked
fence magnetic field with the additional compensation
of IB space charge by thermal electrons. It is shown that
both for short and for long IBs, the optimized additional
space charge compensation by thermal electrons leads
to a reduction of the energy spread of the accelerated IB
at the output of the cusp.
Fig. 1 shows the simulated structure, the configura-
tion of the external magnetic field [9, 10] and the place
of the electron and ion beams injection. The length of
the cusp is Lz = 10.24 cm, its radius is Lr = 10.24 cm,
[0, Iz ] and [ IIz , Lz ] are the drift spaces, Iz = 4.8 cm,
IIz = 5.44 cm, [ Iz , IIz ] is the accelerating gap.
Fig. 1. Configuration of the external magnetic field
and regions of electron and ion bunches injection
into the computation domain
The minimal and maximal radius of the electron and
ion bunches are the same: minr = 1.32 cm, maxr = 1.48 cm.
At the injection time 0000 iiee vnvn = , the electron bunch
density is 0en = 7.12⋅1013 cm-3, the electron bunch ve-
locity is 0ev = 0.95⋅c, the initial velocity of the ion
bunch (protons) is 0iv = 0.285⋅c, c is the speed of light.
The external magnetic field has a cusp configuration [9,
10] with amplitude 0H = 47 kGs. The IB length is
Iz⋅5.0 (short IB), and Iz⋅36 (long IB). In computer
simulations (see below) in regions [ ] [ ]maxmin ,,0 rrzI × ,
ISSN 1562-6016. ВАНТ. 2014. №3(91) 108
[ ] [ ]maxmin ,, rrzz LII × , there were a generation of Maxwellian
electrons (ME) with temperature eT = 1 keV. These elec-
trons are intended to further compensation of the IB
space charge. The generation rate is chosen so that at
the time of its termination the electron density comp
en
was the specified value. The outer boundaries of the
system are perfectly conducting metal walls. Particles
that fall into the boundaries are removed from the simu-
lation. Particle in cell simulation scheme is described in
detail in [9, 10, 16].
SIMULATION RESULTS
Fig. 2 show the simulation results for the transport of
the high-current compensated IB through the cusp with
additional compensation of the IB space charge by
means of the ME, and without additional compensation.
The ion distribution functions (IDFs) depending on en-
ergy (IEDF) and transverse coordinate at the exit of the
cusp are presented. The IB length is Iz⋅5.0 . To generate
ME, each of the regions [ ] [ ]maxmin ,,0 rrzI × and
[ ] [ ]maxmin ,, rrzz LII × is divided into 30 sub-areas
[ ] [ ]maxmin
1 ,, rrzz j
I
j
I ×+ and [ ] [ ]maxmin
1 ,, rrzz k
II
k
II ×+ of
equal length in the longitudinal direction. In each sub-
domain the generation of ME starts at the moment when
the front of the IB crosses its left edge, and ends when
the front of the IB crosses its right edge. The generation
rate is chosen so that at the time of its termination the
ME density comp
en = 0.7 0 .in In this case
00 i
comp
ee nnn =+ . Fig. 2,a – no ME generation,
Fig. 2,b – the generation of ME only in the right half of
the cusp, Fig. 2,c – the generation of ME only in the left
half of the cusp, Fig. 2,d – the generation of ME in the
left and right halves of the cusp.
As can be seen from Fig. 2, the IB is well focused in
the transverse direction. However, after passing the
cusp, IEDFs differ greatly and depends on the location
in which the ME are generated. If the space charge of
the IB is compensated with ME in the right half of the
cusp (see Fig. 2,b), the IEDF is almost monochromatic.
The additional compensation of the IB space charge in
the left half of the cusp (see Fig. 2,c), or in the left and
right semicusps (see Fig. 2,d), leads to a considerable
spread in ion energy. The increase in the ion energy
spread can be explained by the fact that the compensat-
ing ME loaded IB, taking part its kinetic energy. This is
clearly seen in the ME energy distribution function on
the right edge of the cusp – ME from the left side of the
cusp always have an average energy exceeding the ini-
tial one. Thus, the optimal is the compensation after the
accelerating gap.
Fig. 3 show the simulation results for the accelera-
tion of the high-current compensated IB in the cusp. The
accelerating potential is 1 MB. IDFs depending on en-
ergy and transverse coordinate at the right cusp bounda-
ry are presented. Fig. 3,a – no ME generation, Fig. 3,b –
the generation of ME only in the right half of the cusp,
Fig. 3,c – the generation of ME only in the left half of
the cusp, Fig. 3,d – the generation of ME in the left and
right halves of the cusp. The generation rate is chosen
so that at the time of its termination the ME density
comp
en = 0.7 0in .
a b
c d
Fig. 2. IDFs vs energy and transverse coordinate at the
exit of the cusp: a – the generation of ME is absent;
b – ME generated in the right half of the cusp;
c – ME generated in the left half of the cusp;
d – ME generated in the left and right halves of the
cusp. At the time of the termination of the ME genera-
tion comp
en =0.7 0in . Accelerating potential is 0 MB
a b
c d
Fig. 3. IDFs vs energy and transverse coordinate at the
exit of the cusp: a – the generation of ME is absent;
b – ME generated in the right half of the cusp;
c – ME generated in the left half of the cusp;
d – ME generated in the left and right halves of the
cusp. At the time of the termination of the ME genera-
tion comp
en =0.7 0in . Accelerating potential is 1 MB
As can be seen from Fig. 3, IBs are well focused in
the transverse direction, however, as in the case of
transport, after the passage of the cusp, the IEDFs are
significantly different depending on the location, where
the compensating ME are generated. The IEDF is much
more monochromatic, if the space charge compensation
of the accelerated IB, using ME, takes place in the right
half of the cusp, i.e., after the accelerating gap (see
Fig. 3,b), in comparison with the compensation of the
accelerated IB in the left half of the cusp (see Fig. 3,c),
or in the left and right semicusps (see Fig. 3,d). The
increase in the ion energy spread can be explained, as in
ISSN 1562-6016. ВАНТ. 2014. №3(91) 109
the case of transport, by the fact that the compensating
ME loaded IB, consuming part its its kinetic energy.
This is clearly visible from the ME energy distribution
function on the right boundary of the cusp – ME from
the left side of the cusp always have an average energy
exceeding the initial one. Thus, the optimal space
charge compensation of the IB is the compensation after
the accelerating gap.
Fig. 4 show the computer simulation results for
transport and acceleration of long compensated high-
current IB (bunch length Iz⋅36 ) without additional IB
space charge compensation by thermal electrons. The
IDFs depending on energy and transverse coordinate on
the right edge of the cusp are presented. Fig. 4,a – the
accelerating field is absent, Fig. 4,b – the accelerating
potential is 1 MB. The behavior of IEDs on the acceler-
ator output, depending on the accelerating potential, do
not differ significantly from the previously studied case
of "infinitely long" beam [9 - 13]. Since the accompany-
ing electron beam kinetic energy is enough to overcome
the potential in 1 MV for ion acceleration, the electron
beam does not load the ion beam. And, therefore, the
IDF energy width on the right edge of the cusp, at an
accelerating potential of 1 MV, practically does not dif-
fer from the IDF energy width in the absence of the ac-
celerating field.
a b
Fig. 4. IDFs vs energy and transverse coordinate at the
exit of the cusp: a – the accelerating potential is absent;
b – the accelerating potential is 1 MB
Fig. 5 show the computer simulation results for the
acceleration of long compensated high-current IB
(bunch length Iz⋅36 ) with additional IB space charge
compensation by thermal electrons. The accelerating
potential is 1 MB. The ME generation occurs only in the
right half of the cusp – in the region
[ ] [ ]maxmin ,, rrzz LII × (see Fig. 1). The ME generation
starts at a time when the leading edge of the IB cross the
left border of the drift gap, and ends when the leading
edge of the bunch cross right border of the drift gap.
The generation rate is chosen so that at the time of its
termination the ME electron density comp
en is 0.5 0in
(undercompensation) (see Fig. 5,a), 0.7 0in (see
Fig. 5,b), and 1.0 0in (overcompensation) (see Fig. 5,c).
As can be seen from Fig. 5,a, the additional compen-
sation of the IB space charge by thermal electrons leads
to a decrease in ion energy spread at the exit of the ac-
celerator (compare with Fig. 4,b). The IB space charge
overcompensation leads to an increase in the energy
spread of the IB at the output of the cusp (see Fig. 5,c).
Fig. 6 show the computer simulation results for the
acceleration of long compensated high-current IB
(bunch length Iz⋅36 ) with additional IB space charge
compensation by thermal electrons. The accelerating
potential is 1 MB.
a
b
c
Fig. 5. IDFs vs energy and transverse coordinate at the
exit of the cusp: a – at the time of the termination of the
ME generation comp
en =0.5 0in ; b – at the time of the
termination of the ME generation comp
en =0.7 0in ;
c – at the time of the termination of the ME generation
comp
en =1.0 0in . The ME generation occurs only
in the right half of the cusp. The accelerating potential
is 1 MB
The ME generation occurs in the left and right
halves of the cusp, i.e., in the regions
[ ] [ ]maxmin ,,0 rrzI × and [ ] [ ]maxmin ,, rrzz LII × (see
Fig. 1). The ME generation starts at a time when the
leading edge of the IB cross the left border of the ap-
propriate drift gap, and stops when the leading edge of
the bunch cross its right border. The generation rate is
chosen so that at the time of its termination the ME
electron density comp
en is 0.5 0in (see Fig. 6,a), 0.7 0in
(see Fig. 6,b), and 1.0 0in (see Fig. 6,c).
As can be seen from Fig. 6, an additional space
charge compensation of the IB by ME in the left half of
the cusp (before accelerating gap) leads to deterioration
of the IDF, compared with the cases shown in Fig. 5.
ISSN 1562-6016. ВАНТ. 2014. №3(91) 110
a
b
c
Fig. 6. IDFs vs energy and transverse coordinate at the
exit of the cusp: a – at the time of the termination of the
ME generation comp
en =0.5 0in ; b – at the time of the
termination of the ME generation comp
en =0.7 0in ;
c – at the time of the termination of the ME generation
comp
en =1.0 0in . The ME generation occurs in the left
and right halves of the cusp. The accelerating potential
is 1 MB
CONCLUSIONS
The particle in cell simulation results, within the
limits of the complete set of the Maxwell-Vlasov equa-
tions, of the short (the ion bunch length is much smaller
than the cusp length) and long (the ion bunch length is
much longer than the cusp length) high-current compen-
sated tubular ion bunches transportation and accelera-
tion in the peaked fence magnetic field are presented.
The ion bunch current, at injection in the cusp, is com-
pensated by an accompanying electron bunch. Addi-
tional compensation of the ion bunch space charge by
means of thermal electrons generated in the drift space
has been studied. It is shown that both for short and for
long ion bunches, the optimized in space and time addi-
tional space charge compensation by thermal electrons
leads to a reduction of the energy spread of the acceler-
ated ion bunch at the exit of the cusp.
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Article received 19.11.2013
ЧИСЛЕННОЕ МОДЕЛИРОВАНИЕ ТРАНСПОРТИРОВКИ И УСКОРЕНИЯ СИЛЬНОТОЧНЫХ
ИОННЫХ СГУСТКОВ С ДОПОЛНИТЕЛЬНОЙ КОМПЕНСАЦИЕЙ ОБЪЕМНОГО ЗАРЯДА
ТЕПЛОВЫМИ ЭЛЕКТРОНАМИ
О.В. Мануйленко, В.И. Карась
Приведены результаты численного моделирования методом макрочастиц в рамках полной системы урав-
нений Власова-Максвелла, транспортировки и ускорения коротких (длина ионного сгустка значительно
меньше длины каспа) и длинных (длина ионного сгустка значительно больше длины каспа) сильноточных
трубчатых ионных сгустков в магнитном поле остроугольной геометрии. Ток ионного сгустка при инжекции
в касп скомпенсирован сопровождающим электронным сгустком. Изучена дополнительная компенсация
объемного заряда ионного сгустка тепловыми электронами. Показано, что как в случае коротких, так и в
случае длинных ионных сгустков оптимизированная дополнительная компенсация объемного заряда тепло-
выми электронами приводит к уменьшению энергетического разброса ускоряемого ионного пучка на выхо-
де из каспа.
ЧИСЛОВЕ МОДЕЛЮВАННЯ ТРАНСПОРТУВАННЯ ТА ПРИСКОРЕННЯ
ПОТУЖНОСТРУМОВИХ ІОННИХ ЗГУСТКІВ З ДОДАТКОВОЮ КОМПЕНСАЦІЄЮ
ЇХ ОБ'ЄМНОГО ЗАРЯДУ ТЕПЛОВИМИ ЕЛЕКТРОНАМИ
О.В. Мануйленко, В.І. Карась
Наведено результати числового моделювання методом макрочасток у рамках повної системи рівнянь
Власова-Максвелла, транспортування та прискорення коротких (довжина іонного згустка значно менше до-
вжини каспа) та довгих (довжина іонного згустка значно більша за довжину каспа) сильнострумових труб-
частих іонних згустків у магнітному полі гострокутової геометрії. Струм іонного згустка при інжекції в
касп, скомпенсовано електронним згустком. Досліджено додаткову компенсацію об'ємного заряду іонного
згустка за допомогою теплових електронів. Показано, що як у випадку коротких, так і у випадку довгих іон-
них згустків додаткова оптимізована компенсація об'ємного заряду тепловими електронами призводить до
зменшення енергетичного розкиду іонного пучка, який прискорюється на виході з каспа.
INTRODUCTION
SIMULATION RESULTS
CONCLUSIONS
REFERENCES
численное моделирование ТРАНСПОРТИРОВКИ и Ускорения сильноточнЫХ ионнЫХ сгусткОВ с дополнительной компенсацией объемного заряда тепловЫми электронами
числове моделювання ТРАНСПОРТУВАННЯ ТА ПРИСКОРЕННЯ ПОТУЖНОСТРУМОВИХ ІОННИХ ЗГУСТКІВ З ДОДАТКОВОЮ КОМПЕНСАЦІЄЮ ЇХ ОБ'ЄМНОГО ЗАРЯДУ ТЕПЛОВИМИ ЕЛЕКТРОНАМИ
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