Stability of the high-current ion beam in drift gap of linear induction accelerator
The results of numerical simulation of compensated ion beam (CIB) transport with current density 9 MA/m² through the drift gap of a linear induction accelerator (LIA) are presented. The CIB stability for the three methods of compensation in the charge of the ion beam in the absence and presence of a...
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nasplib_isofts_kiev_ua-123456789-1119352025-02-09T14:41:40Z Stability of the high-current ion beam in drift gap of linear induction accelerator Cтійкість сильнострумового іонного пучка в дрейфовому проміжку лінійного індукційного прискорювача Устойчивость сильноточного ионного пучка в дрейфовом промежутке линейного индукционного ускорителя Karas, V.I. Manuilenko, O.V. Tarakanov, V.P. Fedorovskaya, O.V. Новые методы ускорения заряженных частиц The results of numerical simulation of compensated ion beam (CIB) transport with current density 9 MA/m² through the drift gap of a linear induction accelerator (LIA) are presented. The CIB stability for the three methods of compensation in the charge of the ion beam in the absence and presence of an external magnetic field is considered. It is shown that in the presence of an external magnetic field instabilities development does not lead to a significant deterioration in the ion beam quality regardless of the compensation way. It is shown, that the most effective addition compensation of the ion beam in charge is applying of self-consistent injection of additional electrons, which leads to the conservation of the CIB parameters, sufficient for its use in heavy-ion inertial fusion (HIF). Представлені результати чисельного моделювання транспортування КІП густиною струму 9 МА/м² через дрейфовий проміжок лінійного індукційного прискорювача. Розглянута стійкість КІП для трьох методів компенсації іонного пучка за зарядом при відсутності та наявності зовнішнього магнітного поля. Показано, що при наявності зовнішнього магнітного поля розвиток нестійкостей не призводе до суттєвого погіршення якості іонного пучка незалежно від способу компенсації. Показано, що найбільш ефективною докомпенсацією іонного пучка за зарядом є застосування самоузгодженої інжекції додаткових електронів, що призводить до збереження параметрів КІП, достатніх для його використання у важкоіонному інерціальному синтезі. Представлены результаты численного моделирования транспортировки КИП плотностью тока 9 МА/м² через дрейфовый промежуток линейного индукционного ускорителя. Рассмотрена устойчивость КИП для трех методов компенсации ионного пучка по заряду в отсутствие и при наличии внешнего магнитного поля. Показано, что при наличии внешнего магнитного поля развитие неустойчивостей не приводит к существенному ухудшению качества ионного пучка независимо от способа компенсации. Показано, что наиболее эффективной докомпенсацией ионного пучка по заряду является применение самосогласованной инжекции дополнительных электронов, что приводит к сохранению параметров КИП, достаточных для его использования в тяжелоионном инерциальном синтезе. 2013 Article Stability of the high-current ion beam in drift gap of linear induction accelerator / V.I. Karas’, O.V. Manuilenko, V.P. Tarakanov, O.V. Fedorovskaya // Вопросы атомной науки и техники. — 2013. — № 4. — С. 64-68. — Бібліогр.: 34 назв. — англ. 1562-6016 PACS: 41.75.-i, 52.40.Mj, 52.58.Hm, 52.59.-f, 52.65.Rr https://nasplib.isofts.kiev.ua/handle/123456789/111935 en Вопросы атомной науки и техники application/pdf Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
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Новые методы ускорения заряженных частиц Новые методы ускорения заряженных частиц |
| spellingShingle |
Новые методы ускорения заряженных частиц Новые методы ускорения заряженных частиц Karas, V.I. Manuilenko, O.V. Tarakanov, V.P. Fedorovskaya, O.V. Stability of the high-current ion beam in drift gap of linear induction accelerator Вопросы атомной науки и техники |
| description |
The results of numerical simulation of compensated ion beam (CIB) transport with current density 9 MA/m² through the drift gap of a linear induction accelerator (LIA) are presented. The CIB stability for the three methods of compensation in the charge of the ion beam in the absence and presence of an external magnetic field is considered. It is shown that in the presence of an external magnetic field instabilities development does not lead to a significant deterioration in the ion beam quality regardless of the compensation way. It is shown, that the most effective addition compensation of the ion beam in charge is applying of self-consistent injection of additional electrons, which leads to the conservation of the CIB parameters, sufficient for its use in heavy-ion inertial fusion (HIF). |
| format |
Article |
| author |
Karas, V.I. Manuilenko, O.V. Tarakanov, V.P. Fedorovskaya, O.V. |
| author_facet |
Karas, V.I. Manuilenko, O.V. Tarakanov, V.P. Fedorovskaya, O.V. |
| author_sort |
Karas, V.I. |
| title |
Stability of the high-current ion beam in drift gap of linear induction accelerator |
| title_short |
Stability of the high-current ion beam in drift gap of linear induction accelerator |
| title_full |
Stability of the high-current ion beam in drift gap of linear induction accelerator |
| title_fullStr |
Stability of the high-current ion beam in drift gap of linear induction accelerator |
| title_full_unstemmed |
Stability of the high-current ion beam in drift gap of linear induction accelerator |
| title_sort |
stability of the high-current ion beam in drift gap of linear induction accelerator |
| publisher |
Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
| publishDate |
2013 |
| topic_facet |
Новые методы ускорения заряженных частиц |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/111935 |
| citation_txt |
Stability of the high-current ion beam in drift gap of linear induction accelerator / V.I. Karas’, O.V. Manuilenko, V.P. Tarakanov, O.V. Fedorovskaya // Вопросы атомной науки и техники. — 2013. — № 4. — С. 64-68. — Бібліогр.: 34 назв. — англ. |
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Вопросы атомной науки и техники |
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| fulltext |
ISSN 1562-6016. ВАНТ. 2013. №4(86) 64
STABILITY OF THE HIGH-CURRENT ION BEAM IN DRIFT GAP
OF LINEAR INDUCTION ACCELERATOR
V.I. Karas’1,3, O.V. Manuilenko1, V.P. Tarakanov2, O.V. Fedorovskaya1
1National Science Center “Kharkov Institute of Physics and Technology”, Kharkov, Ukraine;
2Joint Institute for High Temperature, Moscow, Russia;
3V.N. Karazin Kharkov National University, Kharkov, Ukraine
E-mail: karas@kipt.kharkov.ua
The results of numerical simulation of compensated ion beam (CIB) transport with current density 9 MA/m2
through the drift gap of a linear induction accelerator (LIA) are presented. The CIB stability for the three methods of
compensation in the charge of the ion beam in the absence and presence of an external magnetic field is considered.
It is shown that in the presence of an external magnetic field instabilities development does not lead to a significant
deterioration in the ion beam quality regardless of the compensation way. It is shown, that the most effective addi-
tion compensation of the ion beam in charge is applying of self-consistent injection of additional electrons, which
leads to the conservation of the CIB parameters, sufficient for its use in heavy-ion inertial fusion (HIF).
PACS: 41.75.-i, 52.40.Mj, 52.58.Hm, 52.59.-f, 52.65.Rr
INTRODUCTION
One of the most perspective methods of obtaining
the high-current ion beams for HIF is based on using
LIAs. The method of collective focusing of a high-
current tubular ion beam proposed at the National Sci-
ence Center “Kharkov Institute of Physics and Technol-
ogy” [1 - 3] allows constructing a compact accelerator
that can be used as an efficient driver for HIF and also
as device for other areas of technology applications. The
use of the cusp magnetic field in accelerating gaps of
the linac leads to their effective magnetic insulation
(suppression of electron current, see [1 - 3]) without the
need for an additional central conductor, which greatly
simplifies the linac construction. The advantage of such
a method of magnetic insulation was noted in [4].
The mechanism of space charge neutralization of the
ion beam by an electron beam in the axisymmetric ac-
celerating gap was investigated in [5 - 7].
The possibility of transport and acceleration of a
high-current CIB in 1-6 cusps was demonstrated in [8 -
12] by means of numerical simulation within the frame
of complete set of Vlasov-Maxwell equations with the
help of 2.5-dimensional XOOPIC code [13, 14] that
based on the particle-in-cell (PIC) method.
The quasi-linear stage of the instability of plasma
with an anisotropic electron distribution function was
studied in [15 - 17]. Nonlinear stage of relativistic elec-
tron beams filamentation in dense plasmas was numeri-
cally simulated by the authors of [18 - 24]. It was shown
that, as a rule, the fastest process in the development of
instability was not squeeze of the beam as a whole, but
rather breaking it into thin threads (the first stage), the
scale of which corresponds to the maximum increment
of instability, with following compression of the fila-
ments. In the second stage of instability, the compress-
ing filaments are attracted together and coalesce. Simul-
taneously the transverse temperature increases that ulti-
mately determines the maximum transverse size of the
formed filament.
Filamentation instability of the ion beam in the LIA
with a collective focusing has been studied theoretically
and experimentally in [25 - 30]. It is shown that while
the CIB current density is less than the 10 MA/m2 ion
beam remains uniform and development of filamenta-
tion instability does not manifest itself.
At current densities in LIA [2, 25] higher 10 MA/m2
ion beam becomes filament inhomogeneous as the result
of the filamentation instability nonlinear stage. In [28 -
30, 31] the development of filamentation instability,
both in the absence and in the presence of an external
magnetic field, and particles collisions was studied. It is
shown that filamentation instability can be suppressed
by a strong longitudinal magnetic field in the absence of
collisions between all particles in the LIA. Filamentary
instability increments were obtained in the presence or
in the absence of a magnetic field and collisions be-
tween all particles.
In this paper we numerically studied filamentation
and high-frequency beam instabilities of CIB in the drift
gap, both in the absence and in the presence of an exter-
nal magnetic field. We examine the cases of CIB trans-
port: in the absence of additional electrons, in the pres-
ence of a stationary additional electron injection, in the
presence of a self-consistent additional electron injection
[32]. It is shown that in the absence of an external longi-
tudinal magnetic field the instabilities development pro-
duce a significant degradation of both a compensating
electron beam and a compensated ion beam regardless of
availability of the additional thermal electrons injection in
the drift gap. The presence of an external magnetic field
leads to the improvement of the CIB quality. It is found
that the self-consistent additional thermal electron injec-
tion give the CIB best quality and allows to make effi-
cient transport of CIB through the drift gap at the pres-
ence of the external longitudinal magnetic field.
THE SIMULATION RESULTS
For the numerical study of instabilities it is required
a powerful code which allows to solve such complex
problems. In this section the instabilities are studied
using a 3-dimensional code KARAT. KARAT is fully
electromagnetic code based on PIC method. It designed
for solving of nonstationary electrodynamics problems
with complex geometry and including dynamics, in gen-
eral, relativistic particles (electrons, ions, neutrals) [32].
A real ion linac contains drift gaps with a homogene-
ous external longitudinal magnetic field alternating with
ISSN 1562-6016. ВАНТ. 2013. №4(86)
65
the accelerating gaps, the magnetically insulated accel-
erating gaps being much shorter (by a factor of 10 - 20)
than the drift gaps. Therefore, the study of instabilities
in the drift gap makes sense. Consequently, the most
severe restrictions on parameters of the electron and ion
beams, which ensure the required quality of the ion
beam, are expected to be obtained from study of insta-
bilities in the drift gap.
Fig. 1 shows the geometry of the problem, where z
∈[0, zLD], zLD is the length of the drift gap. In the simu-
lation: zLD = 0.5 m, the transverse dimension of
xL = 0.1 m. In the computational region between
xmin = 0.042 m, xmax = 0.06 m in the initial time are the
electrons with density ne = 1.9·1017 m-3 and the longitu-
dinal speed Ve0 = 0.99 c, where c – speed of light, ions
with density ni = 6.967·1017 m-3 and the longitudinal
velocity Vi0 = 0.27 c, and thermal electrons with number
density nthe = 5.067·1017 m-3 and a temperature of 20 eV.
The conditions ensuring current and charge compensa-
tion were created in the drift gap, i.e., there were not
self-consistent electric and magnetic fields.
During the pulse on the left into the computational
region, that is infinite along the y, electron and ion
beams are continuously injected. The minimum and
maximum dimensions of the beams are same:
xmin = 0.042 m, xmax = 0.06 m, velocities of ion and elec-
tron beams are respectively Vi0 = 0.27 c, Ve0 = 0.99 c,
the current densities at the time of injection are equal,
and their magnitudes 9.02 MA/m2. Densities of electron
and ion beams are ne = 1.9·1017 m-3 and
ni = 6.967·1017 m-3, respectively. And also the injection
of addition electrons with density nthe = 5.067·1017 m-3
and the longitudinal velocity Vthe = 0.004 c can be made.
Fig. 1. Area of electron and ion beams (between xmin
and xmax) injection in the computational region (xL×zLD)
The three cases: 1) the presence of a stationary addi-
tional thermal electron injection, 2) the presence of a
self-consistent additional thermal electron injection,
3) the absence of the additional electron injection into
the system are considered. In all three cases, the trans-
port of the CIB has been studied both in the presence of
the uniform longitudinal external magnetic field
(H0 = 0.23 T), and in the absence of it.
In the presence of stationary additional electron injec-
tion (first case) and external magnetic field the ion beam
quality remains quite high, despite the development of
filamentation and high-frequency instabilities. The CIB
dynamics for this case is detailed in [33]. It is shown
that the development of beam instability of the electron
beam leads to its modulation (focusing and defocusing
regions arise). The arising of transverse magnetic field
By is because of the electron beam filamentation. The
development of these instabilities leads to a significant
deterioration in quality of the electron beam, as in the
absence (perturbation amplitude is high), and in the
presence of an external magnetic field (perturbation
amplitude is low). In the presence of an external mag-
netic field the ion beam is monoenergetic and keeps its
parameters are close to the initial one.
The presence of the self-consistent injection of addi-
tional thermal electrons in the drift gap (second case)
leads to almost complete charge compensation of the
ion beam even after the seven electron beam transit
times through the system. In this case, unlike the sta-
tionary injection (case one), the fresh thermal electrons
practically replace the initially loaded thermal electrons.
The absence of thermal electrons injection, leads
eventually to a higher CIB undercompensation, than in
the cases of injection presence. That results to CIB
transverse broadening and increasing of the energy
spread of the ion beam. It is clearly seen the difference
between the three cases from dependence of the CIB
kinetic energy on the longitudinal coordinate z after one
time of compensating electron beam flight through the
system (Fig. 2). It is seen that in the absence of thermal
electrons injection and magnetic field, CIB slows down
in the beginning, where the thermal electron density is
already small (see Fig. 2,a). The presence of the external
magnetic field prevents losses of the initially loaded
thermal electrons. As the result, the ion beam energy
losses are not so significant (see Fig. 2,b). The presence
of additional electron injection provides the ion beam
compensation, resulting to the absence of “sagging” of
ion energy at the beginning (see Fig. 2,c,d). The pres-
ence of additional electron self-consistent injection re-
duces the energy spread of the CIB (see Fig. 2,e,f).
After seven times of compensating electron beam
flight through the system, at the presence of external
magnetic field (H0 = 0.23 T), in all cases there is a slow-
ing down of the ion beam (Fig. 3). In the case of self-
consistent thermal electrons injection, the slowing down
of the ion beam takes place at the end of the drift gap
(see Fig 3,c). The largest energy dispersion and energy
losses occur in the absence of additional thermal elec-
tron injection (see Fig. 3,a). The presence of additional
electron injection reduces ion beam energy spread, as
self-consistent electric fields decrease (see Fig. 3,b).
The presence of the self-consistent injection of addi-
tional thermal electrons, which completely replace the
initially loaded thermal electrons, preserves the CIB is
practically uniform over the cross section for the dura-
tion of its transport due to the almost complete charge
compensation of the ion beam. In this case, the energy
spread of the ion beam was about ± 1%, and the energy
losses of the beam did not exceed 0.5 MeV at the exit of
accelerator (see Fig. 3,c).
ISSN 1562-6016. ВАНТ. 2013. №4(86) 66
Fig. 2. The dependence of the CIB kinetic energy Wk versus the longitudinal coordinate z:
(a, b) corresponds to the absence of additional electrons, and (c, d) – presence of additional electrons injection,
(e, f) – the presence of a self-consistent injection of additional electrons, the left column corresponds to absence
of magnetic field, the right – to the magnetic field H0 = 0.23 T
Fig. 3. The dependence of the kinetic energy of the CIB
Wk versus the longitudinal coordinate z: (a) corresponds
to the absence of additional electrons,
and (b) – the presence of additional electron injection,
and (c) – the presence of a self-consistent injection
of additional electrons, (a, b, c) corresponds
to the presence of external magnetic field H0 = 0.23 T
Fig. 4 shows the (x,z)-space for the ions in the pre-
sence of self-consistent injection of additional electrons
in the absence of the external magnetic field (see Fig. 4,a)
and in its presence (see Fig. 4,b).
Fig. 4. The dynamics of the ion beam at its transport
through the drift gap after seven electron beam transit-
time of the calculated region in the space (x, z):
(a) corresponds to the absence of an external magnetic
field, (b) – the magnetic field H0 = 0.23 T
It is seen, that the CIB diverges at the edges as a re-
sult of the self-consistent electromagnetic field effect.
On the other hand, the redistribution of the additional
thermal electrons density and the density of the electron
beam leads to the focusing of the ion beam in the ab-
sence of the external magnetic field. In the presence of
the external magnetic field spread of the ion beam is
much smaller, and its distribution over the cross section as
a result of the electromagnetic field influence is more uni-
form.
In Fig. 5 the ion energy distribution function is
shown.
We see that even in the absence of the external mag-
netic field, the ion beam remains almost monoenergetic
(see Fig. 5,a). The presence of the external magnetic
field leads to improving of the ion energy distribution
function quality (see Fig. 5,b).
ISSN 1562-6016. ВАНТ. 2013. №4(86)
67
Fig. 5. Ion distribution function over energy Wki at the
presence of electron self-consistent injection:
a) corresponds to the absence of an external magnetic
field, b) – the magnetic field H0 = 0.23 T
CONCLUSIONS
It is shown, that at the transport of ion beam with
current density of about 9 MA/m2 through drift gap
high-frequency beam and filamentation instabilities
develop. The considered cases are: presence of addi-
tional electron injection, the presence of an additional
electron self-consistent injection, the absence of any
injection. In all three studied cases as filamentation and
high frequency beam instabilities take place. But the
behavior of the particles depending on the injection of
additional thermal electrons is somewhat different.
The self-consistent injection of additional thermal
electrons in the drift gap, in the presence of the external
magnetic field, leads both to CIB monochromaticity,
and reduces the ion beam radius. At the same time, de-
spite the development of instabilities compensating
electron and compensated ion beams keep the current
density closed to the initial one.
In all the cases, in the absence of an external mag-
netic field instabilities development significantly re-
duces the quality of the ion beam. In the presence of an
external longitudinal magnetic field CIB quality remains
acceptable even in the absence of additional thermal
electrons, but the injection of additional electrons con-
siderably improves the parameters of the ion beam.
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УСТОЙЧИВОСТЬ СИЛЬНОТОЧНОГО ИОННОГО ПУЧКА
В ДРЕЙФОВОМ ПРОМЕЖУТКЕ ЛИНЕЙНОГО ИНДУКЦИОННОГО УСКОРИТЕЛЯ
В.И. Карась, О.В. Мануйленко, В.П. Тараканов, О.В. Федоровская
Представлены результаты численного моделирования транспортировки КИП плотностью тока 9 МА/м2
через дрейфовый промежуток линейного индукционного ускорителя. Рассмотрена устойчивость КИП для
трех методов компенсации ионного пучка по заряду в отсутствие и при наличии внешнего магнитного поля.
Показано, что при наличии внешнего магнитного поля развитие неустойчивостей не приводит к существен-
ному ухудшению качества ионного пучка независимо от способа компенсации. Показано, что наиболее эф-
фективной докомпенсацией ионного пучка по заряду является применение самосогласованной инжекции
дополнительных электронов, что приводит к сохранению параметров КИП, достаточных для его использо-
вания в тяжелоионном инерциальном синтезе.
СТІЙКІСТЬ СИЛЬНОСТРУМОВОГО ІОННОГО ПУЧКА В ДРЕЙФОВОМУ ПРОМІЖКУ
ЛІНІЙНОГО ІНДУКЦІЙНОГО ПРИСКОРЮВАЧА
В.І. Карась, О.В. Мануйленко, В.П. Тараканов, О.В. Федорівська
Представлені результати чисельного моделювання транспортування КІП густиною струму 9 МА/м2 через
дрейфовий проміжок лінійного індукційного прискорювача. Розглянута стійкість КІП для трьох методів
компенсації іонного пучка за зарядом при відсутності та наявності зовнішнього магнітного поля. Показано,
що при наявності зовнішнього магнітного поля розвиток нестійкостей не призводе до суттєвого погіршення
якості іонного пучка незалежно від способу компенсації. Показано, що найбільш ефективною докомпенсаці-
єю іонного пучка за зарядом є застосування самоузгодженої інжекції додаткових електронів, що призводить
до збереження параметрів КІП, достатніх для його використання у важкоіонному інерціальному синтезі.
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