Numerical simulation of 3D ion ribbon beam dynamics in RF undulator linac
The ion ribbon beam can be bunched and accelerated in linear accelerator with RF undulator (UNDULAC-RF). The acceleration and focusing of beam are realized without using a synchronous wave in such an accelerator. The results of numerical simulation of 3D self-consistent ribbon ion beam dynamics ar...
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irk-123456789-793702015-04-01T03:02:35Z Numerical simulation of 3D ion ribbon beam dynamics in RF undulator linac Masunov, E.S. Polozov, S.M Динамика пучков The ion ribbon beam can be bunched and accelerated in linear accelerator with RF undulator (UNDULAC-RF). The acceleration and focusing of beam are realized without using a synchronous wave in such an accelerator. The results of numerical simulation of 3D self-consistent ribbon ion beam dynamics are presented. The limit current and current transmission coefficients are calculated. Стрічковий іонний пучок може бути згрупований і прискорений у лінійному високочастотному ондуляторному прискорювачі (UNDULAC-RF). У UNDULAC-RF прискорення і фокусування відбуваються при відсутності в системі синхронної з пучком гармоніки. Було проведено чисельне моделювання самоузгодженої тривимірної динаміки стрічкового іонного пучка в UNDULAC-RF. Визначено граничний струм пучка і максимальний коефіцієнт струмопроходження. Ленточный ионный пучок может быть сгруппирован и ускорен в линейном высокочастотном ондуляторном ускорителе (UNDULAC-RF). В UNDULAC-RF ускорение и фокусировка происходят при отсутствии в системе синхронной с пучком гармоники. Было проведено численное моделирование самосогласованной трехмерной динамики ленточного ионного пучка в UNDULAC-RF. Определен предельный ток пучка и максимальный коэффициент токопрохождения. 2004 Article Numerical simulation of 3D ion ribbon beam dynamics in RF undulator linac / E.S. Masunov, S.M. Polozov // Вопросы атомной науки и техники. — 2004. — № 2. — С. 141-143. — Бібліогр.: 4 назв. — англ. 1562-6016 PACS: 41.75.L, 41.85.E, 29.27.F http://dspace.nbuv.gov.ua/handle/123456789/79370 en Вопросы атомной науки и техники Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
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Динамика пучков Динамика пучков |
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Динамика пучков Динамика пучков Masunov, E.S. Polozov, S.M Numerical simulation of 3D ion ribbon beam dynamics in RF undulator linac Вопросы атомной науки и техники |
| description |
The ion ribbon beam can be bunched and accelerated in linear accelerator with RF undulator (UNDULAC-RF).
The acceleration and focusing of beam are realized without using a synchronous wave in such an accelerator. The
results of numerical simulation of 3D self-consistent ribbon ion beam dynamics are presented. The limit current and
current transmission coefficients are calculated. |
| format |
Article |
| author |
Masunov, E.S. Polozov, S.M |
| author_facet |
Masunov, E.S. Polozov, S.M |
| author_sort |
Masunov, E.S. |
| title |
Numerical simulation of 3D ion ribbon beam dynamics in RF undulator linac |
| title_short |
Numerical simulation of 3D ion ribbon beam dynamics in RF undulator linac |
| title_full |
Numerical simulation of 3D ion ribbon beam dynamics in RF undulator linac |
| title_fullStr |
Numerical simulation of 3D ion ribbon beam dynamics in RF undulator linac |
| title_full_unstemmed |
Numerical simulation of 3D ion ribbon beam dynamics in RF undulator linac |
| title_sort |
numerical simulation of 3d ion ribbon beam dynamics in rf undulator linac |
| publisher |
Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
| publishDate |
2004 |
| topic_facet |
Динамика пучков |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/79370 |
| citation_txt |
Numerical simulation of 3D ion ribbon beam dynamics in RF undulator linac / E.S. Masunov, S.M. Polozov // Вопросы атомной науки и техники. — 2004. — № 2. — С. 141-143. — Бібліогр.: 4 назв. — англ. |
| series |
Вопросы атомной науки и техники |
| work_keys_str_mv |
AT masunoves numericalsimulationof3dionribbonbeamdynamicsinrfundulatorlinac AT polozovsm numericalsimulationof3dionribbonbeamdynamicsinrfundulatorlinac |
| first_indexed |
2025-07-06T03:26:30Z |
| last_indexed |
2025-07-06T03:26:30Z |
| _version_ |
1836866486458646528 |
| fulltext |
NUMERICAL SIMULATION OF 3D ION RIBBON BEAM
DYNAMICS IN RF UNDULATOR LINAC
E.S. Masunov, S.M. Polozov
Moscow Engineering Physics Institute, Russia, masunov@dinus.mephi.ru
The ion ribbon beam can be bunched and accelerated in linear accelerator with RF undulator (UNDULAC-RF).
The acceleration and focusing of beam are realized without using a synchronous wave in such an accelerator. The
results of numerical simulation of 3D self-consistent ribbon ion beam dynamics are presented. The limit current and
current transmission coefficients are calculated.
PACS: 41.75.L, 41.85.E, 29.27.F
1. INTRODUCTION
The ribbon ion beam acceleration is one of possible
methods of beam current increasing. The linac called
Ribbon Radiofrequency Focusing (RRF) accelerator [1]
and some types of linear undulator accelerators [2] were
proposed for this goal. The ribbon ion beam can be ac-
celerated in linear undulator accelerators with electro-
static undulator (UNDULAC-E) [2,3] and radio-fre-
quency undulator (UNDULAC-RF) [4]. The bunching,
acceleration and focusing can be realized in the undula-
tor linac without using the RF field synchronous space
harmonic. The accelerating force is to be driven by a
combination of two non-synchronous waves (two RF
field space harmonics of periodical resonator, Fig.1) in
UNDULAC-RF and by a combination of RF field space
harmonic and space harmonic of electrostatic undulator
field in UNDULAC-E.
2. 3D DYNAMICS FOR UNDULAC-RF
The investigation of beam dynamics in undulator
linacs can be done using both the analytical methods
and the numerical simulation. The results of such inves-
tigations are considered in. [2,3].
Fig. 1. The plane structure of UNDULAC-RF
UNDULAC-RF was studied using analytical averag-
ing methods in. [4]. The Hamiltonian form of the mo-
tion equation was obtained by this method. This equa-
tion includes the effective potential function effU , de-
pending only on the particle phase in the combined
wave field and slowly varying transverse coordinates.
The acceleration, transverse focusing conditions and the
coupling between transverse and longitudinal motions
can be studied using effU . The analytical study was
done in assumption that the beam interacts with only
two space harmonics of RF field. It was shown that the
ribbon ion beams can be accelerated in UNDULAC-RF
using the transverse or longitudinal RF field with 0=µ
and π=µ modes. The rate of energy gain in UNDU-
LAC-RF is proportional to ( )s,vϕ2sin but not ( )s,vϕcos
as in conventional accelerators. This peculiarity pro-
vides formation of two bunches on one RF field period.
The rate of an energy gain in UNDULAC-RF using
π=µ RF field mode is two times higher as for RF field
with 0=µ mode. The analytical study of particles lon-
gitudinal motion shows that the optimal ratio of RF field
harmonics amplitudes 01 E/E=χ is realized in UN-
DULAC-RF. This ratio is equal 0.3-0.4 for UNDULAC-
RF using π=µ mode and 0.6-0.7 for 0=µ mode. The
influence of fast oscillations of RF field is the lowest at
these χ values. The transverse focusing conditions can
be obtained by means of effective potential function. It
was shown that the transverse focusing is realized inde-
pendently of χ value for UNDULAC-RF using π=µ
mode RF field. This result shows an advantage of this
type of undulator linac from RRF accelerator. It should
be noted that ≈χ 10 value is necessary to obtain the ef-
fective focusing in the RRF accelerator [1]. The ampli-
tudes of RF field harmonics must be equal for effective
transverse focusing in UNDULAC-RF using еру 0=µ
mode RF field ( ≈χ 1). However the smaller χ values
can be used in UNDULAC-RF with the 0=µ mode RF
field. The effective potential function has a local maxi-
mum in this case and a cross-section of ion beam will
have a hollow form. The acceptance of UNDULAC
channel and frequencies of phase and transverse oscilla-
tions can be obtained by means of the effective potential
function.
The undulator linac includes two sections for beam
bunching and acceleration. The synchronous phase of
the combined wave s,vϕ will decrease linearly and am-
plitudes of RF field harmonics increases as a sine in the
first part (buncher). In the second part (accelerator) the
amplitudes of harmonics and s,vϕ are constant. It is
shown that the current transmission coefficient Kt for
UNDULAC-RF with π=µ mode RF field is equal to
90...95% and 85...90% for 0=µ mode.
The investigation of beam dynamics in smooth ap-
proximation does not take into account the fast oscilla-
tions of a particle velocity and phase. That is why the
numerical simulation of the beam dynamics in a full
polyharmonic field is necessary to find the optimum ac-
celerator parameters. An influence of a space charge
field on the beam dynamics can also be studied by
means of this model.
___________________________________________________________
PROBLEMS OF ATOMIC SIENCE AND TECHNOLOGY. 2004. № 2.
Series: Nuclear Physics Investigations (43), p.141-143. 141
3. UNDULAC-RF USING LONGITUDINAL
RF FIELD (π MODE)
The numerical simulation was done for ribbon beam
of deuterium ions with the following parameters: initial
velocity of deuterium ions Win=150 keV ( inβ =0.013),
accelerator channel length 2.5 m, accelerator channel
cross-section size 2a×2b=0.8×20 cm, wave length λ
=1.5 m. The effective amplitude of combined wave was
chosen constant and equal 30
2 10
0
=
βπ
λ= EE
W
eEeff
kV/cm and the output beam energy equal to
1.3...1.5 MeV for this amplitude. It should be noted that
for the ion beam under acceleration in smooth approxi-
mated field the current transmission coefficient may be
as high as Кt=90...95% for the beam with the initial size
2l×2t=10×0.4 cm2. The loss of particles takes place due
to not optimum synchronous phase and RF field ampli-
tude functions.
The current transmission coefficient is appreciably
reduced if the beam dynamics simulation is done for the
fast oscillating RF field. The current transmission coef-
ficient is equal to 75...80% for the paraxial injected
beam (2l×2t=1×0.04 cm2) and the optimum value of χ
is 0.3...0.4 (see Fig.2, curve 1) that coincides with the
analytically founded value. This ratio can be easily real-
ized. It was found that Kt significantly decreases if the
beam size is larger than the critical value (along 2l×2t=5
×0.3 cm2). The size of accelerator channel can be re-
duced to 2a×2b=0.7×10 cm. The particle loss is caused
by fast oscillations of particle phases and longitudinal
velocities. The figure 2 (curve 2) shows the current
transmission coefficient versus χ with the initial beam
size equal 2l×2t=5×0.3 cm2. It is clear that Kt does not
exceed 60 % in this case. It can be shown that Kt de-
creases with the large initial RF field amplitude E(z=0):
Kt=50% if E0,1,in=0,2E0,1,max (see Fig.2, curve 3). The op-
timal length of bunching section equals to the accelera-
tor half length.
Fig.2. Current transmission coefficient versus ratio of
RF field space harmonic amplitudes χ
Numerical simulation of beam dynamics in the full
RF field and in the space charge field shows that the
limiting current in UNDULAC-RF is lower than the an-
alytically predicted value and its value is
Imax=0.2...0.25 A (limiting current density
Jmax=0.12 A/cm2) with 2l×2t =5×0.3 cm2.
Fig.3. Initial and output beam cross-section (a), nor-
malized transverse emittance Ey (b), phase (c)
and energy (d) spectra.
(“points” – initial values, “×” – output)
The initial and output beam cross-section (a), nor-
malized transverse emittance ε y (b), phase (c) and ener-
gy (d) spectra are plotted on figure 3. This figure illus-
trates the two bunches formation on one RF field period.
The output normalized emittance is two times lager than
the initial one. The limit initial emittance is equal ε
y=0,7π mm⋅mrad, ε x=30π mm⋅mrad,
ε ϕ=25 keV⋅mrad.
4. UNDULAC-RF USING TRANSVERSE
RF FIELD (π MODE)
The parameters of simulation are the same for UN-
DULAC-RF using transverse and longitudinal RF field
for π=µ mode. In smooth approximation the current
142
transmission coefficient is equal 75...80% for UNDU-
LAC-RF using transverse RF field. It is higher than one
for longitudinal RF field. The optimal RF field harmon-
ics amplitudes ratio is equal 0.35 (see Fig.4, curve 1)
and bunching section length is equal to the half of accel-
erator length too. The limit initial beam size is bigger
than for UNDULAC-RF using longitudinal field: 2l×2t
=7×0,3 cm. The current transmission coefficient is equal
65% (see Fig.4, curve 2) for this initial beam size. The
limit current equals 300...350 mA for this type of undu-
lator linac. In a buncher there are no loses due to a
phase motion and all loses are caused by transverse mo-
tion. The transverse emittance increases 3-4 times and
increases the transverse particles velocity and beam
size. The halo is not forming. The limit initial emittance
ε y is significantly smaller that for UNDULAC-RF us-
ing longitudinal field: ε y=0.06π mm⋅mrad and ε х=45π
mm⋅mrad, ε ϕ=25 keV⋅mrad.
Fig.4. Current transmission coefficient versus ratio
of RF field space harmonic amplitudes χ
5. UNDULAC-RF USING LONGITUDINAL
AND TRANSVERSE RF FIELD (0 MODE)
The numerical simulation of ribbon ion beam dy-
namics in the polyharmonic field of UNDULAC-RF for
0=µ mode RF field shows that the current transmis-
sion coefficient is very low. The simulation in the
smooth approximated field shows that the current trans-
mission coefficient equals 85...90% for the paraxially
injected beam. If the simulation is done a polyharmonic
field, Kt decreases to 55...60% for paraxial injected
beam. For larger beam cross-sections the current trans-
mission coefficient reduces to 30...35% (UDULAC-RF
using longitudinal field) and to 5...10% (using trans-
verse field). These results are in conformity with the an-
alytical investigation which was done earlier [5]. It
should be noted that the transverse focusing is provided
by the first RF field harmonic only for this type of UN-
DULAC-RF. The optimum value of the combined wave
effective amplitude is equal to 20=effE kV/cm and the
output energy equals to 0.9...1.1 MeV. The limiting cur-
rent was not calculated for this type of undulator linac
because the current transmission coefficient is low.
6. CONCLUSIONS
The results of numerical simulation of beam dynam-
ics in the UNDULAC-RF accelerator are discussed. It
was shown that the UNDULAC-RF using π=µ mode
RF field is more preferable for the further design. The
ribbon beam of deuterium ions can be bunched and ac-
celerated to the output energy of 1...1.5 MeV with a lim-
iting current up to 350 mA and the current transmission
coefficient Kt=65% in this type of undulator linac. It is
supposed that the coefficient of current transmission can
be increased by means of numerical optimization of the
synchronous phase function and the RF field harmonic
amplitude variation.
REFERENCES
1. E.S. Masunov, S.M. Polozov, N.E. Vinogradov.
Space charge effects and RF focusing of ribbon
beam in ion linac // Problems of Atomic Science
and Technolog. 2001, № 5, p.71–73.
2. E.S. Masunov // Sov. Phys Tech. Phys. 1990, v.35,
№8, p.962-965.
3. E.S. Masunov, S.M. Polozov, A.S. Roshal,
N.E. Vinogradov // Problems of Atomic Science
and Technology. 2001, № 5, p.51–53.
4. E.S. Masunov // Technical Physics. 2001, v.46,
No.11, p.1433-1436.
ЧИСЛЕННОЕ МОДЕЛИРОВАНИЕ ТРЕХМЕРНОЙ ДИНАМИКИ ЛЕНТОЧНОГО ИОННОГО
ПУЧКА В ЛИНЕЙНОМ ВЫСОКОЧАСТОТНОМ ОНДУЛЯТОРНОМ УСКОРИТЕЛЕ
Э.С. Масунов, С.М. Полозов
Ленточный ионный пучок может быть сгруппирован и ускорен в линейном высокочастотном ондуля-
торном ускорителе (UNDULAC-RF). В UNDULAC-RF ускорение и фокусировка происходят при отсутствии
в системе синхронной с пучком гармоники. Было проведено численное моделирование самосогласованной
трехмерной динамики ленточного ионного пучка в UNDULAC-RF. Определен предельный ток пучка и мак-
симальный коэффициент токопрохождения.
ЧИСЕЛЬНЕ МОДЕЛЮВАННЯ ТРИВИМІРНОЇ ДИНАМІКИ СТРІЧКОВОГО ІОННОГО ПУЧКА
В ЛІНІЙНОМУ ВИСОКОЧАСТОТНОМУ ОНДУЛЯТОРНОМУ ПРИСКОРЮВАЧІ
Е.С. Масунов, С.М. Полозов
Стрічковий іонний пучок може бути згрупований і прискорений у лінійному високочастотному
ондуляторному прискорювачі (UNDULAC-RF). У UNDULAC-RF прискорення і фокусування відбуваються
при відсутності в системі синхронної з пучком гармоніки. Було проведено чисельне моделювання
самоузгодженої тривимірної динаміки стрічкового іонного пучка в UNDULAC-RF. Визначено граничний
струм пучка і максимальний коефіцієнт струмопроходження.
___________________________________________________________
PROBLEMS OF ATOMIC SIENCE AND TECHNOLOGY. 2004. № 2.
Series: Nuclear Physics Investigations (43), p.141-143. 141
пучка в линейном высокочастотнОм ондуляторном ускорителе
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