Using BEAMDULAC code for multi-beam dynamics investigation in ion linac
The BEAMDULAC code was developed for beam dynamics investigation in RF linacs and transport channels. The beam dynamics can be studied with the accurate treatment of space charge effects by means of this code. In this paper the space charge neutralization of positive and negative charged ions is inv...
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Національний науковий центр «Харківський фізико-технічний інститут» НАН України
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nasplib_isofts_kiev_ua-123456789-1115352025-02-09T15:03:35Z Using BEAMDULAC code for multi-beam dynamics investigation in ion linac Використання програми BEAMDULAC для дослідження динаміки багатокомпонентних іонних пучків Использование программы BEAMDULAC для исследования динамики многокомпонентных ионных пучков Masunov, E.S. Polozov, S.M. Новые методы ускорения, сильноточные пучки The BEAMDULAC code was developed for beam dynamics investigation in RF linacs and transport channels. The beam dynamics can be studied with the accurate treatment of space charge effects by means of this code. In this paper the space charge neutralization of positive and negative charged ions is investigated using the BEAMDULAC code. The progress in code development is discussed. Програма BEAMDULAC розроблена для дослідження динаміки пучків у лінійних високочастотних прискорювачах і каналах транспортування. Моделювання динаміки пучку проводиться з точним обліком впливу власного поля пучку. У даній статті за допомогою програми BEAMDULAC вивчається можливість компенсації впливу просторового заряду позитивно і негативно заряджених іонів. Також розглядаються нові можливості програми. Программа BEAMDULAC разработана для исследования динамики пучков в линейных высокочастотных ускорителях и каналах транспортировки. Моделирование динамики пучка проводится с точным учетом влияния собственного поля пучка. В данной статье с помощью программы BEAMDULAC изучается возможность компенсации влияния пространственного заряда положительно и отрицательно заряженных ионов. Также рассматриваются новые возможности программы. 2008 Article Using BEAMDULAC code for multi-beam dynamics investigation in ion linac / E.S. Masunov, S.M. Polozov // Вопросы атомной науки и техники. — 2008. — № 5. — С. 136-139. — Бібліогр.: 6 назв. — англ. 1562-6016 PACS: 29.17.+w, 29.27.Bd https://nasplib.isofts.kiev.ua/handle/123456789/111535 en Вопросы атомной науки и техники application/pdf Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
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Новые методы ускорения, сильноточные пучки Новые методы ускорения, сильноточные пучки |
| spellingShingle |
Новые методы ускорения, сильноточные пучки Новые методы ускорения, сильноточные пучки Masunov, E.S. Polozov, S.M. Using BEAMDULAC code for multi-beam dynamics investigation in ion linac Вопросы атомной науки и техники |
| description |
The BEAMDULAC code was developed for beam dynamics investigation in RF linacs and transport channels. The beam dynamics can be studied with the accurate treatment of space charge effects by means of this code. In this paper the space charge neutralization of positive and negative charged ions is investigated using the BEAMDULAC code. The progress in code development is discussed. |
| format |
Article |
| author |
Masunov, E.S. Polozov, S.M. |
| author_facet |
Masunov, E.S. Polozov, S.M. |
| author_sort |
Masunov, E.S. |
| title |
Using BEAMDULAC code for multi-beam dynamics investigation in ion linac |
| title_short |
Using BEAMDULAC code for multi-beam dynamics investigation in ion linac |
| title_full |
Using BEAMDULAC code for multi-beam dynamics investigation in ion linac |
| title_fullStr |
Using BEAMDULAC code for multi-beam dynamics investigation in ion linac |
| title_full_unstemmed |
Using BEAMDULAC code for multi-beam dynamics investigation in ion linac |
| title_sort |
using beamdulac code for multi-beam dynamics investigation in ion linac |
| publisher |
Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
| publishDate |
2008 |
| topic_facet |
Новые методы ускорения, сильноточные пучки |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/111535 |
| citation_txt |
Using BEAMDULAC code for multi-beam dynamics investigation in ion linac / E.S. Masunov, S.M. Polozov // Вопросы атомной науки и техники. — 2008. — № 5. — С. 136-139. — Бібліогр.: 6 назв. — англ. |
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Вопросы атомной науки и техники |
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USING BEAMDULAC CODE FOR MULTI-BEAM DYNAMICS
INVESTIGATION IN ION LINAC
E.S. Masunov, S.M. Polozov
Moscow Engineering Physics Institute, Kashirskoe shosse, 31, 115409, Moscow, Russia
E-mail: smpolozov@mephi.ru
The BEAMDULAC code was developed for beam dynamics investigation in RF linacs and transport channels.
The beam dynamics can be studied with the accurate treatment of space charge effects by means of this code. In this
paper the space charge neutralization of positive and negative charged ions is investigated using the BEAMDULAC
code. The progress in code development is discussed.
PACS: 29.17.+w, 29.27.Bd
1. INTRODUCTION
The investigation of a self-consistent beam dynam-
ics in linear RF accelerators and beam transport chan-
nels is one of traditional goals. The influence of the
beam Coulomb field is the main problem for low-energy
high intensity ion accelerators. The accurate calculation
of this field can be made by numerical simulation.
The BEAMDULAC code is developing in Moscow
Engineering Physics Institute by E.S. Masunov,
N.E. Vinogradov and S.M. Polozov since 1999. By
means of this code was early computed the self-consistent
beam dynamics study in the axisymmetric radio frequen-
cy focusing (ARF), the ribbon radio frequency focusing
(RRF) accelerators and the undulator accelerators (UN-
DULAC). 2D and 3D versions were developed for ax-
isymmetric structures and for ribbon beams respectively.
The main features of BEAMDULAC code were briefly
observed bellow.
The linear undulator accelerator (UNDULAC) was
proposed by E.S. Masunov [1, 2] as a possible method of
beam intensity enlarging. This method of acceleration in
fields without a synchronous wave has been suggested
and studied in [1-3]. It was shown that the high intensity
ion beam can be accelerated in UNDULAC [3-4]. The
especial peculiarity of UNDULAC is the possibility of
negative and positive charged ions acceleration in the
same bunch. This peculiarity can provides to the limit
beam current enlarging by the space charge neutralization.
The possibility of the space charge neutralization in
UNDULAC was studied analytically and verified by
numerical simulation [5]. The simulation was provided
using the especially developed code BEAMDULAC-2B
for multi-ion beam dynamics study in linacs.
2. BEAMDULAC CODE
The BEAMDULAC code is developing for self-con-
sistent beam dynamics investigation in RF linacs and
transport channels as it is noted above [4, 6]. The dy-
namics of axi-symmetrical and ribbon ion beams can be
studied by means of this code. The BEAMDULAC code
utilizes the cloud-in-cell (CIC) method for accurate
treatment of the space charge effects that are especially
important in the case of a high-intensity beam. The mo-
tion equation for each particle is solved in the external
fields and the inter-particle Coulomb field simultane-
ously. The charge density is deposited on the grid points
using the CIC technique. To determine the potential of
the Coulomb field, the Poisson equation is solved on the
grid with periodic boundary conditions at both ends of
the domain in the longitudinal direction. The aperture of
the channel is represented as an ideally conducting sur-
face of rectangular or circular cross-section. Therefore
the Dirichlet boundary conditions are applied at trans-
verse boundaries of the simulation domain. In such an
approach, the interaction of the bunch space charge with
the accelerating channel boundaries is taken into ac-
count. This allows consideration of the shielding effect,
which is sufficiently important for transverse focusing
in the narrow channel. The fast Fourier transform (FFT)
algorithm is used to solve the Poisson equation on a 3D
grid. The Fourier series for the space charge potential
obtained can be analytically differentiated, and thus
each component of the Coulomb electrical field can be
found as a series with known coefficients. The Coulomb
repulsion force is the main factor limiting the beam cur-
rent in high-intensity linacs. In our code, the space
charge field can be calculated with the same precision
as the Coulomb potential without numerical differentia-
tion. Time is used as an independent variable and stan-
dard fourth-order Runge-Kutta method is applied for in-
tegration of the motion equation. The external fields in
BEAMDULAC code can be represented three different
methods: analytically, as a series of space harmonics
(the field amplitude is representing as a polynomial co-
efficient series) and in “real field” which is defined on
2D or 3D grid by electrodynamics simulation codes or
experimental measurement [6]. BEAMDULAC code
can be used for the numerical simulation of ion dynam-
ics with different charge to mass ratio in low energy
transport system, RF buncher and linac. The several of
new code versions are discussed bellow in this paper.
3. LINEAR UNDULATOR ACCELERATOR
The linear undulator accelerator was proposed as the
new structure provides to enlarge the intensity of ion
beam. UNDULAC can be realized in periodical IH
structure where a field has no spatial harmonics in
synchronism with the beam. The physical acceleration
mechanism is similar to an inverse free electron laser. In
UNDULAC the accelerating force is driven by a
combination of two non-synchronous waves (two
undulators) in a periodical RF structure. The phase
velocity of undulator wave must differ significantly
from the beam velocity. There are three different types
of undulator that can be used to design the required
configuration of nonsynchronous fields: magnetic,
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PROBLEMS OF ATOMIC SCIENCE AND TECHNOLOGY. 2008. № 5.
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136
electrostatic and RF undulator. It has been shown that
one of the undulator must be only RF type and the
second can be a magnetic, electrostatic (UNDULAC-E)
or radio frequency (UNDULAC-RF) type.
The main factor limiting beam intensity in ion accel-
erator is a space charge force. There exist, at least, two
ways to increase ion beam intensity: (i) to enlarge beam
cross section and (ii) to use space charge neutralization.
One of the possible methods of the beam cross-section
enlarging is the ribbon beam using. It was shown that
the high intensity ribbon ion beams could be accelerated
in UNDULAC-RF and UNDULAC-E. [2-4]. These
methods will be studied analytically and verified by nu-
merical simulation for UNDULAC.
In a conventional RF linac (RFQ, DTL) the opportu-
nity substantially to increase beam intensity is absent.
Actually, in this structure an accelerating force is pro-
portional to the charge sign of the particles, and oppo-
sitely charged ions are bunched in different phases of
the accelerating wave. Two bunches with positive and
negative charges become separated and don’t overlap
each other, excluding the initial bunching subsection. In
this case the beam intensity can be doubled. In undula-
tor linear accelerator the accelerating force value is pro-
portional to squared particle charge and oppositely
charged ions with the identical charge-to-mass ratio can
be accelerated simultaneously within the same bunch
[5]. The space charge compensation can be realized in
UNDULAC along.
4. BEAMDULAC-2B AND SPACE CHARGE
NEUTRALIZATION IN UNDULAC-RF
The positive and negative charged ions can be accel-
erated in the same bunch in UNDULAC as it is shown
above. But beam dynamics study can not be provided
correctly by means of analytical methods only. The space
charge effects can be considered by means of numerical
simulation. The correct treatment of space charge for dual
beam is not easily. The especial code version BAMDU-
LAC-2B was developed for this investigation.
The code modification was provided for the investi-
gation of multi ion beam dynamics in RF accelerator.
The Coulomb field calculation was updated mainly. The
Poisson equation is solving in BEADULAC code by the
conventional FFT algorithm: the particle distribution on
3D grid is calculating on first stage. The Fourier series
coefficients for charge are defining at second and the al-
gebraic equation connecting Fourier coefficients for
charge and potential is solving on grid. The final stage
is the Fourier synthesis for Coulomb potential and its
differentiation for space charge field components defin-
ing. The modification of space charge distribution cal-
culation and algebraic equation for Fourier coefficients
was provided for multi ion beam self-consistent dynam-
ics simulation in especial BEAMDULAC code version.
It should be noted that such BEAMDULAC-2B version
can be used not only for simultaneously positive and
negative ion beam dynamics study. The simulation of
beam dynamics is now possible in case when beam con-
tains the ions with different charge or mass. Such case is
observing in ion source, beam transport and in heavy
ion accelerators also.
The numerical simulation was provided for ribbon
beam of deuterium D- ions in UNDULAC-RF [3-4]. Let
us consider briefly the results of simulation. The simula-
tion was provided with next parameters: initial energy
of deuterium ions Win=100 keV (βin=0.01), length of ac-
celerator channel 2 m, accelerator channel cross-section
size (0.8×12) cm2, length of wave λ =1.5 m. The limit
zero harmonics amplitude of the RF field E0 was chosen
equal 230 kV/cm, coefficient χ=E1/E0 =0.3. In this case
the output beam energy is equal 1 MeV. The numerical
simulation of beam dynamics when a space charge field
is taken into account shows that current transmission co-
efficient, Kt, is not exceeding to 85…90% for beam size
(5×0.3) cm2. The optimal for maximal current transmis-
sion value of χ is equal to 0.3 and coincides with analyt-
ically founded value. In UNDULAC-RF the limit cur-
rent Imax=0.2…0.25 A.
Fig.1. The results of the neutral dual beams dynamics
simulation
Let us represent some results of dual beam dynamics
simulation provided by means of BAMDULAC-2B.
The output normalised transverse emittances in (y,βy)
phase plane are shown at Fig.1,a. The output parameters
of dual beams are shown for D+ by “×” and solid black
line and for D- by points and dot line. The oscillations of
phase mass centre are plotted at Fig.1,b for both particle
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PROBLEMS OF ATOMIC SCIENCE AND TECHNOLOGY. 2008. № 5.
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137
types. Figure also shows the borders of combined wave
separatrix and reference particle phase variation. The
output phase spectra for D+ and D- ions are shown at
Fig.1,c. The beam bunching is illustrated in Fig.2,
which shows the longitudinal beam emittance for diffe-
rent z coordinates. As it was proposed D+ and D- ions
are accelerating in the same bunch in UNDULAC. The
phase trajectories for positive and negative ions are
oscillating in different directions.
Fig.2. The bunching of the neutral dual beams
The numerical simulation shows that the output
beam flux of neutral dual beams in UNDULAC-RF can
be done very large (see Fig.3,a).
Fig.3. The current transmission coefficient (a)
and transverse beam emittance (b) of neutral dual
beams versus the input beam current
The current transmission coefficient is not reduced
with enlarging current for every beam in case when
intensities of ion beams D+ and D- are equal: |I(+)| = |I(-)|. In
this case total Coulomb field compensation is observed.
The nonlinear Coulomb effects cause the decreasing of
current transmission and beam emittance enlarging only
when the current of every beam is larger than 4 A (see
Fig.3,b).
It is interesting to study dynamics of quasi neutral
dual beams when |I(+)| ≠ |I(-)|. The transmission
coefficient for D+ ions, Kt
(+), is larger in case when |I(+)|
< |I(-)|. In dual beams the transmission coefficient for D-,
Kt
(-), is equal approximately to transmission coefficient
for a single ion beam D- with current I=|I(-)|-|I(+)|. The
transmission coefficient increases for D+ and decreases
for D- with |I(-)| / |I(+)| ratio enlarging and Kt
(+)=Kt
(-) when
|I(+)| ≈ |I(-)|. This effect is observing when the both beam
currents are not very large. It should be noted that beam
with smaller current has the smaller output emittance.
5. NEW BEAMDULAC CODE VERSIONS
Let us observed the new versions of BEAMDULAC
code developed last two years.
5.1. NEW BEAMDULAC CODE FOR RF LINACS
Early designed versions of BEAMDULAC code allows
to investigate the beam dynamics in accelerators with
different types of RF focusing (ARF, RRF) and undula-
tor linear accelerators. The new versions were devel-
oped for beam dynamics study in conventional RFQ and
DTL accelerators and structures with independently
phased superconducting resonator and superconducting
solenoids. Such structures are now developing for large
heavy ion accelerator projects as RIA, FZJ etc. The
codes for DTL not utilize the traditional matrix method
for beam dynamics calculation. The motion equation is
integrating step-by-step which provides to correctly
treat the space charge influence to the beam dynamics.
The structure parameters as period length, accelerating
gap length and potentials between the drift tubes are
used as parameters of simulation.
5.2. TRANSPORT CHANNELS
The BEAMDULAC includes codes for beam dy-
namic simulation in transport channels. As an example
BEAMDULAC code is using for beam dynamics study
in the plane electrostatical undulator, which proposed
for ribbon ion beam transport in ITEP-MEPhI common
project of ion implanter. The parameters of undulator
were investigated for boron, phosphorus and other high
intensity beams by using of BEAMDULAC-Tr.
One of problem solved by means of this code is the
study of multi ion beam dynamics in transport line. This
problem arises because the ions with different charge-
to-mass ratio are providing by Bernas ion source uses in
implanter. The ions can be produced in channel also.
The problem of multi ion beam dynamics study was
solved using the BEAMDULAC-2B algorithm.
5.3. CONSTRUCTION ERRORS INFLUENCE
The accelerator channel construction errors can in-
fluence to the beam dynamics. The correct treatment of
this influence is one of difficult problem in accelerator
design. The exhaustive methods are commonly uses for
138
а
б
error treatment. Very extensive statistics and very large
number of calculations are necessary for this.
The different method was proposed for this goal.
The method has two stages. At first, the field
distribution in channel is calculating for all possible
types construction errors. Five-ten calculations are
necessary for each type. The field distributions defining
on channel axis and in 2-4 different lines which are
parallel to the axis. The field on lines distributes by
coefficients of Fourier series. This distribution provides
to find the high order harmonics amplitudes. In real
structure all high order harmonics amplitudes varying
for different construction errors values. But for not
critical errors this variation is close to linear.
Fig.4. The results of construction errors influence study
The tables of Fourier coefficients are used for beam
dynamics study in linac or transport channel. The errors
can be taken into account as a statistical value, which is
not larger, that in coefficients table. The influence of
beam construction errors can be studied by means of
this method and a several calculations are necessary.
An example illustrating this method is presented in
Fig.4. The ribbon beam dynamics of boron ion was
studied in transport channel with the next parameters:
the beam current 1 mA, ion energy 10 keV, the channel
has 25 periods. The output transverse emittance in (β
y, y) and (βx, x) planes and beam cross-section are shown
for “ideal” channel (no constriction errors, left figures)
and with treatment of electrodes shift along longitudinal
axis (right figures). The maximal shift of electrodes is
equal 300 µ in this example. It is clear from figures that
such error can be critical for ion beam transport.
CONCLUSION
The new versions of BEAMDULAC code are
observed. The dynamics of oppositely charged ion beams
was studied in radio frequency undulator linac and the
results of dual beams dynamics simulation are presented.
Such results are studied by means of BEAMDULAC-2B
code, which provides to simulate the multi ion beam
dynamics. It was shown the flux intensity of neutralized
dual beams in UNDULAC-RF can be very large. The
several of new code versions were observed.
REFERENCES
1. E.S. Masunov // Tech. Phys. 1990, v.35, №8, p.962-
965 (in Russian)
2. E.S. Masunov // Tech. Phys. 2001, v.46, №11,
р.1433-1436.
3. E.S. Masunov, S. M. Polozov. Numerical simula-
tion of 3D ion ribbon beam dynamics in RF undu-
lator linac // Problems of Atomic Science and Tech-
nology. Series “Nuclear Physics Investigations”
(43). 2004, №2, p.141-143.
4. E.S. Masunov, S.M. Polozov. BEAMDULAC code
for numerical simulation of 3D beam dynamics in a
high-intensity undulator linac // NIM. 2006, A558,
p.184-187.
5. E.S. Masunov, S.M. Polozov. Space-Charge Neu-
tralization in Ion Undulator Linear Accelerator //
Proc. of PAC’2007.
6. E.S. Masunov, S.M. Polozov. The new versions of
BEAMDULAC code for high intensity ion beam
dynamics investigation // Problems of Atomic Sci-
ence and Technology. Series “Nuclear Physics In-
vestigations” (47). 2006, №3, p.119-121.
Статья поступила в редакцию 07.09.2007 г.
ИСПОЛЬЗОВАНИЕ ПРОГРАММЫ BEAMDULAC ДЛЯ ИССЛЕДОВАНИЯ ДИНАМИКИ
МНОГОКОМПОНЕНТНЫХ ИОННЫХ ПУЧКОВ
Э.С. Масунов, С.М. Полозов
Программа BEAMDULAC разработана для исследования динамики пучков в линейных высокочастотных
ускорителях и каналах транспортировки. Моделирование динамики пучка проводится с точным учетом
влияния собственного поля пучка. В данной статье с помощью программы BEAMDULAC изучается возмож-
ность компенсации влияния пространственного заряда положительно и отрицательно заряженных ионов.
Также рассматриваются новые возможности программы.
ВИКОРИСТАННЯ ПРОГРАМИ BEAMDULAC ДЛЯ ДОСЛІДЖЕННЯ ДИНАМІКИ
БАГАТОКОМПОНЕНТНИХ ІОННИХ ПУЧКІВ
Е.С. Масунов, С.М. Полозов
Програма BEAMDULAC розроблена для дослідження динаміки пучків у лінійних високочастотних
прискорювачах і каналах транспортування. Моделювання динаміки пучку проводиться з точним обліком
впливу власного поля пучку. У даній статті за допомогою програми BEAMDULAC вивчається можливість
компенсації впливу просторового заряду позитивно і негативно заряджених іонів. Також розглядаються нові
можливості програми.
____________________________________________________________
PROBLEMS OF ATOMIC SCIENCE AND TECHNOLOGY. 2008. № 5.
Series: Nuclear Physics Investigations (50), p.136-139.
139
ВИКОРИСТАННЯ ПРОГРАМИ BEAMDULAC ДЛЯ ДОСЛІДЖЕННЯ ДИНАМІКИ БАГАТОКОМПОНЕНТНИХ ІОННИХ ПУЧКІВ
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