New versions of the BEAMDULAC code for high intensity ion beam dynamics investigation
New versions of the BEAMDULAC code are described. Such code can be used for high intensity ion beam dynamics
 investigation in linear accelerators. New abilities of the code are presented and the code testing is observed.
 A code version for beam dynamics investigation in a beam tran...
Saved in:
| Published in: | Вопросы атомной науки и техники |
|---|---|
| Date: | 2006 |
| Main Authors: | , |
| Format: | Article |
| Language: | English |
| Published: |
Національний науковий центр «Харківський фізико-технічний інститут» НАН України
2006
|
| Subjects: | |
| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/79863 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | New versions of the BEAMDULAC code for high intensity ion beam dynamics investigation / E.S. Masunov, S.M. Polozov // Вопросы атомной науки и техники. — 2006. — № 3. — С. 119-121. — Бібліогр.: 5 назв. — англ. |
Institution
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1860000906091692032 |
|---|---|
| author | Masunov, E.S. Polozov, S.M. |
| author_facet | Masunov, E.S. Polozov, S.M. |
| citation_txt | New versions of the BEAMDULAC code for high intensity ion beam dynamics investigation / E.S. Masunov, S.M. Polozov // Вопросы атомной науки и техники. — 2006. — № 3. — С. 119-121. — Бібліогр.: 5 назв. — англ. |
| collection | DSpace DC |
| container_title | Вопросы атомной науки и техники |
| description | New versions of the BEAMDULAC code are described. Such code can be used for high intensity ion beam dynamics
investigation in linear accelerators. New abilities of the code are presented and the code testing is observed.
A code version for beam dynamics investigation in a beam transport channel is also discussed.
Рассматриваются новые варианты программы BEAMDULAC. Эта программа предназначена для изучения динамики сильноточных ионных пуков в линейных ускорителях. Рассматриваются новые возможности программы и результаты тестирования. Также обсуждается вариант программы, предназначенный для исследования динамики пучков в каналах транспортировки.
Розглядаються нові варіанти програми BEAMDULAC. Ця програма призначена для вивчення динаміки
потужнострумових іонних пуків у лінійних прискорювачах. Розглядаються нові можливості програми і
результати тестування. Також обговорюється варіант програми, призначений для дослідження динаміки
пучків у каналах транспортування.
|
| first_indexed | 2025-12-07T16:35:59Z |
| format | Article |
| fulltext |
NEW VERSIONS OF THE BEAMDULAC CODE FOR HIGH INTENSITY
ION BEAM DYNAMICS INVESTIGATION
E.S. Masunov, S.M. Polozov
Moscow Engineering Physics Institute, Moscow, Russia
E-mail: masunov@dinus.mephi.ru, fax / phone: +7(095) 324-2111/324-2995
New versions of the BEAMDULAC code are described. Such code can be used for high intensity ion beam dy-
namics investigation in linear accelerators. New abilities of the code are presented and the code testing is observed.
A code version for beam dynamics investigation in a beam transport channel is also discussed.
PACS: 29.17.+w, 29.27.Bd
1. INTRODUCTION
The correctly investigation of a self-consistent beam
dynamics in linear RF accelerators and beam transport
channels is one of traditional tasks. The influence of the
beam Coulomb field is the main problem for low-energy
high intensity ion accelerators. The accurate calculation
of this field is a problem in beam dynamics. Several
methods of Coulomb field treatment are well known: a
uniformly charged ellipsoid, particle-to-particle meth-
ods and particle-in-cell methods.
A number of codes for beam dynamics study, such
as DYNAMION, TRACE, PARMELA, COBRA and et-
cetera are well known. Each of these codes has own
range of the application, own abilities and drawbacks,
different methods for Poisson and motion equations
solving are used.
The BEAMDULAC code was developed at Moscow
Engineering Physics Institute by E.S. Masunov,
N.E. Vinogradov, and S.M. Polozov in 1999. This code
was early computed for self-consistent beam dynamics
study in an axisymmetric radio frequency focusing
(ARF, [1]), a ribbon radio frequency focusing (RRF,
[2]) accelerators and undulator accelerators (UNDU-
LAC, [3, 4]). 2D and 3D versions were developed for
axisymmetric structures and ribbon beams, respectively.
Let us briefly observe the old versions of the
BEAMDULAC code.
2. BEAMDULAC 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 motion equation for each par-
ticle is solved in the external fields and the inter-particle
Coulomb field. 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 surface of rectangular or circular cross-sec-
tion. Therefore, the Dirichlet boundary conditions are
applied at transverse boundaries of the simulation do-
main. In such an approach, the interaction of the bunch
space charge with the accelerating channel boundaries is
taken into account. This allows consideration of the
shielding effect, which is sufficiently important for
transverse focusing of ribbon beams. 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 differenti-
ated, and thus each component of the Coulomb electri-
cal field can be found as a series with known coeffi-
cients. The Coulomb repulsion force is the main factor
limiting the beam current in high-intensity linacs. In our
code, the space charge field can be calculated with the
same precision as the Coulomb potential without nu-
merical differentiation.
The external fields in the BEAMDULAC code are
represented as a series of space harmonics. The field
amplitude is represented as a polynomial coefficient se-
ries. 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 different version of BEAMDULAC code was
used for beam dynamics investigation in RF accelera-
tors noted above. The especial version was computed
for dynamics study in UNDULAC-E linac in which the
RF and electrostatic fields are used.
3. NEW CODE
The external fields in old version of the BEAMDU-
LAC code are represented analytically as a series of
space harmonics as it was noted above. This disadvan-
tage does not permits to use such code for beam dynam-
ics study in a “real field” which is defined on 2D or 3D
grid by electrodynamics simulation codes or experimen-
tal measurement. The new code versions were designed
for this case.
3.1. 2D GRID
The investigation of beam dynamics in external
fields represented on grid is not an easily task. A correct
multidimensional interpolation is the main problem. The
traditional methods of interpolation as a polynomial or
spline can not be used in this case because the field can
be fast oscillating and have a great number of local ex-
tremums and zeros on a grid.
The code version for 2D grid (BEAMDULAC-G2D)
utilizes the well known “area weighted interpolation”
(Fig.1) method for this goal. Let us recall the main char-
acteristics of this method. For clarity, we will consider
this method with a constant grid step for both r and z di-
rections, namely hz and hr. Let us suppose a particle is
located at a point µ and the field is known in four node
points Ei,j, Ei+1,j, Ei,j+1 and Ei+1,j+1. The grid cell area is
known S= hz⋅hr. The desired point µ puts into rectangu-
lar cell center, which sides are hz and hr. Let us have
____________________________________________________________
PROBLEMS OF ATOMIC SCIENCE AND TECHNOLOGY. 2006. № 3.
Series: Nuclear Physics Investigations (47), p.119-121. 119
mailto:masunov@dinus.mephi.ru
four cells with areas Si,j, Si+1,j, Si,j+1 and Si+1,j+1. Next, the
field Eµ can be calculated by means of the area weighted
method:
∑ ∑
+ +
µ ⋅=
1 1
,,
1 i
i
j
j
jiji SE
S
E . (1)
This method can be easily used with a varying grid step
also.
Fig.1. Area weighted interpolation method
The choosing of extrapolation methods is also im-
portant for the simulation. The traditional Fourier ex-
trapolation technique was used in the BEAMDU-
LAC-G2D code for calculations in a longitudinal direc-
tion. It is possible because the field in accelerators is pe-
riodical. The field is represented as a series of space
harmonics for transverse interpolation. The harmonic
amplitudes can be calculated in this case and the field is
extrapolated by a series of Bessel functions.
3.2. 3D GRID
The “volume weighted interpolation” is used in the
BEAMDULAC-G3D. This method is similar to previ-
ously observed for the 2D case. The external field must
be defined in eight grid points and a grid sell volume V
must be known. The field in a desired point µ is equal
now to:
∑ ∑ ∑
+ + +
µ ⋅=
1 1 1
,,,,
1 i
i
j
j
k
k
kjikji VE
V
E . (2)
The similar extrapolation techniques are used for the
2D and 3D simulation. Fourier extrapolation is used in
the longitudinal direction and the series of space harmon-
ics and hyperbolic sine and cosine for the transverse one.
4. ERRORS OF SIMULATION AND BEAM-
DULAC-GRID TESTING
A high accuracy of simulation was achieved by
means of the area and volume weighting interpolation
methods. An interpolation error in the field calculation
is no more than 0.5% for the 2D case and 2% for the 3D
case. An extrapolation error in the longitudinal direction
is 0.5…2%. In the transverse directions it is 1…3% for
2D dynamics and 1…5% for 3D.
The results of beam dynamics simulation in the RF
field defined on a grid was compared with the results
obtained for the analytically defined field. The compari-
son was provided for the ARF, RRF and UNDULAC
linacs. Some results of ion beam dynamics simulation
with the analytically defined and “real field” are shown
in Fig.2,3. The longitudinal and transverse emittances
are plotted for the ARF structure (2D beam dynamics)
in Fig.2. The output longitudinal and input (“×”-s) and
output (“points”) transverse emittances were calculated
for an ion with a charge-to-mass ratio A/Z=1/60 in the
analytically defined field (Fig.2,a and 2,c respectively)
and in the “real field” (Fig.2,b and 2,d). It is clear from
the figure that the simulation results are similar and sim-
ulation on a grid was performed with the high accuracy.
Fig.2. 2D beam dynamics simulation results
The input and output transverse emittances of a deu-
terium ion beam are shown in Fig.3. The beam dynam-
ics was calculated for the UNDULAC-RF accelerator
120
(3D dynamics). The beam has a small halo if the beam
dynamics was calculated in the “real field” (see
Fig.3,b). It is come through the extrapolation error.
Fig.3. 3D beam dynamics simulation results
5. BEAMDULAC-T FOR BEAM TRANSPORT
CHANNELS
The transport of low energy ion beams from a source
to an accelerator or target is very difficult. The choice of
an effective beam transport system design depends on
the main beam parameters, such as initial transverse
emittance, ion energy, charge to mass ratio, beam cur-
rent. The transport design of high intensity low energy
(W=0.1...1 keV/u) ion beams for A/Z=1/10...1/120 is
very complicated. Generally, systems of magnetic or
electrostatic lenses are used for the axisymmetrical
beam focusing. For transport of intensive ribbon ion
beams a special beam line is needed. The periodic sys-
tem of electrostatical lenses (electrostatic undulator)
was suggested for this goal [5]. The version of the
BEAMDULAC code was developed for beam dynamics
study in electrostatic transport channels.
It was shown using the BEAMDULAC-T code that
the heavy ion low energy beams could be transported at
a distance of several meters by the electrostatic undula-
tor. The beam quality does not degrade.
6. CONCLUSION
The new BEADULAC code versions are observed.
The codes are computed for beam dynamics investiga-
tion in RF field defined on 2D and 3D grid. It was
shown that these new code versions are effective for ion
beam dynamics study in RF linacs and transport chan-
nels. The simulation methods allow having the high ac-
curacy of calculation. In future, a code will be devel-
oped for beam dynamics study in crossed electric and
magnetic field. Versions for the RFQ and multi-ion
beams are in future plans as well.
The work was supported by RFBR: Grant
04-02-16667.
REFERENCES
1. E.S. Masunov, N.E. Vinogradov // Phys. Rev. ST
Accel. Beams, 2001, №7, 070101.
2. 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 Technology. Series: Nuclear Physics Investiga-
tions. 2001, №5(39), p.71-73.
3. E.S. Masunov, S.M. Polozov, A.S. Roshal. Undula-
tor linear accelerator as a generator of ribbon high
power ion beams // Radiation Physics and Chem-
istry, 2001, v.61, р.491-493.
4. E.S. Masunov, S.M. Polozov. Numerical simulation
of 3D ion ribbon beam dynamics in RF undulator
linac // Problems of Atomic Science and Technolo-
gy. Series: Nuclear Physics Investigations. 2004,
№2(43), p.141-143.
5. E.S. Masunov, S.M. Polozov. Low energy beam
transport for heavy ions in electrostatic undulator.
Proc. of RuPAC 2004, p.225-227.
НОВЫЕ ВАРИАНТЫ ПРОГРАММЫ BEAMDULAC ДЛЯ ИЗУЧЕНИЯ ДИНАМИКИ
ИНТЕНСИВНЫХ ИОННЫХ ПУЧКОВ
Э.С. Масунов, С.М. Полозов
Рассматриваются новые варианты программы BEAMDULAC. Эта программа предназначена для изуче-
ния динамики сильноточных ионных пуков в линейных ускорителях. Рассматриваются новые возможности
программы и результаты тестирования. Также обсуждается вариант программы, предназначенный для ис-
следования динамики пучков в каналах транспортировки.
НОВІ ВАРІАНТИ ПРОГРАМИ BEAMDULAC ДЛЯ ВИВЧЕННЯ ДИНАМІКИ ІНТЕНСИВНИХ
ІОННИХ ПУЧКІВ
Е.С. Масунов, С.М. Полозов
Розглядаються нові варіанти програми BEAMDULAC. Ця програма призначена для вивчення динаміки
потужнострумових іонних пуків у лінійних прискорювачах. Розглядаються нові можливості програми і
результати тестування. Також обговорюється варіант програми, призначений для дослідження динаміки
пучків у каналах транспортування.
____________________________________________________________
PROBLEMS OF ATOMIC SCIENCE AND TECHNOLOGY. 2006. № 3.
Series: Nuclear Physics Investigations (47), p.119-121. 121
2. BEAMDULAC code
|
| id | nasplib_isofts_kiev_ua-123456789-79863 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1562-6016 |
| language | English |
| last_indexed | 2025-12-07T16:35:59Z |
| publishDate | 2006 |
| publisher | Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
| record_format | dspace |
| spelling | Masunov, E.S. Polozov, S.M. 2015-04-05T16:12:23Z 2015-04-05T16:12:23Z 2006 New versions of the BEAMDULAC code for high intensity ion beam dynamics investigation / E.S. Masunov, S.M. Polozov // Вопросы атомной науки и техники. — 2006. — № 3. — С. 119-121. — Бібліогр.: 5 назв. — англ. 1562-6016 PACS: 29.17.+w, 29.27.Bd https://nasplib.isofts.kiev.ua/handle/123456789/79863 New versions of the BEAMDULAC code are described. Such code can be used for high intensity ion beam dynamics
 investigation in linear accelerators. New abilities of the code are presented and the code testing is observed.
 A code version for beam dynamics investigation in a beam transport channel is also discussed. Рассматриваются новые варианты программы BEAMDULAC. Эта программа предназначена для изучения динамики сильноточных ионных пуков в линейных ускорителях. Рассматриваются новые возможности программы и результаты тестирования. Также обсуждается вариант программы, предназначенный для исследования динамики пучков в каналах транспортировки. Розглядаються нові варіанти програми BEAMDULAC. Ця програма призначена для вивчення динаміки
 потужнострумових іонних пуків у лінійних прискорювачах. Розглядаються нові можливості програми і
 результати тестування. Також обговорюється варіант програми, призначений для дослідження динаміки
 пучків у каналах транспортування. The work was supported by RFBR: Grant
 04-02-16667. en Національний науковий центр «Харківський фізико-технічний інститут» НАН України Вопросы атомной науки и техники Ускорители заряженных частиц New versions of the BEAMDULAC code for high intensity ion beam dynamics investigation Новые варианты программы BEAMDULAC для изучения динамики интенсивных ионных пучков Нові варіанти програми BEAMDULAC для вивчення динаміки інтенсивних іонних пучків Article published earlier |
| spellingShingle | New versions of the BEAMDULAC code for high intensity ion beam dynamics investigation Masunov, E.S. Polozov, S.M. Ускорители заряженных частиц |
| title | New versions of the BEAMDULAC code for high intensity ion beam dynamics investigation |
| title_alt | Новые варианты программы BEAMDULAC для изучения динамики интенсивных ионных пучков Нові варіанти програми BEAMDULAC для вивчення динаміки інтенсивних іонних пучків |
| title_full | New versions of the BEAMDULAC code for high intensity ion beam dynamics investigation |
| title_fullStr | New versions of the BEAMDULAC code for high intensity ion beam dynamics investigation |
| title_full_unstemmed | New versions of the BEAMDULAC code for high intensity ion beam dynamics investigation |
| title_short | New versions of the BEAMDULAC code for high intensity ion beam dynamics investigation |
| title_sort | new versions of the beamdulac code for high intensity ion beam dynamics investigation |
| topic | Ускорители заряженных частиц |
| topic_facet | Ускорители заряженных частиц |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/79863 |
| work_keys_str_mv | AT masunoves newversionsofthebeamdulaccodeforhighintensityionbeamdynamicsinvestigation AT polozovsm newversionsofthebeamdulaccodeforhighintensityionbeamdynamicsinvestigation AT masunoves novyevariantyprogrammybeamdulacdlâizučeniâdinamikiintensivnyhionnyhpučkov AT polozovsm novyevariantyprogrammybeamdulacdlâizučeniâdinamikiintensivnyhionnyhpučkov AT masunoves novívaríantiprogramibeamdulacdlâvivčennâdinamíkiíntensivnihíonnihpučkív AT polozovsm novívaríantiprogramibeamdulacdlâvivčennâdinamíkiíntensivnihíonnihpučkív |