Code PHASCOL for computation of space charge effects in the cyclotrons and synchrocyclotrons
Development of the code is connected with the project of external injection into the JINR Phasotron. General description of the code PHASCOL intended for particle dynamic calculation that takes into account Coulomb interaction between cycling particles is given. A method of large particles is used i...
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| Опубліковано в: : | Вопросы атомной науки и техники |
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| Дата: | 2001 |
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Національний науковий центр «Харківський фізико-технічний інститут» НАН України
2001
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| Цитувати: | Code PHASCOL for computation of space charge effects in the cyclotrons and synchrocyclotrons / L.M. Onischenko, E.V. Samsonov // Вопросы атомной науки и техники. — 2001. — № 5. — С. 163-165. — Бібліогр.: 5 назв. — англ. |
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Onischenko, L.M. Samsonov, E.V. 2015-03-24T17:16:06Z 2015-03-24T17:16:06Z 2001 Code PHASCOL for computation of space charge effects in the cyclotrons and synchrocyclotrons / L.M. Onischenko, E.V. Samsonov // Вопросы атомной науки и техники. — 2001. — № 5. — С. 163-165. — Бібліогр.: 5 назв. — англ. 1562-6016 PACS numbers: 29.20.Bd, 83.10.Rs https://nasplib.isofts.kiev.ua/handle/123456789/79009 Development of the code is connected with the project of external injection into the JINR Phasotron. General description of the code PHASCOL intended for particle dynamic calculation that takes into account Coulomb interaction between cycling particles is given. A method of large particles is used in the code. Visual graphical possibilities of the Microsoft FPS 4.0 are applied for on-line representations of the main results of computations. Contemporary PC makes it possible to carry out in the course of 24 hrs the calculations of interaction of 2000 particles for 100 turns. Some first results of computation regarding to the JINR Phasotron with energy 680 MeV and four-sector cyclotron-injector with energy 5 MeV and beam currents up to 10 mA are presented. en Національний науковий центр «Харківський фізико-технічний інститут» НАН України Вопросы атомной науки и техники Code PHASCOL for computation of space charge effects in the cyclotrons and synchrocyclotrons Программа PHASCOL для расчета эффектов пространственного заряда в циклотронах и фазотронах Article published earlier |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| title |
Code PHASCOL for computation of space charge effects in the cyclotrons and synchrocyclotrons |
| spellingShingle |
Code PHASCOL for computation of space charge effects in the cyclotrons and synchrocyclotrons Onischenko, L.M. Samsonov, E.V. |
| title_short |
Code PHASCOL for computation of space charge effects in the cyclotrons and synchrocyclotrons |
| title_full |
Code PHASCOL for computation of space charge effects in the cyclotrons and synchrocyclotrons |
| title_fullStr |
Code PHASCOL for computation of space charge effects in the cyclotrons and synchrocyclotrons |
| title_full_unstemmed |
Code PHASCOL for computation of space charge effects in the cyclotrons and synchrocyclotrons |
| title_sort |
code phascol for computation of space charge effects in the cyclotrons and synchrocyclotrons |
| author |
Onischenko, L.M. Samsonov, E.V. |
| author_facet |
Onischenko, L.M. Samsonov, E.V. |
| publishDate |
2001 |
| language |
English |
| container_title |
Вопросы атомной науки и техники |
| publisher |
Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
| format |
Article |
| title_alt |
Программа PHASCOL для расчета эффектов пространственного заряда в циклотронах и фазотронах |
| description |
Development of the code is connected with the project of external injection into the JINR Phasotron. General description of the code PHASCOL intended for particle dynamic calculation that takes into account Coulomb interaction between cycling particles is given. A method of large particles is used in the code. Visual graphical possibilities of the Microsoft FPS 4.0 are applied for on-line representations of the main results of computations. Contemporary PC makes it possible to carry out in the course of 24 hrs the calculations of interaction of 2000 particles for 100 turns. Some first results of computation regarding to the JINR Phasotron with energy 680 MeV and four-sector cyclotron-injector with energy 5 MeV and beam currents up to 10 mA are presented.
|
| issn |
1562-6016 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/79009 |
| citation_txt |
Code PHASCOL for computation of space charge effects in the cyclotrons and synchrocyclotrons / L.M. Onischenko, E.V. Samsonov // Вопросы атомной науки и техники. — 2001. — № 5. — С. 163-165. — Бібліогр.: 5 назв. — англ. |
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2025-11-27T01:19:03Z |
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| fulltext |
CODE PHASCOL FOR COMPUTATION OF SPACE CHARGE EFFECTS
IN THE CYCLOTRONS AND SYNCHROCYCLOTRONS
L.M. Onischenko, E.V. Samsonov
Joint Institute for Nuclear Research (JINR), Dubna, Russia
Development of the code is connected with the project of external injection into the JINR Phasotron. General de-
scription of the code PHASCOL intended for particle dynamic calculation that takes into account Coulomb interac-
tion between cycling particles is given. A method of large particles is used in the code. Visual graphical possibilities
of the Microsoft FPS 4.0 are applied for on-line representations of the main results of computations. Contemporary
PC makes it possible to carry out in the course of 24 hrs the calculations of interaction of 2000 particles for 100
turns. Some first results of computation regarding to the JINR Phasotron with energy 680 MeV and four-sector
cyclotron-injector with energy 5 MeV and beam currents up to 10 mA are presented.
PACS numbers: 29.20.Bd, 83.10.Rs
1 GENERAL DESCRIPTION OF
CODE PHASCOL
The code PHASCOL is intended for a particle dy-
namic computation taking into account the space charge
effects (SCE). For numerical modeling of SCE a beam
is subdivided into a series of bunches. Each bunch con-
tains a set of large particles. To correct calculation of an
electric field inside the bunch the overall charge of par-
ticles corresponds to the beam current that is modeled.
The following full differential equations [1] of particle
motion written in cylindrical coordinate system are used
in PHASCOL:
)]([ 2
2
2
zrzr zrr
c
rBzBr
E
qcrr εεϕεϕεϕ ϕϕ
++−+−+=
)]([ 2
2
zrrz zrr
c
zBrBr
E
qcz εεϕεϕε ϕϕ
++−−+=
)]([2
2
2
zrrz zrr
c
rBzBr
rE
qc
r
r εεϕεϕεϕϕ ϕϕ
++−−++−=
where (r, ϕ, z) – particle coordinates, (Br, Bϕ, Bz), (εr, εϕ,
εz) – components of the magnetic and electric fields,
q - particle charge, с – velocity of light, E – full particle
energy, dot means a differentiation respect to time. The
Runge-Cutter method of 4-th order is used for numerical
integration of the equations. All computations are ful-
filled in double precision mode.
The magnetic field is entered making use the radial
dependencies of Furrier’s harmonics in a median plane
of accelerator. Outside the median plane the magnetic
field components are computed in accordance to the
Maxwell’s equations. A magnetic field created by the
beam current is not considered by the code.
The electric field is represented as a sum of an accel-
eration system field and a proper beam field:
SC
zr
RF
zzr ,,,,, ϕϕϕ εεε += .
The acceleration system field is written as:
∫ +=
t
z
RF
z dttf
0
max
,, ))(2cos( ψπεε ϕϕ ,
where: f(t) – frequency program of the synchrocyclotron
( it is constant for the cyclotron), ψ – particle starting
phase relatively accelerating field. The analytical de-
scription [2] is adopted for calculation of the amplitudes
max
ϕε , max
zε . To compute the proper field of bunch, on
each step of integration the following expressions are
used:
[ ]∑∑
=
=
=
=
−+−=
Nk
k
ikki
Nk
k
iikkii
SC
r dyydxxqi
1
3
1
3
0
/)(sin/)(cos
4
)( ϕϕ
π ε
ε ,
[ ]∑∑
=
=
=
=
−−−=
Nk
k
ikki
Nk
k
iikkii
SC dxxdyyqi
1
3
1
3
0
/)(sin/)(cos
4
)( ϕϕ
π ε
ε ϕ ,
∑
=
=
−=
Nk
k
ikki
SC
z dzzqi
1
3
0
/)(
4
)(
π ε
ε ,
2/1222 ))()()(( kikikiik zzyyxxd −+−+−= ,
where i – the number of particle in the location of which
is calculated electric field, k ≠ i – the numbers of other
particles of the bunch, ikd - distance between i-th and
k–th particles, (x, y, z) - Cartesian coordinates of the
particles, 0ε =8.85⋅10-12 F/m.
If the distance between the particles is less than 0.01
mm, then interaction between them is ignored in order
to avoid noise effects. For the same aim of avoiding
noise effects, the bunch field distribution is recomputed
on each step of integration. Work experience with the
code showed that out of the field of the accelerating sys-
tem the average energy of bunch remains constant with
the accuracy ±10 eV.
On each step of integration a particle gets or loses an
energy in accordance to the sign of the expression:
tzrrqw zr ∆++=∆ )( εεϕε ϕ ,
where ∆t – is time step of integration.
In PHASCOL is a possibility of adding the specific
number of injected bunches, which follow through the
assigned time intervals. This option of the code permits
to model an external injection into JINR Phasotron.
For visual representation of the input data and the
results of computation the graphical possibilities [3] of
the Microsoft FPS 4.0 are applied. These graphs show a
staring and final position of the particles on the trans-
verse and longitudinal phase planes, the radial and axial
particle trajectories on the phase planes as well as
versus time and azimuth angle. A signal of differential
probe located on arbitrary azimuth and having definite
radial size is also computed and shown as a graph
versus radius.
ВОПРОСЫ АТОМНОЙ НАУКИ И ТЕХНИКИ. 2001. №5.
Серия: Ядерно-физические исследования (39), с. 163-165.
163
2 TWO EXAMPLES OF SCE SIMULATION
Computer simulation of the beam dynamics was car-
ried out for the external injection (Fig. 1) into the
Phasotron [4] of the preliminary bunched 5 MeV beam
as well as inside an injector. It was proposed that a 4-
sector cyclotron CI-5 be used as the injector for the
Phasotron. In order to get an average beam current of
about 50 µA in the Phasotron the injected beam must be
of order 10 mA during a capture time duration ∼45 µs.
Fig. 1. Phasotron external injection scheme.
2.1 Simulation of sce in 4 sector cyclotron-injector
Some important parameters of the cyclotron-injector
CI-5 are shown in Table 1.
Table 1.
Type of accelerated particle
Initial energy (MeV)
Final energy (MeV)
Average magnetic field (T)
Betatron frequencies: νr
νz
Radius of injection (cm)
Radius of extraction (cm)
Emittances on injection (π mm⋅mrad)
Phase width of the bunch (°RF)
Orbital frequency (MHz)
Harmonic number
Number of acceleration gaps
Accelerating voltage (kV)
H−
0.5
5.0
0.43
1.1
0.8-0.9
27.0
75.0
50.0
20
6.7965
8
4
115-200
Simulation of particle dynamics was done for a sin-
gle bunch accelerated during 7 turns needed to reach the
final energy 5 MeV. Preliminary a set of particles had
been randomly distributed inside this bunch at starting
position. From 500 to 5000 particles were used in com-
putations. It was observed, if the number of particles
was larger than 2000, then final results (such as emit-
tances or transverse sizes) become fixed. Therefore, to
decrease time consuming, the computations were ful-
filled mainly for 2000 particles.
Figures 2, 3 illustrate the results of computations
done without space charge forces and taking into ac-
count them (I=10 mA) in horizontal and vertical planes.
It is seen the SCE lead to essential increase of the bunch
size in radial and axial dimensions. A free radial zone
between 7-th and 6-th turns required for effective ex-
traction decreases from 25 to 3 mm. At the same time
the SCE induce an enlargement of axial beam size by
approximately two times.
Fig. 2. Comparison of the bunch form during accel-
eration. Complete trajectory of one particle and po-
sition of all particles after each 45° are shown.
Above – no SCE, below – with SCE (10 mA).
Fig. 3. Comparison of particle axial trajectories
during acceleration in CI-5. Above – no SCE, be-
low - SCE (10 mA).
164
2.2 Simulation of sce in the phasotron
It is supposed that the beam delivered from the cy-
clotron after additional bunching and neutralization (H−
→ H0) is injected at the central region of the Phasotron.
Carbon foil will be used in order to get proton beam (H0
→ p). Some parameters of the Phasotron central region
for the scheme of external injection are given in Table
2.
Table 2.
Type of accelerated particle
Initial energy (MeV)
Average magnetic field (T)
Betatron frequencies: νr
νz
Radius of injection (cm)
Phase width of the bunch (°RF)
Harmonic number
Number of acceleration gaps
Accelerating voltage (kV)
p
5.0
1.2
1.01
0.12
27.0
18
1
2
37
There are three important distinctions between the
initial parameters on SCE simulation in CI-5 and Pha-
sotron. First, a longitudinal size of the bunch injected in
the Phasotron is approximately two times greater than
this size at the cyclotron extraction region. Second, a
frequency of axial free oscillations in the central region
of Phasotron (0.12) is appreciably smaller than in the
cyclotron (0.9). Third, an energy gain per turn in the
Phasotron is so small that at least 20 successive bunches
overlap each other at azimuth of injection. So, the accu-
mulation of the space charge of beam occurs in the in-
jection domain. Having in mind last occurrence, 20
bunches were used in computations for accurate simula-
tion of SCE in the Phasotron. The particles were used
with the initial amplitudes of transverse oscillations not
more than 15 mm.
Fig. 4. Comparison of particle axial trajectories
during acceleration in the Phasotron. Above – no
SCE, below – with SCE (10 mA).
The results of computation of the axial particle mo-
tion both without taking into account SCE and consider-
ing SCE for the current 10 mA are compared in Fig. 4.
In these calculations was simulated the sequential injec-
tion of 20 bunches, each of which contained 100 parti-
cles. Then, up to 50 revolutions was calculated the mo-
tion of one bunch, which consists of 2000 particles. It is
evident that the space charge leads to an increase in the
axial size of beam from 28 to approximately 50 mm.
Calculations did not show distinct space-charge ef-
fect on the amplitude of particles radial oscillations. At
the same time, the SCE leads to noticeable changes of
the bunch form and energy spread. Fig. 5 shows as it
changes on the plane an azimuth-radius the form of the
bunch, which consists of 2000 particles, under the ac-
tion of the forces of space charge. It is evident that on
50 turn the deformation of bunch acquires the character-
istic form, which give calculations [5] after 5 turns in
PSI Injector 2.
Fig. 5. Position of particles on the plane azimuth-ra-
dius during 25-th and 50-th turns. To the left –
without taking into account space charge, to the
right -taking into account it.
CONCLUSIONS
Code PASCOL gives important information regard-
ing the beam behaviour influenced by the space charge
forces. No noise effects were detected if number of
large particles was of order several thousands. It is de-
sirable to fulfill analogous calculations by means of oth-
er codes and to compare the obtained results.
REFERENCES
1. V.V.Kolga. Mathematical Simulation on Com-
puters of Dynamic Processes in the Accelerators //
Proc. International School of the Young Scientists,
Minsk, 1979, p. 300, (in Russian).
2. N.Hazewindus et al. The Magnetic Analogue Meth-
od as Used in the Study of a Cyclotron Central Re-
gion // NIM. 1974, v. 118, p. 125.
3. O.V.Bartenev. Visual Fortran, New Possibilities.
Moscow: Dialog-MFEI, 1999, (in Russian).
4. L.M.Onischenko, E.V.Samsonov. External Injec-
tion into JINR Phasotron. Computer Simulation II //
Proc. of International Conference on Cyclotrons
and Their Applications, East Lansing, 2001, P4-04.
5. S.Adam. Space Charge Effects in Cyclotrons-From
ВОПРОСЫ АТОМНОЙ НАУКИ И ТЕХНИКИ. 2001. №5.
Серия: Ядерно-физические исследования (39), с. 165-165.
165
Simulations to Insights // Proc. 14 Int. Cycl. Conf., Cape Town, 1995, p. 446-449.
166
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