Stationary and transient beam dynamics simulation results comparison for travelling wave electron linac with beam loading
The methods of beam dynamic simulation taking into account the beam loading effect are discussed in this paper. It is one of main problems limiting the beam current. The simulation methods for stationary case were described in the paper [1]. The test simulations will discussed for transient mode and...
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| Опубліковано в: : | Вопросы атомной науки и техники |
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Національний науковий центр «Харківський фізико-технічний інститут» НАН України
2012
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| Цитувати: | Stationary and transient beam dynamics simulation results comparison for travelling wave electron linac with beam loading / E.S. Masunov, S.M. Polozov, V.I. Rashchikov, A.V. Voronkov // Вопросы атомной науки и техники. — 2012. — № 4. — С. 96-99. — Бібліогр.: 4 назв. — англ. |
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Masunov, E.S. Polozov, S.M. Rashchikov, V.I. Voronkov, A.V. 2016-11-16T20:56:21Z 2016-11-16T20:56:21Z 2012 Stationary and transient beam dynamics simulation results comparison for travelling wave electron linac with beam loading / E.S. Masunov, S.M. Polozov, V.I. Rashchikov, A.V. Voronkov // Вопросы атомной науки и техники. — 2012. — № 4. — С. 96-99. — Бібліогр.: 4 назв. — англ. 1562-6016 PACS: 29.20.с https://nasplib.isofts.kiev.ua/handle/123456789/108902 The methods of beam dynamic simulation taking into account the beam loading effect are discussed in this paper. It is one of main problems limiting the beam current. The simulation methods for stationary case were described in the paper [1]. The test simulations will discussed for transient mode and stationary case in this paper. The beam dynamics simulation will done using BEAMDULAC-BL and BEAMDULAC-BLNS. These codes were computed to study the beam dynamics in accelerators working on a traveling wave in stationary and transient cases respectively. The results of simulations were compared for both cases. Рассмотрен эффект нагрузки током, являющийся одной из основных проблем, ограничивающих ток пучка. В предыдущих работах были рассмотрены особенности расчета динамики пучка в ускорителях, работающих на бегущей волне с учетом эффектов нагрузки током в стационарном случае. В данной работе сравниваются результаты численного моделирования, произведенные в стационарном и в нестационарном случаях. Произведено моделирование нескольких структур при одинаковых начальных условиях с помощью программ BEAMDULAC-BL и BEAMDULAC-BLNS, позволяющих рассчитывать динамику пучков в ускорителях, работающих на бегущей волне в стационарном и нестационарном случаях соответственно. Розглянуто ефект навантаження струмом, що є однією з основних проблем, що обмежують струм пучка. У попередніх роботах були розглянуті особливості розрахунку динаміки пучка в прискорювачах, що працюють на бігучій хвилі з урахуванням ефектів навантаження струмом у стаціонарному випадку. У цій роботі порівнюються результати чисельного моделювання, вироблені в стаціонарному і в нестаціонарному випадках. Вироблено моделювання декількох структур при однакових початкових умовах за допомогою програм BEAMDULAC-BL і BEAMDULAC-BLNS, що дозволяють розраховувати динаміку пучків у прискорювачах, що працюють на бігучій хвилі в стаціонарному і нестаціонарному випадках відповідно. This work is supported by Federal Program "Scientific and scientific-educational personnel of innovative Russia", contract P571. en Національний науковий центр «Харківський фізико-технічний інститут» НАН України Вопросы атомной науки и техники Динамика пучков Stationary and transient beam dynamics simulation results comparison for travelling wave electron linac with beam loading Сравнение расчетов динамики пучка в ускорителях на бегущей волне с учетом эффектов нагрузки током в нестационарном и стационарном случаях Порівняння розрахунків динаміки пучка у прискорювачі на бігучій хвилі з урахуванням ефектів навантаження струмом у нестаціонарному і стаціонарному випадках Article published earlier |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| title |
Stationary and transient beam dynamics simulation results comparison for travelling wave electron linac with beam loading |
| spellingShingle |
Stationary and transient beam dynamics simulation results comparison for travelling wave electron linac with beam loading Masunov, E.S. Polozov, S.M. Rashchikov, V.I. Voronkov, A.V. Динамика пучков |
| title_short |
Stationary and transient beam dynamics simulation results comparison for travelling wave electron linac with beam loading |
| title_full |
Stationary and transient beam dynamics simulation results comparison for travelling wave electron linac with beam loading |
| title_fullStr |
Stationary and transient beam dynamics simulation results comparison for travelling wave electron linac with beam loading |
| title_full_unstemmed |
Stationary and transient beam dynamics simulation results comparison for travelling wave electron linac with beam loading |
| title_sort |
stationary and transient beam dynamics simulation results comparison for travelling wave electron linac with beam loading |
| author |
Masunov, E.S. Polozov, S.M. Rashchikov, V.I. Voronkov, A.V. |
| author_facet |
Masunov, E.S. Polozov, S.M. Rashchikov, V.I. Voronkov, A.V. |
| topic |
Динамика пучков |
| topic_facet |
Динамика пучков |
| publishDate |
2012 |
| language |
English |
| container_title |
Вопросы атомной науки и техники |
| publisher |
Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
| format |
Article |
| title_alt |
Сравнение расчетов динамики пучка в ускорителях на бегущей волне с учетом эффектов нагрузки током в нестационарном и стационарном случаях Порівняння розрахунків динаміки пучка у прискорювачі на бігучій хвилі з урахуванням ефектів навантаження струмом у нестаціонарному і стаціонарному випадках |
| description |
The methods of beam dynamic simulation taking into account the beam loading effect are discussed in this paper. It is one of main problems limiting the beam current. The simulation methods for stationary case were described in the paper [1]. The test simulations will discussed for transient mode and stationary case in this paper. The beam dynamics simulation will done using BEAMDULAC-BL and BEAMDULAC-BLNS. These codes were computed to study the beam dynamics in accelerators working on a traveling wave in stationary and transient cases respectively. The results of simulations were compared for both cases.
Рассмотрен эффект нагрузки током, являющийся одной из основных проблем, ограничивающих ток пучка. В предыдущих работах были рассмотрены особенности расчета динамики пучка в ускорителях, работающих на бегущей волне с учетом эффектов нагрузки током в стационарном случае. В данной работе сравниваются результаты численного моделирования, произведенные в стационарном и в нестационарном случаях. Произведено моделирование нескольких структур при одинаковых начальных условиях с помощью программ BEAMDULAC-BL и BEAMDULAC-BLNS, позволяющих рассчитывать динамику пучков в ускорителях, работающих на бегущей волне в стационарном и нестационарном случаях соответственно.
Розглянуто ефект навантаження струмом, що є однією з основних проблем, що обмежують струм пучка. У попередніх роботах були розглянуті особливості розрахунку динаміки пучка в прискорювачах, що працюють на бігучій хвилі з урахуванням ефектів навантаження струмом у стаціонарному випадку. У цій роботі порівнюються результати чисельного моделювання, вироблені в стаціонарному і в нестаціонарному випадках. Вироблено моделювання декількох структур при однакових початкових умовах за допомогою програм BEAMDULAC-BL і BEAMDULAC-BLNS, що дозволяють розраховувати динаміку пучків у прискорювачах, що працюють на бігучій хвилі в стаціонарному і нестаціонарному випадках відповідно.
|
| issn |
1562-6016 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/108902 |
| citation_txt |
Stationary and transient beam dynamics simulation results comparison for travelling wave electron linac with beam loading / E.S. Masunov, S.M. Polozov, V.I. Rashchikov, A.V. Voronkov // Вопросы атомной науки и техники. — 2012. — № 4. — С. 96-99. — Бібліогр.: 4 назв. — англ. |
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| fulltext |
ISSN 1562-6016. ВАНТ. 2012. №4(80) 96
STATIONARY AND TRANSIENT BEAM DYNAMICS SIMULATION
RESULTS COMPARISON FOR TRAVELLING WAVE ELECTRON
LINAC WITH BEAM LOADING
E.S. Masunov, S.M. Polozov, V.I. Rashchikov, A.V. Voronkov
National Research Nuclear University “Moscow Engineering Physics Institute”,
Moscow, Russia
E-mail: smpolozov@mephi.ru
The methods of beam dynamic simulation taking into account the beam loading effect are discussed in this pa-
per. It is one of main problems limiting the beam current. The simulation methods for stationary case were described
in the paper [1]. The test simulations will discussed for transient mode and stationary case in this paper. The beam
dynamics simulation will done using BEAMDULAC-BL and BEAMDULAC-BLNS. These codes were computed
to study the beam dynamics in accelerators working on a traveling wave in stationary and transient cases respec-
tively. The results of simulations were compared for both cases.
PACS: 29.20.с
INTRODUCTION
Charged particles linear accelerators are useful in
experimental physics and in some areas of technology at
present. The main advantages of linear accelerators are:
high rate of energy gain, high limit beam intensity, sim-
ple beam extraction.
The beam space charge influence is the main factors
limiting the beam current and accurate treatments of the
beam own space charge field and its influence on the
beam dynamics is one of the main problems in design of
high current RF accelerators. Coulomb field, beam ra-
diation and beam loading effect are the main factors of
the own space charge. Typically, only one of the space
charge field components takes into account for different
types of accelerators. It is the Coulomb field for low
energy linacs and radiation and beam loading for higher
energies. But both factors should be treated in modern
low and high energy high intensity linacs. The mathe-
matical model should be developed for self consistent
beam dynamics study taking into account both Coulomb
field and beam loading influence in stationary case and
transient mode. That is why three-dimensional self-
consistent computer simulation of high current beam is
very actually.
Let us describe the beam loading effect briefly. The
beam dynamics in an accelerator should be studied self-
consistently taking into account both external field and
beam own space charge field. The RF field induced by
the beam in the accelerating structure depends on the
beam velocity as well as the current pulse shape and
duration. The influence of the beam loading can de-
crease the external field amplitude and provide the irra-
diation in the wide eigen frequency modes. Therefore
we should solve the motion equations simultaneously
with Maxwell’s equations for accurate simulation of
beam dynamic.
The method of kinetic equation and the method of
large particles are most useful methods for self-
consistent problem solving. Maxwell’s equation solving
can be replaced by solving of the Poisson equation if we
take into account only Coulomb part of the own beam
field. This equation can be solved by means of the well-
known large particles methods as particle in cell (PIC)
or cloud in cell (CIC). There is no easy method of beam
dynamics simulation that takes into account the beam
loading effect.
The methods of beam dynamic simulations and
three-dimensional code BEAMDULAC-BL were con-
sidered in [1-2]. The BEAMDULAC code is developing
in MEPhI since 1999 [3] for high intensity beam dy-
namics simulation in linear accelerators and transport
channels. The self-consistent beam dynamics can be
studied using BEAMDULAC-BL code version taking
into account the beam loading effect only for linacs,
working on a traveling wave mode in a stationary case.
Similar methods, algorithms and code should be de-
signed to study the beam dynamic taking into account
the beam loading effect for transient mode. The beam
loading for transient mode was early considered by E.S.
Masunov and mail equations were done [4].
The beam dynamics can be calculated for only one
beam part that has the phase length equal to one period
of the external RF field in the stationary case. It is nec-
essary to calculate the dynamics for all beam particles
for the transient case. We must to take into account all
particles of short current pulse which are inside of the
accelerating structure in the time moment. In this case,
the analyzed beam can be represented in 2D or 3D
phase space as a number of the large particles. These
large particles would have the torus form (a ring with
finite-size) with a rectangular cross-section for 2D
simulation due to the axial symmetry of the task. The
parallelepiped form large particles are conveniently use
in 3D case.
Now it would be interesting to compare the simula-
tion results for the stationary case and the transient mode.
Let us consider the algorithm of beam dynamics
simulations taking into account the beam loading effect
in accelerators, working on a traveling wave in the tran-
sient mode.
1. THE EQUATION OF MOTION IN SELF
CONSISTENT FIELD AND SIMULATION
METHODS FOR TRANSIENT MODE
The charge of any large particle is:
Q=Jpulse⋅τpulse/N, (1)
where Jpulse – the pulse beam current, τpulse − the duration
of the current pulse, N – the number of large particles.
The dynamics of every large particle should be
simulated in the external field and in the own space
charge field self-consistently. The initial particles distri-
ISSN 1562-6016. ВАНТ. 2012. №4(80) 97
bution in the start of simulations is given with the help
of especial algorithm in the 2D or 3D phase space. The
initial particles distribution should takes into account
the delay of each particle input into accelerating struc-
ture. Further on, the system will be defined self-
consistently.
The beam which is traveling inside of the resonant
structure decreases the amplitude and changes the phase
of the external RF field. It also excites a number of wake
fields for all resonant eigen frequencies of the structure.
Let we consider for example waveguide section with
βv>βgr>0, where βv and βgr are phase and group velocities
of the wave, respectively. For simplicity we will consider
only one (base) RF field harmonic with ν = 1. The field
acting in the beam cross section with coordinate z differ
on value ),(~),(~~
1 kk zEzEE ττ −=Δ +
+ for the k-th and
(k+1)-th beam bunches, i.e. during the time equals to
pulse length Tb the field is changed to +ΔE~ :
( ) ( )
( ) ( )( ) ( )tI
zzP
TzEzEE
qgrs
bksks
111
1
00 ~
2
~
−−
++
−
=Δ
νν
, (2)
where vq – particles velocity, 0
sE − the amplitude of the
accelerating field in the s-th bandwidth; sP − the power
of the s-th bandwidth, 1
~I − pulse beam current.
In the other hand, if we do not takes into account the
attenuation of RF power in the walls and structure dis-
persion, the field will change at a fixed time t to the
same value +ΔE~ on the length equal to:
b
grq
qgr Tz
νν
νν
−
=Δ . (3)
Indeed, in accordance with ( ) ( ) fbqgr NTzz =−ττ ,
where Nf – number of bunches, which are radiates into
the structure and get part of the own space charge field
in the coordinate z, the own field influence will increase
with a displacement Δz in case when:
( ) ( ) )1( +=Δ+−Δ+ fbqgr NTzzzz ττ . (4)
and equation (3) can be easily rewritten.
Let we introduce the new variable:
( ) ( ) ∑
⎥
⎥
⎦
⎤
⎢
⎢
⎣
⎡
⎟
⎟
⎠
⎞
⎜
⎜
⎝
⎛
−Δ+Δ=−+= j
qgr
jjqgr ztzzt
νν
τττ 11 , (5)
where j is the large particle number. According to the
noted above
1
~~
IRE
sh
gr
gr
ν−ν
νν
−=
τΔ
Δ +
, (6)
where Rsh – series impedance of the structure in the base
band width. When a large number of bunches are con-
sidered and 0→τΔ we will have
1
~~~
IR
z
EE
sh
gr
gr
gr
gr
νν
νν
νν
νν
τ −
−=
∂
∂
−
+
∂
∂ ++
. (7)
It is easy to generalize this equation taking into ac-
count the field attenuation in the structure and the struc-
ture dispersion [4]. It should be remembered that for the
fixed time t and for the length Δz the field value is addi-
tionally reduced by the small amount of
+
⎟⎟
⎠
⎞
⎜⎜
⎝
⎛
Δ
Δ
−− E
z
R
R
sh
sh
~
2
1α . Here α is the RF power attenua-
tion. As the result we will have finally the equation of
beam motion in the point of bunch placement taken into
account the beam loading effect for the transient mode:
( ).,~
~
2
1~~11
1 tzIR
E
dz
dR
Rz
EE
sh
sh
shgr
−=
=⎟⎟
⎠
⎞
⎜⎜
⎝
⎛
−+
∂
∂
+
∂
∂
⎟
⎟
⎠
⎞
⎜
⎜
⎝
⎛
−− +
++
α
τνν (8)
For waveguide system with negative dispersion in
the same way we can obtain:
( ).,~
~
2
1~~11
1 tzIR
E
dz
dR
Rz
EE
sh
sh
shgr
=
=⎟⎟
⎠
⎞
⎜⎜
⎝
⎛
−+
∂
∂
+
∂
∂
⎟
⎟
⎠
⎞
⎜
⎜
⎝
⎛
+− +
++
α
τνν (9)
There are no limitations on the amount of the group
velocity in the derivation of non-stationary equations of
excitation (8), (9). So they will be used just like for
highly dispersed systems and for the weak dispersion of
waveguide systems.
The solution of the equations (8), (9) should be done
with the given initial and boundary conditions. For ex-
ample, if the beam is injected with t=0 into the empty
waveguide with length L, they will have two parts:
( ) 00, ==+ tzE and
( )
( ) ⎪⎭
⎪
⎬
⎫
<==
>==
+
+
.0,0,
,0,0,0
gr
gr
vtLzE
vtzE
(10)
Equation (10) can be generalized to take into ac-
count the reflection at ends of the waveguide. The field
can be considered as the sum of direct +E~ and back-
ward −E~ waves for reflection treatment. The backward
wave does not interact with the beam but is produced by
the reflection from the waveguide end (the wave source
is stationary placed and v=0). Indeed we can to obtain
the motion equation for the regular waveguide:
0~~~1
=α+
∂
∂
−
τ∂
∂
ν
−
−−
E
z
EE
gr
(11)
instead of Eq. (8) The boundary conditions can be writ-
ten as:
( ) ( )LtEГLtE nn ,~~,~
2
+− = , ( ) ( )0,~~,~
11 tEГLtE nn
−+
+ = , (12)
where 1
~Г and 2
~Г are complex reflection coefficients,
and [ ]
cgrtn τ= / – the passes number of the wave front.
In the simplest case, when the waveguide has com-
plete reflection from both ends 1~~
21 ≈≈ ГГ and
0>>> grb VV . The solution to this problem allows us to
formulate the physical limitations of the excitation
equation of a long cavity:
( ) ',0'' ~
2
~~
rr
v
sh
rr I
QL
RJEvi
dt
Ed
ω=ω−ω+− , (13)
( ) ( )
∫
−
=
L
zhhi
v
rr
v dzetzI
L
I rr
0
, ''
,1~ . (13,a)
Let we assume that wave amplitudes +E~ and −E~
have negligible attenuation during the one pass time of
the wave front ( )Lgrτ and after each reflection
−+ = EE ~~ . It is possible in case of low beam loading
effect influence. We can summarize the equation for the
forward and backward waves and do the longitudinal
coordinate z averaging neglecting z∂∂ / derivative
comparatively with tvgr ∂∂− / 1 . Then we can obtain the
equation for −+ += EEE ~~~ :
ISSN 1562-6016. ВАНТ. 2012. №4(80) 98
( ) ztzIR
L
v
JEvE
t
L
sh
gr
gr d,~~
d
d
1
0
0 ∫−=α+ (14)
which has the same form as the equation (7) with
/
rω=ω ,
gr
r
v
Q
α
ω
=
2
/
и
QL
R
Rv shuntr
shgr 2
/ω
= . Here /
rω is
the real part of the complex resonant frequency ω, Q is
the Q-factor and Rshunt is the series impedance for the
base band width and J0 is the average bunch current.
The transient mode field excited by the beam with
fpulse T<τ can be calculated using Eq. (8) and (11) with
the boundary conditions (12). Indeed the transient mode
beam loading problem can be solved for the resonant
system for different matching conditions at the
waveguide section ends and without any limitations to
the beam current value and the group velocity grv .
The time dependence in Eq. (8) disappears for the long
pulse duration fpulse T>τ and we can obtain the equation:
1
~
2
1~
IRE
dz
dR
Rdz
Ed
sh
sh
sh
m=⎟⎟
⎠
⎞
⎜⎜
⎝
⎛
−α+ +
+
. (15)
The field stationary distribution and the current har-
monics magnitudes along of the longitudinal coordinate
z could be calculated using this equation. We can obtain
the well-known waveguide excitation equation when the
value of the series impedance does not depend versus z.
Until now, we consider the excitation equations tak-
ing into account only one (base) spatial field harmonic.
The phase velocity of the base harmonic is close to the
beam velocity. The consideration of other (non-
synchronous) spatial harmonics can be performed for a
periodic structure in a similar way. More general can be
written for polyharmonic case as:
( ) ,~
2
1~~11
)(
2
0
1
)(
)()(
1
1
1
ll
D
l
l
lsh
l
sh
sh
ll
gr
ekzIRE
dz
dR
Rdz
Ed
dt
Ed
−
π∞
=
∑=×
×⎟⎟
⎠
⎞
⎜⎜
⎝
⎛
−α++⎟
⎟
⎠
⎞
⎜
⎜
⎝
⎛
ν
−
ν
−
m
(16)
where )(~ lE is the complex amplitude of the synchro-
nous field harmonic, 1=lk , )( 11
llkl ≠ is the ratio of the
nonsynchronous harmonic amplitude to the synchronous
one )()( /1
1
ll
l EEk = .
Thus the calculation of RF fields excited in the
waveguide systems can be done for not relativistic or
relativistic beams with the long duration of the current
pulse fb TT >> and in transient mode fb TT < also.
Same equations with zero right side (the homogeneous
equation) describe the self-consistent beam dynamics
taken into account external RF field and own space
charge field in the stationary case. The self-consistent
electromagnetic field can be founded from equations
(7)-(9) using correct initial and boundary conditions.
Equations (7)-(9) can be easily rewritten taking into
account all own space charge RF field harmonics.
The algorithm of simulation for the transient mode is
mainly similar to the algorithm developed for the sta-
tionary case [1-2]. The method of Coulomb field treat-
ment used for BAMDULAC-BL and BAMDULAC-
BLNS code was discussed in [3].
2. ELECTRON BEAM DYNAMICS
SIMULATION
The results of beam dynamics simulation were com-
pared with the measurement data obtained for the travel-
ing wave electron linac U-28 of Radiation-Accelerating
Centre of National Research Nuclear University "ME-
PhI". The main U-28 characteristics are given in Table.
Three-dimensional code BEAMDULAC-BL has been
used for beam dynamics simulation in U-28 for station-
ary case and new 3D code BEAMDULAC-BLNS was
used for transient mode. It should be noted, that the
comparison of simulation and measurement can be done
only for beam current I<0.44 A and other results are
interpolation.
Stationary mode Transient mode
Fig.1. Electron beam bunching in U-28 linac
Parameters of U-28 linac
Parameter Value
Average output energy, MeV 10
Range output energy, MeV 2…12
Max pulse beam current, mA 440
Max average beam current, µA 170
Normalized energy spectrum
(∆W/W)min, % 3
Pulse duration, µs 0.5…2.5
Pulse repetition rate, 1/s 400
ISSN 1562-6016. ВАНТ. 2012. №4(80) 99
Beam bunching process simulation results are pre-
sented in Fig.1. It was shown, that beam loading influ-
ence is negligible small for beam with current I≤0.2 A.
The results of numerical simulation are in a good
agreement with experimental one for I<0.44 A. It was
shown that the results of the particle dynamics in sta-
tionary and transient case are in good agreement also.
Fig.2. The current transmission coefficient versus of the
initial pulse beam current for stationary (red lines) and
transient (blue) modes
The current transmission coefficient and the output
beam energy versus of the initial pulse beam current for
stationary and transient modes are shown in Fig.2 and 3
respectively. Some tests of Coulomb field and beam
loading influence were done to define which influence
is more essentially. The simulation was done taking into
account both beam loading and Coulomb field (solid
lines), taking into account only the Coulomb field
(points) and only beam loading (dot lines). It is clear
from figures that the beam loading effect has the more
essential influence to the dynamics for the long structure
as it can be predicted analytically.
Fig.3. The output beam energy versus of the initial pulse
beam current for stationary (red lines) and transient
(blue) modes
CONCLUSIONS
The basic equations of beam motion in waveguide ac-
celerating system were considered taking into account
the beam loading effect. The beam loading can be stud-
ied for stationary beam mode and for transient mode
also. Some results of beam dynamics simulation taking
into account beam loading in both modes were pre-
sented and compared.
This work is supported by Federal Program "Scien-
tific and scientific-educational personnel of innovative
Russia", contract P571.
REFERENCES
1. E.S. Masunov, et al. / Proc. of IPAC’2010, p.1348.
2. E.S. Masunov, et al. / Proc. of HB 2010, p.123.
3. E.S. Masunov, S.M. Polozov // Phys. Rev. ST AB,
2008, 11, 074201.
4. E.S. Masunov // Sov. Phys. Ser. “Tech. Phys”. 1977,
v.47, p.146.
Статья поступила в редакцию 23.09.2011 г.
СРАВНЕНИЕ РАСЧЕТОВ ДИНАМИКИ ПУЧКА В УСКОРИТЕЛЯХ НА БЕГУЩЕЙ ВОЛНЕ
С УЧЕТОМ ЭФФЕКТОВ НАГРУЗКИ ТОКОМ В НЕСТАЦИОНАРНОМ И СТАЦИОНАРНОМ
СЛУЧАЯХ
Э.С. Масунов, С.М. Полозов, В.И. Ращиков, А.В. Воронков
Рассмотрен эффект нагрузки током, являющийся одной из основных проблем, ограничивающих ток пуч-
ка. В предыдущих работах были рассмотрены особенности расчета динамики пучка в ускорителях, рабо-
тающих на бегущей волне с учетом эффектов нагрузки током в стационарном случае. В данной работе срав-
ниваются результаты численного моделирования, произведенные в стационарном и в нестационарном слу-
чаях. Произведено моделирование нескольких структур при одинаковых начальных условиях с помощью
программ BEAMDULAC-BL и BEAMDULAC-BLNS, позволяющих рассчитывать динамику пучков в уско-
рителях, работающих на бегущей волне в стационарном и нестационарном случаях соответственно.
ПОРІВНЯННЯ РОЗРАХУНКІВ ДИНАМІКИ ПУЧКА У ПРИСКОРЮВАЧІ НА БІГУЧІЙ ХВИЛІ
З УРАХУВАННЯМ ЕФЕКТІВ НАВАНТАЖЕННЯ СТРУМОМ У НЕСТАЦІОНАРНОМУ
І СТАЦІОНАРНОМУ ВИПАДКАХ
Е.С. Масунов, С.М. Полозов, В.І. Ращиков, А.В. Воронков
Розглянуто ефект навантаження струмом, що є однією з основних проблем, що обмежують струм пучка.
У попередніх роботах були розглянуті особливості розрахунку динаміки пучка в прискорювачах, що пра-
цюють на бігучій хвилі з урахуванням ефектів навантаження струмом у стаціонарному випадку. У цій роботі
порівнюються результати чисельного моделювання, вироблені в стаціонарному і в нестаціонарному випад-
ках. Вироблено моделювання декількох структур при однакових початкових умовах за допомогою програм
BEAMDULAC-BL і BEAMDULAC-BLNS, що дозволяють розраховувати динаміку пучків у прискорювачах,
що працюють на бігучій хвилі в стаціонарному і нестаціонарному випадках відповідно.
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