On transversal instability of beam in powerful S-band linear electron accelerators
High pulse current of electrons in a linear resonance accelerator assists the increase of overall efficiency of the facility. At the same time, there is a danger of development of transversal instability of a beam (BBU), especially in linacs consisting of a few accelerating sections. In the paper...
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| Zitieren: | On transversal instability of beam in powerful S-band linear electron accelerators / M.I. Aizatsky, E.U. Kramarenko, I.V. Khodak, V.A. Kushnir, V.V. Mytrochenko, S.A. Perezhogin // Вопросы атомной науки и техники. — 2006. — № 2. — С. 131-133. — Бібліогр.: 4 назв. — англ. |
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Aizatsky, M.I. Kramarenko, E.U. Khodak, I.V. Kushnir, V.A. Mytrochenko, V.V. Perezhogin, S.A. 2015-03-22T09:12:58Z 2015-03-22T09:12:58Z 2006 On transversal instability of beam in powerful S-band linear electron accelerators / M.I. Aizatsky, E.U. Kramarenko, I.V. Khodak, V.A. Kushnir, V.V. Mytrochenko, S.A. Perezhogin // Вопросы атомной науки и техники. — 2006. — № 2. — С. 131-133. — Бібліогр.: 4 назв. — англ. 1562-6016 PACS: 41.20.Jb, 41.75.Fr https://nasplib.isofts.kiev.ua/handle/123456789/78876 High pulse current of electrons in a linear resonance accelerator assists the increase of overall efficiency of the facility. At the same time, there is a danger of development of transversal instability of a beam (BBU), especially in linacs consisting of a few accelerating sections. In the paper the method of calculation of starting current of regenerative BBU instability in the tapered disc loaded waveguides is presented as well as simulation results of BBU buildup in the linac consisting of a few accelerating sections. Приведены методика расчета порогового тока регенеративной поперечной неустойчивости в неоднородных цилиндрических диафрагмированных волноводах и результаты моделирования развития поперечной неустойчивости в ускорителе, состоящем из нескольких ускоряющих секций. Приведено методику розрахунку стартового струму регенеративної поперечної нестійкості в неоднорідних циліндричних діафрагмованих хвилеводах та результати моделювання розвитку поперечної нестійкості в прискорювачі, що складається з декількох прискорювальних секцій. The work was partially supported through the STCU grant #3151. en Національний науковий центр «Харківський фізико-технічний інститут» НАН України Вопросы атомной науки и техники Линейные ускорители заряженных частиц On transversal instability of beam in powerful S-band linear electron accelerators Моделирование поперечной неустойчивости пучка в мощных линейных ускорителях электронов Моделювання поперечної нестійкості пучка в потужних лінійних прискорювачах електронів Article published earlier |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| title |
On transversal instability of beam in powerful S-band linear electron accelerators |
| spellingShingle |
On transversal instability of beam in powerful S-band linear electron accelerators Aizatsky, M.I. Kramarenko, E.U. Khodak, I.V. Kushnir, V.A. Mytrochenko, V.V. Perezhogin, S.A. Линейные ускорители заряженных частиц |
| title_short |
On transversal instability of beam in powerful S-band linear electron accelerators |
| title_full |
On transversal instability of beam in powerful S-band linear electron accelerators |
| title_fullStr |
On transversal instability of beam in powerful S-band linear electron accelerators |
| title_full_unstemmed |
On transversal instability of beam in powerful S-band linear electron accelerators |
| title_sort |
on transversal instability of beam in powerful s-band linear electron accelerators |
| author |
Aizatsky, M.I. Kramarenko, E.U. Khodak, I.V. Kushnir, V.A. Mytrochenko, V.V. Perezhogin, S.A. |
| author_facet |
Aizatsky, M.I. Kramarenko, E.U. Khodak, I.V. Kushnir, V.A. Mytrochenko, V.V. Perezhogin, S.A. |
| topic |
Линейные ускорители заряженных частиц |
| topic_facet |
Линейные ускорители заряженных частиц |
| publishDate |
2006 |
| language |
English |
| container_title |
Вопросы атомной науки и техники |
| publisher |
Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
| format |
Article |
| title_alt |
Моделирование поперечной неустойчивости пучка в мощных линейных ускорителях электронов Моделювання поперечної нестійкості пучка в потужних лінійних прискорювачах електронів |
| description |
High pulse current of electrons in a linear resonance accelerator assists the increase of overall efficiency of the
facility. At the same time, there is a danger of development of transversal instability of a beam (BBU), especially in
linacs consisting of a few accelerating sections. In the paper the method of calculation of starting current of regenerative
BBU instability in the tapered disc loaded waveguides is presented as well as simulation results of BBU buildup
in the linac consisting of a few accelerating sections.
Приведены методика расчета порогового тока регенеративной поперечной неустойчивости в неоднородных цилиндрических диафрагмированных волноводах и результаты моделирования развития поперечной неустойчивости в ускорителе, состоящем из нескольких ускоряющих секций.
Приведено методику розрахунку стартового струму регенеративної поперечної нестійкості в
неоднорідних циліндричних діафрагмованих хвилеводах та результати моделювання розвитку поперечної
нестійкості в прискорювачі, що складається з декількох прискорювальних секцій.
|
| issn |
1562-6016 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/78876 |
| citation_txt |
On transversal instability of beam in powerful S-band linear electron accelerators / M.I. Aizatsky, E.U. Kramarenko, I.V. Khodak, V.A. Kushnir, V.V. Mytrochenko, S.A. Perezhogin // Вопросы атомной науки и техники. — 2006. — № 2. — С. 131-133. — Бібліогр.: 4 назв. — англ. |
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| first_indexed |
2025-11-24T19:48:20Z |
| last_indexed |
2025-11-24T19:48:20Z |
| _version_ |
1850494675272597504 |
| fulltext |
ON TRANSVERSAL INSTABILITY OF BEAM IN POWERFUL
S-BAND LINEAR ELECTRON ACCELERATORS
M.I. Aizatsky, E.U. Kramarenko, I.V. Khodak, V.A. Kushnir, V.V. Mytrochenko,
S.A. Perezhogin
NSC KIPT, Kharkov, Ukraine
E-mail: ayzatsky@kipt.kharkov.ua
High pulse current of electrons in a linear resonance accelerator assists the increase of overall efficiency of the
facility. At the same time, there is a danger of development of transversal instability of a beam (BBU), especially in
linacs consisting of a few accelerating sections. In the paper the method of calculation of starting current of regener-
ative BBU instability in the tapered disc loaded waveguides is presented as well as simulation results of BBU build-
up in the linac consisting of a few accelerating sections.
PACS: 41.20.Jb, 41.75.Fr
1. INTRODUCTION
Phenomena of beam pulse shortening occurring in
power linear electron accelerators (linacs) were discov-
ered in the middle of the past century [1]. Some late
analogous phenomena came out during commissioning
of multi-sectional high-energy linacs [1,2]. Extensive
researches on the problem have shown that such effect
is caused by beam-excited waves (mostly E11 like wave)
propagated in the higher pass bands of the disk-loaded
waveguide (DLW). At some condition interaction be-
tween beam and waves causes exponential growth of
transversal oscillations of the particles until they hit into
the linac walls. Occurrence of such phenomenon in
linacs consisting of just one accelerating section is
called as regenerative BBU in contradistinction to cu-
mulative BBU that is characteristic for multisectional
linacs. Although BBU has rather long history of study
there is no cardinal solution for its complete suppression
till now.
Usage of the tapered DLWs is the one method for
diminishing of starting current of regenerative BBU in-
stability. In such waveguides besides providing the syn-
chronism between the particles and wave propagating in
the fundamental pass band, a region where particles can
interact effectively with waves in the higher pass bands
is well shorter than waveguide length. Owing this fact,
for example, the starting current of regenerative BBU
instability in the piece-wise homogeneous section
“Kharkov-85” is more than tenfold higher than that in
the homogeneous section “Kharkov-65” [2]. Accelerat-
ing sections of the KUT type [3,4] are steeply tapered
1.24 m long DLWs with 2π/3 mode of oscillation and
relative phase velocity 1phβ = . They have high effi-
ciency (more than 80% at current accelerated of 1 A)
During operation of linacs consisting one or two such
sections at current accelerated more than 1 A there was
no beam pulse shortening observed. We plan to upgrade
the power linac for industrial purposes [4] to provide
higher beam energy at beam current about 1 A by in-
stalling the third accelerating section. Because absence
of pulse shortening does not mean that the BBU insta-
bility does not develop, we anticipate appreciable influ-
ence of possible BBU instability developing in the
three-section linac on beam transversal characteristics.
It forced us to start developing a new computer code to
simulate the process of 11E wave excitation in DLW
during acceleration of electron beam with pulse length τ
of several microseconds.
There are the two main questions needed to be an-
swered at BBU instability studding. Firstly, it is neces-
sary to estimate the starting current value of regenera-
tive BBU instability1. Secondly, conditions of cumula-
tive BBU instability arising in the multisectional linac
need to be studied.
This work is dedicated to description of the mathe-
matical model that the code developed is based. Results
of preliminary study of BBU instability development in
the three-sectional linac with the pilot version of the
code also are presented.
2. MATHEMATICAL MODEL
The code under development is based on the mathe-
matical model that represents a DLW as a chain of cou-
pled resonators. The model has the following substan-
tially new feature. Motion of particles in the self-consis-
tent field of the chain in the fundamental pass-band that
is excited both by particles and external RF source tak-
ing into account input and output couplers and their
transversal motion in the self-consistent field in the
higher pass-band that corresponds to the E110 oscillations
of the single cell of the chain are simulated simultane-
ously. We do know about existent of similar developed
codes that realized such possibilities.
The mathematical model of such combined excita-
tion is based on the two sets of coupled equations. The
sets have the similar structure but their physical mean-
ing is substantially different. Because DLW is presented
as the chain of coupled resonators, electromagnetic field
in each cell of the chain can be written in the form of
1, ,010 2, ,110( ) ( ) ( ) ( )n n n n nE t E r t E r= +
r r r
E E ,
1, ,010 2, ,110( ) ( ) ( ) ( )n n n n nH t H r t H r= +
r r r
n nH H .
The time dependent functions obey the following
systems of coupled equations:
1 In general, operating current of a linac should be
less than the BBU instability starting current.
__________________________________________________________
PROBLEMS OF ATOMIC SCIENCE AND TECHNOLOGY. 2006. № 2.
Series: Nuclear Physics Investigations (46), p.131-133. 131
mailto:ayzatsky@kipt.kharkov.ua
( )
2
1, 1, ,0 1, 2
1, 1,2
1,
2 (1) (1)
1, ,0 , 1 1, 1 , 1 1, 1
, ,010
1,
1
n
n n n
n n
n
n n n n n n n
z z n
n V
d d
Q d td t
d j E dV
N d t
ω
ω
ω µ µ+ + − −
+ + =
= + −
− т
n n
n
n n
E E
E
E E
( )
2
2, 2, ,0 2, 2
2, 2,2
2,
2 (2) (2)
2, ,0 , 1 2, 1 , 1 2, 1
2,
, ,110
2, n
n n n
n n
n
n n n n n n n
n
z z n
n V
d d
Q d td t
j E dV
N
ω
ω
ω µ µ
ω
+ + − −
+ + =
= + +
+ т
n n
n
n n
H H
H
H H
where , , 0i nω and ,i nω are the eigen frequencies of sepa-
rated cell without and with taking into account influence
of coupling holes, correspondently. These systems have
to be combined with the equations that connect the cur-
rent zj with the excited fields.
During interaction of a beam consisting of a long
bunch train with DLW, the dominant role will be played
by storage processes of field excitation by numbers of
particles at time range that is long as compare with os-
cillation periods. Therefore, it is possible to assume that
maximal spectral components of excited electromagnet-
ic oscillations will be localized mostly around the linac
operating frequency and in the higher pass-bands of
DLW. The spectral components of heterodyne frequen-
cies will be negligible excluding particular cases, which
are rarely realized in practice. Then, time dependence of
excited fields can be presented as the product of the
slow amplitudes and the fast oscillating exponents.
However, a methodological problem concerned with the
fact that frequencies of E010 and E110 oscillations are not
multiple each other is aroused during the simultaneous
simulation both beam acceleration described by the first
set of equations (0.1) and BBU instability excitation de-
scribed by the second set of equations (0.2). This prob-
lem even at slow amplitude varying of both oscillations
does not allow us to use efficient method of fast oscilla-
tion averaging both for substantial simplification of
equations and for computational resource decrease. We
use the method of fast oscillation averaging to find solu-
tion of (0.1). To obtain solution of the second set of
equations (0.2) we used another method based on more
detailed time consideration. The last one uses the two
assumptions. First one is about slow varying amplitudes
of E110 oscillations during particles pass through the in-
teraction region and second one is about independence
of longitudinal motion from transversal motion while
detailed time dependent characteristics of longitudinal
particle motions (energy and position) are used at simu-
lation of transversal dynamics, which is defined by E110
oscillations.
3. SIMULATION RESULTS
On a basis of the above-mentioned mathematical
model we have developed the computer code that allows
us to carry out numerical simulations simultaneously
both self-consisted transient process of particle accelera-
tion and self-consisted transient beam dynamics in the
transversal plane that defined by the Е110 oscillations.
The code developed takes into account the fine beam
structure, particularly: bunch shape, energy distribution
of particles and their change with time, etcetera. Simula-
tion of beam dynamics can be carried out for arbitrary
number of accelerating sections.
We also developed the auxiliary technique to ana-
lyze the higher eigen modes of oscillations in the KUT
type accelerating sections using the characteristics of
the Е110 oscillation of each cell. Because these sections
are strong tapered DLWs, the most dangerous modes
are located near the section entrance as calculations in-
dicate. Fig.1 shows comparison of the measured distri-
bution of the longitudinal component of the lowest non-
axisymmetrical mode of the KUT type accelerating sec-
tion with simulated one.
0 100 200 300 400
0
0 .1
0 .2
0 .3
0 .4
0 .5
0 .6
0 .7
0 .8
0 .9
1
Z (m m )
E
z (
a
rb
. U
n
its
)
E xp
S im
Fig. 1. Distribution of the longitudinal component of the
lowest non-axisymmetrical mode along the initial part
of the section
The field distribution was measured by bead-pull
method. Because of technical reasons the bead did not
have enough selectivity to measure the transversal and
longitudinal components of the electric field separately,
the experimental distribution showed in Fig.1 was ob-
tained with following procedure. There were two mea-
surements of field distribution with the same bead. The
first measurement was carried out on the section axis,
while the second one was carried out at 5 mm off the
axis. Using the fact that the longitudinal component of
the electrical field is zero on the axis while its transver-
sal component is weakly dependent on the transversal
coordinate, the experimental curve in Fig.2 was ob-
tained by subtraction of the on-axis field distribution
from the off-axis one. A good agreement of experimen-
tal and simulated data is evident.
During the next stage of our research we studied
processes of BBU instability build-up in the first accel-
erating section of the linac described in reference [4]
(piece-wise homogeneous section) and the starting cur-
rent of regenerative BBU instability was derived.
The time dependent field amplitudes of the Е110 os-
cillations in the fourth cell of the DLW are shown in
Fig.2 for the set of accelerated current.
It follows from Fig.2 that the starting current of re-
generative BBU instability is about 0.65 А. Time depen-
dent transversal size of bunches at the section exits for
the three-sectional linac are shown in Fig.3. The first
section was piece-wise homogeneous section, the sec-
__________________________________________________________
PROBLEMS OF ATOMIC SCIENCE AND TECHNOLOGY. 2006. № 2.
Series: Nuclear Physics Investigations (46), p.131-133. 131
ond one was a smooth tapered section and the third one
was the same as the first section. Accelerated current
corresponded to the starting current in the first section
(I=0.65 A). Root mean square transversal size of a
bunch
( ) 2
,s qX x x= −
was chosen as the analyzed characteristic.
Fig. 2. Time dependent field amplitudes of the Е110 os-
cillations in the fourth cell for the set of accelerated
current (1 – I=0.54 А, 2 - I=0.65 А, 3 - I=0.72 А,
4 - I=0.78 А, 4- I=0.98 А)
Fig. 3. Time dependent transversal size of bunches at
the section exits at accelerated current of I=0.65 A
Analysis of these dependences shows that transver-
sal size of bunches in the second and third section has
tendency to increasing however it does not growth ex-
ponential with time. Simulation shows that acceleration
of a beam with a current that is higher than starting one,
causes exponential growth of transversal size of bunch-
es with time.
4. CONCLUSION
Results of transversal particle dynamic simulation
outlined in this work have shown that BBU instability
caused by excitation of Е110 oscillations in high current
linacs consisting of few accelerating sections does not
yet have cumulative character with exponential growth
of beam size up to the starting current of the regenera-
tive BBU instability in the first accelerating section.
The work was partially supported through the STCU
grant #3151.
REFERENCES
1. G.A. Loew. Electron Linac Instabilities // IEEE
Trans. Nucl. Sci., 1967, v.14, №3, p.529-540.
2. E.Z. Biller, A.N. Dovbnya, B.A. Kushnir et. al. Beam
Current Enhancement in Kharkov Electron Linac //
Part. Accel. 1990, v.27, p.119-124.
3. N.I. Aizatsky, Yu.I. Akchurin, V.A. Gurin et. al.
KUT-industrial technological accelerator. Proc. of the
14th Workshop on Charged Particles Accelerators.
1994, v.4, Protvino, Russia, p.259-263.
4. N.I. Ayzatsky, E.Z. Biller, V.N. Boriskin et. al. High
Power Electron S-band Linac for Industrial Purposes.
Proc. of PAC03. Portland. 2003, p.2878-2880.
МОДЕЛИРОВАНИЕ ПОПЕРЕЧНОЙ НЕУСТОЙЧИВОСТИ ПУЧКА В МОЩНЫХ ЛИНЕЙНЫХ
УСКОРИТЕЛЯХ ЭЛЕКТРОНОВ
Н.И. Айзацкий, Е.Ю. Крамаренко, И.В. Ходак, В.А. Кушнир, В.В. Митроченко, С.А. Пережогин
Приведены методика расчета порогового тока регенеративной поперечной неустойчивости в неоднород-
ных цилиндрических диафрагмированных волноводах и результаты моделирования развития поперечной
неустойчивости в ускорителе, состоящем из нескольких ускоряющих секций.
МОДЕЛЮВАННЯ ПОПЕРЕЧНОЇ НЕСТІЙКОСТІ ПУЧКА В ПОТУЖНИХ ЛІНІЙНИХ
ПРИСКОРЮВАЧАХ ЕЛЕКТРОНІВ
М.І. Айзацький, К.Ю. Крамаренко, І.В. Ходак, В.А. Кушнір, В.В. Митроченко, С.А. Пережогін
Приведено методику розрахунку стартового струму регенеративної поперечної нестійкості в
неоднорідних циліндричних діафрагмованих хвилеводах та результати моделювання розвитку поперечної
нестійкості в прискорювачі, що складається з декількох прискорювальних секцій.
124
4. conclusion
МОДЕЛИРОВАНИЕ ПОПЕРЕЧНОЙ НЕУСТОЙЧИВОСТИ ПУЧКА В МОЩНЫХ ЛИНЕЙНЫХ УСКОРИТЕЛЯХ ЭЛЕКТРОНОВ
МОДЕЛЮВАННЯ ПОПЕРЕЧНОЇ НЕСТІЙКОСТІ ПУЧКА В ПОТУЖНИХ ЛІНІЙНИХ ПРИСКОРЮВАЧАХ ЕЛЕКТРОНІВ
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