Wakefield excitation by sequences of relativistic electron bunches in dielectric cavity at detuning bunch repetition frequency and frequency of eigen principal mode
Process of wakefield excitation by short and long sequences of relativistic electron bunches with finite both longitudinal and the transverse sizes is investigated. It is shown that at the presence of detuning between the bunch repetition frequency and the frequency of excited synchronous oscillatio...
Збережено в:
| Опубліковано в: : | Вопросы атомной науки и техники |
|---|---|
| Дата: | 2014 |
| Автори: | , , |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Національний науковий центр «Харківський фізико-технічний інститут» НАН України
2014
|
| Теми: | |
| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/81205 |
| Теги: |
Додати тег
Немає тегів, Будьте першим, хто поставить тег для цього запису!
|
| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Wakefield excitation by sequences of relativistic electron bunches in dielectric cavity at detuning bunch repetition frequency and frequency of eigen principal mode / V.A. Balakirev, I.N. Onishchenko, A.P. Tolstoluzhsky // Вопросы атомной науки и техники. — 2014. — № 6. — С. 91-96. — Бібліогр.: 4 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1859948606010687488 |
|---|---|
| author | Balakirev, V.A. Onishchenko, I.N. Tolstoluzhsky, A.P. |
| author_facet | Balakirev, V.A. Onishchenko, I.N. Tolstoluzhsky, A.P. |
| citation_txt | Wakefield excitation by sequences of relativistic electron bunches in dielectric cavity at detuning bunch repetition frequency and frequency of eigen principal mode / V.A. Balakirev, I.N. Onishchenko, A.P. Tolstoluzhsky // Вопросы атомной науки и техники. — 2014. — № 6. — С. 91-96. — Бібліогр.: 4 назв. — англ. |
| collection | DSpace DC |
| container_title | Вопросы атомной науки и техники |
| description | Process of wakefield excitation by short and long sequences of relativistic electron bunches with finite both longitudinal and the transverse sizes is investigated. It is shown that at the presence of detuning between the bunch repetition frequency and the frequency of excited synchronous oscillations the beating of oscillations in time is formed. The first part of the sequence of bunches loses energy on wakefield excitation resulting in wakefield amplitude growth. The second part of the sequence of bunches gains energy resulting in wakefield amplitude decrease. Thus, in the dielectric cavity the regime of relativistic electrons autoacceleration can be realized by introduction of frequency detuning.
Исследован процесс возбуждения кильватерных полей в диэлектрическом резонаторе как короткой, так и длинной цепочками релятивистских электронных сгустков, имеющих конечные продольные и поперечные размеры. Показано, что при наличии расстройки между частотой следования сгустков и резонансной частотой собственного колебания формируется биение возбуждаемых колебаний. Первая половина сгустков теряет энергию на возбуждение кильватерного поля, при этом амплитуда поля растет. Вторая половина электронных сгустков в цепочке приобретает энергию от поля. Амплитуда кильватерного поля соответственно убывает. Следовательно, в диэлектрическом резонаторе путем введения расстройки может быть реализован режим автоускорения.
Досліджено процес збудження кільватерних полів у діелектричному резонаторі як короткими, так і довгими ланцюжками релятивістських електронних згустків, що мають скінчені поздовжні та поперечні розміри. Показано, що при наявності розладу між частотою проходження згустків і резонансною частотою власного коливання формується биття збуджуваних коливань. Перша половина згустків втрачає енергію на збудження кільватерного поля, при цьому амплітуда поля росте. Друга половина електронних згустків у ланцюжку одержує енергію від поля. Амплітуда кільватерного поля відповідно убуває. Отже, у діелектричному резонаторі шляхом введення розладу може бути реалізовано режим автоприскорення.
|
| first_indexed | 2025-12-07T16:15:42Z |
| format | Article |
| fulltext |
ISSN 1562-6016. ВАНТ. 2014. №6(94)
PROBLEMS OF ATOMIC SCIENCE AND TECHNOLOGY. 2014, №6. Series: Plasma Physics (20), p. 91-96. 91
WAKEFIELD EXCITATION BY SEQUENCES OF RELATIVISTIC
ELECTRON BUNCHES IN DIELECTRIC CAVITY AT DETUNING
BUNCH REPETITION FREQUENCY AND FREQUENCY OF EIGEN
PRINCIPAL MODE
V.A. Balakirev, I.N. Onishchenko, A.P. Tolstoluzhsky
National Science Center “Kharkov Institute of Physics and Technology”, Kharkov, Ukraine
Process of wakefield excitation by short and long sequences of relativistic electron bunches with finite both
longitudinal and the transverse sizes is investigated. It is shown that at the presence of detuning between the bunch
repetition frequency and the frequency of excited synchronous oscillations the beating of oscillations in time is
formed. The first part of the sequence of bunches loses energy on wakefield excitation resulting in wakefield
amplitude growth. The second part of the sequence of bunches gains energy resulting in wakefield amplitude
decrease. Thus, in the dielectric cavity the regime of relativistic electrons autoacceleration can be realized by
introduction of frequency detuning.
PACS:41.75.Jv, 41.75.Lx, 41.75.Ht, 96.50.Pw
INTRODUCTION
For the realization of the wakefield acceleration
method in dielectric slow wave structures the dielectric
cavities can be used [1, 2]. Using of the dielectric cavity
in the most interesting case of the long sequence of
relativistic electron bunches is especially effective. The
number of bunches in the sequence produced with linear
accelerators can reach several thousands. Under
resonance conditions, when the repetition frequency of
bunches coincides with one of the fundamental
frequencies of the dielectric cavity, an effect of the
accumulation of wake field takes place, which will lead
to a significant increase in the amplitude of the excited
field. In this case the problem of accelerated bunches
injection can be solved by introducing a small detuning
between the repetition frequency of bunches and the
fundamental oscillation frequency of the dielectric
cavity. Under these conditions in the dielectric cavity
the temporal wakefield beating is excited, contrary to
the dielectric waveguide when under similar conditions
spatial beating takes place. Certain part of the electron
bunches is decelerated and spends its energy to excite
wakefield in the volume of the dielectric cavity. Then,
starting from a certain point of time a wakefield phase
changes to and subsequent bunches fall into the
accelerating phase of the field and gain energy.
In this paper the process of wakefield excitation by
sequence of relativistic electron bunches in dielectric
cavity at detuning bunch repetition frequency and
frequency of eigen principal mode is investigated.
1. STATEMENT OF PROBLEM. BASIC
EQUATIONS
Consider the problem in the following statement. The
dielectric cavity is formed by a perfectly conducting
metal cylindrical cavity whose volume is completely
filled with a uniform dielectric permittivity . Dielectric
loss is absent. From the left end of the cavity the
periodic sequence of electron bunches with given
longitudinal and transverse profiles of the electron
density is injected. The repetition frequency of bunches
b is different from the frequency of oscillations
mn
in the value of detuning
mn mn b . Let’s find the
wakefield excited in dielectric cavity by a sequence of
relativistic electron bunches in the approximation of a
given motion of the bunches. The problem will be
solved as follows. We will find wakefield of elementary
charge, having the form of a thin ring with charge dQ .
Elementary charge density of an infinitely thin ring has
the form
0 0 0
0
0 0
( , ) ( )
( )
2
b
o
dQ r t r r z
d t t
v r v
, (1)
0 0
0 0 0 0 0
0
( , ) 2
b b b b
r tQ
dQ r t R T r dr dt
v t r t
, (2)
where Q is full charge of bunch,
0t is time of entry of
elementary charge,
0r is radius ring,
0v is bunch
velocity, ,b bt r are characteristic duration and transverse
bunch size, 0 / bR r r is function described transversal
profile of bunch density 2
b br is characteristic
square of bunch transverse section, and 0 / bT t t is
longitudinal profile. These functions are satisfied of the
normalization conditions
1 1
0 0
( ) 1, ( ) 1R x dx T d .
Elementary charge located in the cavity in the time
interval
0 0 0/t L v t t ,
0/L v is time of the passage
of elementary charge through cavity, L is cavity length.
After defining field of the elementary ring bunch (1)
0 0 0( , , , , )ZGE r t r z t t define the wakefield of entire
bunch by integrate on initial radial coordinate
0r , and
time of entry
0t
0 0 0 0 0 0
0 0
2 ( , , , , )
b br t
zw ZGE r dr dt E r t r z t t .
After realization the algorithm described above, we
obtain the following expression for the wake field
excited by a single bunch in the dielectric cavity
2 2 0
0
2 2
21 00
1
( )
8 ( 1)
( )cos( ),
( )
n
b
zw n m m m
n mb
n
r
J
Q c aE S t k z
rv a Lt
J
a
(3)
where
0 0 /v c , a is cavity radius,
92 ISSN 1562-6016. ВАНТ. 2014. №6(94)
1
0
0
( ) ( )b
n n
r
R x J x xdx
a
, (4)
1
0
0 0
0
( ) ( )m mn
b
t
S t T Z t t dt
t
, (5)
00 0
0 2 2
0 0
0
0 02 2
sin ( )( / )
( )
( 1) sin ( / )
( )
sin ( ) sin ( ) ,
m m
mn m
mn m mn mn
m m mn mn
n m
t tt t L v
Z t t
t t L v
t t
t t t t
1/2
2
2
0 2
, / , n
m m m mn m
c
k v k m L k
a
are
frequencies of fundamental oscillations of dielectric
cavity,
1, 0,
( )
0, 0
t
t
t
is Heaviside unit function,
1/ 2 for 0m and 1 for 1m .
In the case of the sequence of N bunches the total
wakefield is the sum of wakefields both of bunches,
which are inside of cavity volume at current time, and
bunches, which passed through the cavity. We choose a
particular form of profile bunches and assume that the
transverse density profile has a Gaussian shape
2
0
220
2
1
b
r
r
b b
r
R e
r r
,
and longitudinal profile has rectangular form
0
0
0 0
1, 1 0
0, 0, 1
b
b
b b
t
tt
T
t tt
t t
.
For such model of the bunch profile the expression for
wakefield of a single bunch is described by the
expression
1 2 0
3 0 0 4 0
( , , ) ( 0, , ) ( / , , )
( / / , , ) ( / , , ).
zw w b w b
w b w b
E t r z E t t r z E L v t t r z
E L v t t L v r z E t L v t r z
First term
1 0 2 2 2
1 0
cos( )
( ) cos cosm m
w n m mn
n m mn m b
k z
E E F r t t
t
,
where
2
2
1
0
2
2
1
( )
( )
( )
n brn
a
n
n
r
J
aF r e
r
J
a
,
2
0
0 2 2
0
8 ( 1)b bQ ct
E
a L
,
describes the field, excited by bunch in the process of its
injection (enter) into cavity 0bt t .
Second term
2 0 2 2 2
1 0
cos ( ) cos )cos( )
( )
cos ( ) cos
m b mm m
w n
n m mn b mnmn m b
t t tk z
E E F r
t t tt
describes the excitation wakefield bunch under its
propagation in the volume of the dielectric
cavity
0/ bL v t t . This time interval corresponds to
the regime excitation which is fully equivalent to a
semi-infinite dielectric waveguides [3, 4].
The third term accounts wakefield excited in the
process of bunch exiting from cavity
0 0/ /bL v t t L v
3 0 2 2 2
1 0
cos( )
( )
cos ( ) cos )
.
cos ( ) ( 1) 1 cos ( )
m m
w n
n m mn m b
m b mn
m
mn b mn b
k z
E E F r
t
t t t
t t t t
And finally, the fourth term describes the field in the
cavity after the bunch left cavity
0/ bt L v t
4 0 02 2 2
1 0
0
cos cos ( )
cos( )
( ) cos ( / )
( 1)
cos ( / )
mn mn b
m m
w n mnm
n m mn m b
mn b
t t t
k z
E E F r t L v
t
t L v t
.
2. WAKEFIELD EXCITATION IN
DIELECTRIC CAVITY BY A SINGLE
ELECTRON BUNCH
At the beginning the dynamics of wakefield
excitation in dielectric cavity by a single bunch with
density profile indicated in the previous section is
considered. The solution of this problem is necessary
for numerical testing the above analytical expressions
for the excited wakefield. Numerical calculations were
performed for the following parameters of the dielectric
cavity and the electron bunch: length of the cavity is
63.85L cm , its radius 4.325a cm , dielectric
permittivity is 2.1 , value of characteristic radius of
bunch is / 0.25br a , bunch duration is
1/ 1/ 6,bt T
1 11/T f ,
1 2.804f GHz is frequency oscillation
which is in Cerenkov resonance with the bunch.
Synchronous with respect to bunch is the oscillation
with indexes 1, 12n m . For a given frequency the
cavity length contains six wavelengths. Particle energy
of the electron bunch is 4.5 MeV , charge of bunch is
0.32Q nC .
Fig. 1. Wakefield distribution in the volume of dielectric
cavity at time / 2 4.5
Fig. 2. Wakefield distribution in the volume of dielectric
cavity at time / 2 40.8
ISSN 1562-6016. ВАНТ. 2014. №6(94) 93
Fig. 3. The dependence of the electric field at the cavity
output end
In Fig. 1 it is shown the distribution of wake electric
field along the length of the cavity at the moment
1/ 2 4.5, 2 f t . The main radial harmonic
( 1n ) takes into account only. At this time, leading
front of the bunch is in a plane / 4.5resz , where
1/res c f is wavelength of resonant oscillation. In this
situation, the regime of semi-infinite dielectric
waveguide is realized [3, 4]. As seen from Fig. 1, in
front of the bunch wakefield is absent. In the region of
bunch the field grows practically under the linear law.
Behind the bunch 3 full oscillations of the Cherenkov
wakefield is excited, and then the tail of the transition
radiation of low level is observed. The transit time of
the bunch through the cavity is / 2 6transit . Group
front passes through the cavity length during
/ 2 12.6g . After bunch left cavity, Cherenkov
radiation pulse propagates with the group velocity.
Multiple reflections and dispersion spreading of the
wave packet leads to monochromatization field
distribution along the cavity (Fig. 2, / 2 40.81 ). In
Fig. 3 dependence on the wake electric field on time at
the output end of the dielectric cavity z L is
presented. Field appears at the time of arrival the bunch
to the output end / 2 6b . After the bunch leaves the
cavity, the pulse of reflected Cherenkov radiation is
formed and the transition radiation is excited when
bunch crosses perfectly conducting end of the cavity.
Increase the number of oscillations in the pulse of
Cherenkov radiation is apparently connected with
superposition of direct and reflected pulses. Further, the
reflected pulse circulates in the cavity with the group
velocity and undergoes dispersion spreading. The pulse
is monochromated with decreasing amplitude. We will
consider now a case of a long bunch / 2 1/ 2b . In
Fig. 4 distribution of wakefield along the cavity is
presented to the same timepoint / 2 4.5 , as in case
of the short bunch. It is seen that the bunch region
contains half length wake wave
Fig. 4. The electric field distribution along the cavity at
the moment / 2 4.5 for bunch length
b
Fig. 5. Dependence of the electric field at the output end
of the cavity for long bunch
excited by the forward front of the bunch. Behind the
back front amplitude wakefield doubles so as wakefield
of forward and back front are added. Next picture
wakefield repeats wakefield of the short-bunch.
In Fig. 5 the dependence of wakefield on time at the
output end of the dielectric cavity with long time of
observation is presented. The dispersive spreading of
the circulating pulse and its monochromatization are
clearly seen. Note, that increasing the duration of the
bunch while keeping its total charge leads to the
decrease of the wakefield amplitude.
Fig. 6. The electric field distribution along the cavity at
the moment / 2 4.5 taking into account five radial
modes, / 3b
Fig. 7. Dependence of the electric field at the output end
of the cavity taking into account 5 radial modes,
/ 3b
Fig. 8. The electric field distribution along the cavity at
the moment / 2 40.81 taking into account 5 radial
modes, / 3b
This result is understandable, since with increasing
duration of the bunch the coherence of wakefield
radiated
94 ISSN 1562-6016. ВАНТ. 2014. №6(94)
by bunch degrades. One-mode approximation ( 1n )
on radial index gives simple qualitative picture of the
excitation wakefield by electron bunch of finite size in
dielectric cavity. A more realistic picture can be
obtained by taking into account all excited radial
harmonics. In Fig. 6 distribution of wakefield of the
short electron bunch / 2 1/ 6b along the cavity is
presented to the timepoint / 2 4.5 taking into
account 5 radial harmonics. The increasing of numbers
of radial harmonics didn't lead to noticeable change of
numerical results. Before the bunch the wakefield is
absent. Then nonsinusoidal pulse of Cherenkov
wakefield is excited. Behind Cherenkov wakefield the
tail of quickly decreasing transition radiation
propagates. In Fig. 7 dependence on time of the
wakefield at the output end of the cavity in the
multimode regime on radial index n is presented. The
field has an appearance of pulses sequences. However,
unlike one-mode regime, oscillations inside pulse are
nonsinusoidal.
In Fig. 8 field distribution along the dielectric cavity
in multimode regime at the timepoint / 2 40.81 is
presented. Distribution of the field has nonregular
character. We will note that in the multimode regime the
maximum value of the wakefield increased,
approximately, twice. Thus duration of peaks of the
field of opposite polarity was significantly reduced.
3. WAKEFIELD EXCITATION IN THE
DIELECTRIC CAVITY BY SEQUENCE OF
ELECTRON BUNCHES OF FINITE SIZE IN
THE PRESENCE OF DETUNING BETWEEN
THE REPETITION FREQUENCY BUNCHES
AND THE FUNDAMENTAL OSCILLATION
FREQUENCY
Wakefield in dielectric cavity excited by a sequence
of relativistic electron bunches is the simple sum of
wakefield single bunches. Let’s consider, firstly, the
simplest case of the short cavity / 2resL
( 10.642res cm ). Wherein the spatial period
repetition of bunches is
res . Thus, in the cavity may be
only one bunch. Duration bunches is
/ / 2 1/ 6b bt T . In Fig. 9,a dependence of the
wakefield on time at the output end of the dielectric
cavity in resonant case is presented. The sequence of
bunches is in the resonance with the main oscillation
1, 1n m of the cavity. The sequence was chosen
from 20 bunches. From this figure it is seen that in the
resonant case the coherent addition of fields of
individual bunches takes place. Amplitude of wakefield
thus linearly grows over time. After cavity passing by
the last bunch amplitude of wake field remains constant.
In the presence of detuning the picture of wakefield
excitation qualitatively changes. (Fig. 9,b). One beating
of the wakefield is formed.
At the chosen number of bunches and detuning shift
of the phase of wakefield behind the last bunch is equal
2 . Therefore value of wakefield behind last bunch
becomes zero. As whole amplitude of wakefield grows
in the beginning and bunches lose energy on wakefield
excitation. After the tenth bunch the phase of wakefield
changes on and the subsequent bunches gain energy
and amplitude of wakefield decreases.
Fig. 9,а. Dependence of wakefield at output end of short
cavity / 2resL . in the case of resonance sequence
bunches, 20N
Fig 9,b. Dependence of wakefield at output end of short
cavity / 2resL in the case of nonresonance sequence
bunches 20N , value of detuning is / 0.02
Secondly, consider the case of long cavity 6 resL .
In Figs. 10,а; 10,b dependences of the wakefield on time
at the output end of the dielectric cavity are presented.
Calculations are performed for 100 bunches.
Oscillations with indexes 40 0, 5 1m n were
considered. In resonant case the linear growth of
amplitude of the wakefield is observed. In the presence
of the detuning
2/ 10 one beating is formed. It
is seen noticeable influence of the nonresonance
longitudinal and transverse harmonics. We will note
also that in the presence of detuning the maximum
amplitude of the wakefield is decreased approximately
by 3 times. In Fig. 10,c the picture of the wakefield
excitation for quantity of bunches in chains 115N
and the same value of the detuning is presented. In this
case after passing of all chain amplitude of wakefield
does not vanish. Last 15 bunches excite field, then the
field amplitude remains constant. In Figs. 11,a; 11,b
results of numerical calculations with number of
bunches 200N are presented. In volume of the cavity
there are at the same time 6 bunches. Bunches are in
synchronism with oscillation 1, 12n m . In
Figs. 12,a; 12,b for comparison dependences of the
wakefield at the output end of cavity taking into account
oscillations with one radial index 1n and longitudinal
indexes 40 0m and taking into account oscillations
with radial and longitudinal indexes
5 1; 40 0n m are presented. It is seen that the
accounting of the highest radial modes doesn't change
quantitative characteristics of the wakefield as well as
the qualitative picture excitation of the wakefield is
conserved. We will note that both in resonant, and in not
resonant cases nonmonotonic change of wakefield
amplitude is observed. This is explained by finite time
ISSN 1562-6016. ВАНТ. 2014. №6(94) 95
of signal circulation with group velocity on feedback
chain. We will note also that the accounting of the
highest radial harmonics leads to some increasing of the
wakefield level behind the last bunch in the presence of
detuning.
We will discuss results of numerical calculations with
different quantity of bunches in chain 400N
(Fig. 13,а) and 900N (Fig. 13,b) and the fixed value
of the detuning 4/ 2.5 10 . In the first case one
beating of the wakefield is formed. In the second case
two beating, and also wake of the wakefield from the
last 100 bunches are observed. Increase of bunches
number in chain to 1000 (Fig. 14) lead to increasing of
intensity wake electric field to 18 keV cm .
Fig. 10,а. Dependence of wakefield at output end of
long cavity in the case of resonant sequence of bunches,
100N
Fig. 10,b. Dependence of wakefield at output end of
long cavity in the case of nonresonant sequence of
bunches, 100N , detuning is
2/ 10
Fig. 10,с. Dependence of wakefield at output end of
long resonator in the case of nonresonanant sequence of
bunches, 115N , detuning is
2/ 10
Fig. 11,а. Dependence of wakefield at output end of
long cavity in the case of resonant sequence of bunches,
200N (one mode regime for radial index 1n )
F
Fig. 11,b. Dependence of wakefield at output end of
long cavity in the case of nonresonant sequence of
bunches, 200N , detuning is 3/ 5 10 ( one
mode regime for radial index 1n )
Fig. 12,а. Dependence of wakefield to output end of
long cavity in the case of resonant sequence of bunches,
200N (multimode regime for radial index 5 1n )
Fig. 12,b. Dependence of wakefield at output end of
long cavity in the case of nonresonant sequence of
bunches, 200N , detuning is
3/ 5 10
(multimode regime for radial index 5 1n )
Fig. 13,а. Dependence of wakefield at output end of
long cavity in the case of nonresonant sequence of
bunches, 400N , detuning is 4/ 2.5 10
(multimode regime for radial index 5 1n )
Fig. 13,b. Dependence of wakefield at output end of
long cavity in the case of nonresonant sequence of
bunches, 900N , detuning is 4/ 2.5 10
(multimode regime for radial index 5 1n )
96 ISSN 1562-6016. ВАНТ. 2014. №6(94)
Fig. 14. Dependence of wakefield at output end of long
cavity in the case of nonresonant sequence of bunches,
1000N , detuning is 4/ 1.0 10 (multimode
regime for radial index 5 1n )
CONCLUSIONS
Thus, in the paper the dynamics of wakefield
excitation by short, and long chains of relativistic
electron bunches having finite both longitudinal and the
transverse sizes is investigated. It is shown that at the
presence of detuning between the bunch repetition
frequency and the frequency of excited synchronous
oscillations the beating of oscillations in time is formed.
The first half of bunches loses energy on wakefield
excitation and field amplitude grows. The second half of
chain of bunches gains energy and amplitude of
wakefield decreases. Thus, in the dielectric cavity by
introduction of detuning the autoacceleration regime can
be realized.
ACKNOWLEDGEMENTS
This work was supported by the US Department of
Energy/NNSA through the Global Initiatives for
Proliferation Prevention (GIPP) Program in Partnership
with the Science and Technology Center in Ukraine
(Project ANL-T2-247-UA and STCU Agreement P522).
REFERENCES
1. V.A. Balakirev, I.N. Onishchenko, D.Y. Sidorenko,
G.V. Sotnikov. Acceleration of charged particles by
wakefield in dielectric cavity with channel for the
exciting bunch // Zh. Tekh. Fiz. Pis’ma. 2003, v. 29,
№14, p. 39-45.
2. J.H. Kim, J. Han, M. Joon, S.Y. Park. Theory of
wakefields in a dielectric-filled cavity // Phys. Rev.
Special Topics-Accelerators and Beams. 2010, v. 13,
№ 071302, p. 071302-1.
3. V.A. Balakirev, I.N. Onishchenko, D.Y. Sidorenko,
G.V. Sotnikov. Excitation of wakefield by relativistic
electron bunch in a semi-infinite dielectric waveguide //
Zh. Eksp. Teor. Fiz. 2001, v. 120, № 1, p. 41-51.
4. I.N. Onishchenko, D.Y. Sidorenko, G.V. Sotnikov.
Structure of electromagnetic field excited by an electron
bunch in a semi-infinite dielectric filled waveguide //
Phys. Rev. E. 2002, v. 65, № 6, p. 066501.
Article received 25.10.2014
ВОЗБУЖДЕНИЕ КИЛЬВАТЕРНЫХ ПОЛЕЙ ПОСЛЕДОВАТЕЛЬНОСТЬЮ РЕЛЯТИВИСТСКИХ
ЭЛЕКТРОННЫХ СГУСТКОВ В ДИЭЛЕКТРИЧЕСКОМ РЕЗОНАТОРЕ ПРИ НАЛИЧИИ
РАССТРОЙКИ МЕЖДУ ЧАСТОТОЙ СЛЕДОВАНИЯ СГУСТКОВ И ЧАСТОТОЙ ОСНОВНОЙ
МОДЫ
В.А. Балакирев, И.Н. Онищенко, А.П. Толстолужский
Исследован процесс возбуждения кильватерных полей в диэлектрическом резонаторе как короткой, так и
длинной цепочками релятивистских электронных сгустков, имеющих конечные продольные и поперечные
размеры. Показано, что при наличии расстройки между частотой следования сгустков и резонансной
частотой собственного колебания формируется биение возбуждаемых колебаний. Первая половина сгустков
теряет энергию на возбуждение кильватерного поля, при этом амплитуда поля растет. Вторая половина
электронных сгустков в цепочке приобретает энергию от поля. Амплитуда кильватерного поля
соответственно убывает. Следовательно, в диэлектрическом резонаторе путем введения расстройки может
быть реализован режим автоускорения.
ЗБУДЖЕННЯ КІЛЬВАТЕРНИХ ПОЛІВ ПОСЛІДОВНІСТЮ РЕЛЯТИВІСТСЬКИХ ЕЛЕКТРОННИХ
ЗГУСТКІВ У ДІЕЛЕКТРИЧНОМУ РЕЗОНАТОРІ ЗА НАЯВНОСТІ РОЗЛАДУ МІЖ ЧАСТОТОЮ
СЛІДУВАННЯ ЗГУСТКІВ І ЧАСТОТОЮ ОСНОВНОЇ МОДИ
В.А. Балакірев, І.М. Онiщенко, О.П. Толстолужський
Досліджено процес збудження кільватерних полів у діелектричному резонаторі як короткими, так і
довгими ланцюжками релятивістських електронних згустків, що мають скінчені поздовжні та поперечні
розміри. Показано, що при наявності розладу між частотою проходження згустків і резонансною частотою
власного коливання формується биття збуджуваних коливань. Перша половина згустків втрачає енергію на
збудження кільватерного поля, при цьому амплітуда поля росте. Друга половина електронних згустків у
ланцюжку одержує енергію від поля. Амплітуда кільватерного поля відповідно убуває. Отже, у
діелектричному резонаторі шляхом введення розладу може бути реалізовано режим автоприскорення.
|
| id | nasplib_isofts_kiev_ua-123456789-81205 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1562-6016 |
| language | English |
| last_indexed | 2025-12-07T16:15:42Z |
| publishDate | 2014 |
| publisher | Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
| record_format | dspace |
| spelling | Balakirev, V.A. Onishchenko, I.N. Tolstoluzhsky, A.P. 2015-05-13T15:58:35Z 2015-05-13T15:58:35Z 2014 Wakefield excitation by sequences of relativistic electron bunches in dielectric cavity at detuning bunch repetition frequency and frequency of eigen principal mode / V.A. Balakirev, I.N. Onishchenko, A.P. Tolstoluzhsky // Вопросы атомной науки и техники. — 2014. — № 6. — С. 91-96. — Бібліогр.: 4 назв. — англ. 1562-6016 PACS:41.75.Jv, 41.75.Lx, 41.75.Ht, 96.50.Pw https://nasplib.isofts.kiev.ua/handle/123456789/81205 Process of wakefield excitation by short and long sequences of relativistic electron bunches with finite both longitudinal and the transverse sizes is investigated. It is shown that at the presence of detuning between the bunch repetition frequency and the frequency of excited synchronous oscillations the beating of oscillations in time is formed. The first part of the sequence of bunches loses energy on wakefield excitation resulting in wakefield amplitude growth. The second part of the sequence of bunches gains energy resulting in wakefield amplitude decrease. Thus, in the dielectric cavity the regime of relativistic electrons autoacceleration can be realized by introduction of frequency detuning. Исследован процесс возбуждения кильватерных полей в диэлектрическом резонаторе как короткой, так и длинной цепочками релятивистских электронных сгустков, имеющих конечные продольные и поперечные размеры. Показано, что при наличии расстройки между частотой следования сгустков и резонансной частотой собственного колебания формируется биение возбуждаемых колебаний. Первая половина сгустков теряет энергию на возбуждение кильватерного поля, при этом амплитуда поля растет. Вторая половина электронных сгустков в цепочке приобретает энергию от поля. Амплитуда кильватерного поля соответственно убывает. Следовательно, в диэлектрическом резонаторе путем введения расстройки может быть реализован режим автоускорения. Досліджено процес збудження кільватерних полів у діелектричному резонаторі як короткими, так і довгими ланцюжками релятивістських електронних згустків, що мають скінчені поздовжні та поперечні розміри. Показано, що при наявності розладу між частотою проходження згустків і резонансною частотою власного коливання формується биття збуджуваних коливань. Перша половина згустків втрачає енергію на збудження кільватерного поля, при цьому амплітуда поля росте. Друга половина електронних згустків у ланцюжку одержує енергію від поля. Амплітуда кільватерного поля відповідно убуває. Отже, у діелектричному резонаторі шляхом введення розладу може бути реалізовано режим автоприскорення. This work was supported by the US Department of Energy/NNSA through the Global Initiatives for Proliferation Prevention (GIPP) Program in Partnership with the Science and Technology Center in Ukraine (Project ANL-T2-247-UA and STCU Agreement P522) en Національний науковий центр «Харківський фізико-технічний інститут» НАН України Вопросы атомной науки и техники Плазменная электроника Wakefield excitation by sequences of relativistic electron bunches in dielectric cavity at detuning bunch repetition frequency and frequency of eigen principal mode Возбуждение кильватерных полей последовательностью релятивистских электронных сгустков в диэлектрическом резонаторе при наличии расстройки между частотой следования сгустков и частотой основной моды Збудження кільватерних полів послідовністю релятивістських електронних згустків у діелектричному резонаторі за наявності розладу між частотою слідування згустків і частотою основної моди Article published earlier |
| spellingShingle | Wakefield excitation by sequences of relativistic electron bunches in dielectric cavity at detuning bunch repetition frequency and frequency of eigen principal mode Balakirev, V.A. Onishchenko, I.N. Tolstoluzhsky, A.P. Плазменная электроника |
| title | Wakefield excitation by sequences of relativistic electron bunches in dielectric cavity at detuning bunch repetition frequency and frequency of eigen principal mode |
| title_alt | Возбуждение кильватерных полей последовательностью релятивистских электронных сгустков в диэлектрическом резонаторе при наличии расстройки между частотой следования сгустков и частотой основной моды Збудження кільватерних полів послідовністю релятивістських електронних згустків у діелектричному резонаторі за наявності розладу між частотою слідування згустків і частотою основної моди |
| title_full | Wakefield excitation by sequences of relativistic electron bunches in dielectric cavity at detuning bunch repetition frequency and frequency of eigen principal mode |
| title_fullStr | Wakefield excitation by sequences of relativistic electron bunches in dielectric cavity at detuning bunch repetition frequency and frequency of eigen principal mode |
| title_full_unstemmed | Wakefield excitation by sequences of relativistic electron bunches in dielectric cavity at detuning bunch repetition frequency and frequency of eigen principal mode |
| title_short | Wakefield excitation by sequences of relativistic electron bunches in dielectric cavity at detuning bunch repetition frequency and frequency of eigen principal mode |
| title_sort | wakefield excitation by sequences of relativistic electron bunches in dielectric cavity at detuning bunch repetition frequency and frequency of eigen principal mode |
| topic | Плазменная электроника |
| topic_facet | Плазменная электроника |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/81205 |
| work_keys_str_mv | AT balakirevva wakefieldexcitationbysequencesofrelativisticelectronbunchesindielectriccavityatdetuningbunchrepetitionfrequencyandfrequencyofeigenprincipalmode AT onishchenkoin wakefieldexcitationbysequencesofrelativisticelectronbunchesindielectriccavityatdetuningbunchrepetitionfrequencyandfrequencyofeigenprincipalmode AT tolstoluzhskyap wakefieldexcitationbysequencesofrelativisticelectronbunchesindielectriccavityatdetuningbunchrepetitionfrequencyandfrequencyofeigenprincipalmode AT balakirevva vozbuždeniekilʹvaternyhpoleiposledovatelʹnostʹûrelâtivistskihélektronnyhsgustkovvdiélektričeskomrezonatoreprinaličiirasstroikimeždučastotoisledovaniâsgustkovičastotoiosnovnoimody AT onishchenkoin vozbuždeniekilʹvaternyhpoleiposledovatelʹnostʹûrelâtivistskihélektronnyhsgustkovvdiélektričeskomrezonatoreprinaličiirasstroikimeždučastotoisledovaniâsgustkovičastotoiosnovnoimody AT tolstoluzhskyap vozbuždeniekilʹvaternyhpoleiposledovatelʹnostʹûrelâtivistskihélektronnyhsgustkovvdiélektričeskomrezonatoreprinaličiirasstroikimeždučastotoisledovaniâsgustkovičastotoiosnovnoimody AT balakirevva zbudžennâkílʹvaternihpolívposlídovnístûrelâtivístsʹkihelektronnihzgustkívudíelektričnomurezonatorízanaâvnostírozladumížčastotoûslíduvannâzgustkívíčastotoûosnovnoímodi AT onishchenkoin zbudžennâkílʹvaternihpolívposlídovnístûrelâtivístsʹkihelektronnihzgustkívudíelektričnomurezonatorízanaâvnostírozladumížčastotoûslíduvannâzgustkívíčastotoûosnovnoímodi AT tolstoluzhskyap zbudžennâkílʹvaternihpolívposlídovnístûrelâtivístsʹkihelektronnihzgustkívudíelektričnomurezonatorízanaâvnostírozladumížčastotoûslíduvannâzgustkívíčastotoûosnovnoímodi |