Influence of the finite Q-factor on excitation of wakefield oscillations in dielectric cavity by a sequence of relativistic electron bunches in the presence of detuning between the resonant frequency and the bunch repetition frequency
Excitation of Cerenkov wakefield oscillations in dielectric cavity with finite value of Q-factor in the presence of detuning between the bunch repetition frequency and the resonant frequency of the excited oscillations is investigated. It is shown that the picture of wake oscillations excitation is...
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| Date: | 2015 |
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Національний науковий центр «Харківський фізико-технічний інститут» НАН України
2015
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| Cite this: | Influence of the finite q-factor on excitation of wakefield oscillations in dielectric cavity by a sequence of relativistic electron bunches in the presence of detuning between the resonant frequency and the bunch repetition frequency/ V.A. Balakirev, I.N. Onishchenko, A.P. Tolstoluzhsky // Вопросы атомной науки и техники. — 2015. — № 1. — С. 122-126. — Бібліогр.: 3 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1860267073993703424 |
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| author | Balakirev, V.A. Onishchenko, I.N. Tolstoluzhsky, A.P. |
| author_facet | Balakirev, V.A. Onishchenko, I.N. Tolstoluzhsky, A.P. |
| citation_txt | Influence of the finite q-factor on excitation of wakefield oscillations in dielectric cavity by a sequence of relativistic electron bunches in the presence of detuning between the resonant frequency and the bunch repetition frequency/ V.A. Balakirev, I.N. Onishchenko, A.P. Tolstoluzhsky // Вопросы атомной науки и техники. — 2015. — № 1. — С. 122-126. — Бібліогр.: 3 назв. — англ. |
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| container_title | Вопросы атомной науки и техники |
| description | Excitation of Cerenkov wakefield oscillations in dielectric cavity with finite value of Q-factor in the presence of detuning between the bunch repetition frequency and the resonant frequency of the excited oscillations is investigated. It is shown that the picture of wake oscillations excitation is determined by the ratio between the value of the Q-factor and frequency detuning parameter πω/δω. For the high Q-factor dielectric cavity Q >>πω/δω picture of wake oscillations excitation is the same as in the cavity without ohmic losses. If the opposite condition is satisfied, the process of wakefield excitation occurs almost as well as in the case of resonant excitation. Linear growth of the wakefield amplitude at initial stage reaches its saturation level.
Изучен процесс возбуждения кильватерных колебаний в диэлектрическом резонаторе с конечным значением добротности Q при наличии расстройки между частотой следования сгустков и частотой резонансного колебания. Показано, что картина возбуждения кильватерных колебаний определяется соотношением между значением добротности Q и параметром частотной расстройки πω/δω. В случае высокой добротности диэлектрического резонатора Q >>πω/δω картина возбуждения кильватерных колебаний такая же, как и в резонаторе без омических потерь. В диэлектрическом резонаторе формируется биение кильватерного поля. Если выполнено противоположное условие, картина возбуждения кильватерных колебаний практически не отличается от случая резонансного возбуждения. После начального линейного роста амплитуды имеет место ее насыщение на постоянном уровне.
Вивчено процес збудження кільватерних коливань у діелектричному резонаторі із скінченним значенням добротності Q при наявності розстройки між частотою проходження згустків і частотою резонансного коливання. Показано, що картина збудження кільватерних коливань визначається співвідношенням між значенням добротності Q й параметром частотної розстройки πω/δω. У випадку високої добротності діелектричного резонатора Q >>πω/δω картина збудження кільватерних коливань така ж, як і в резонаторі без омічних втрат. У діелектричному резонаторі формується биття кільватерного поля. Якщо виконана протилежна умова, картина збудження кільватерних коливань практично не відрізняється від випадку резонансного збудження. Після початкового лінійного росту амплітуди має місце її насичення на постійному рівні.
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| first_indexed | 2025-12-07T19:01:56Z |
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PLASMA ELECTRONICS
ISSN 1562-6016. ВАНТ. 2015. №1(95)
122 PROBLEMS OF ATOMIC SCIENCE AND TECHNOLOGY. 2015, № 1. Series: Plasma Physics (21), p. 122-126.
INFLUENCE OF THE FINITE Q-FACTOR ON EXCITATION OF
WAKEFIELD OSCILLATIONS IN DIELECTRIC CAVITY BY A
SEQUENCE OF RELATIVISTIC ELECTRON BUNCHES IN THE
PRESENCE OF DETUNING BETWEEN THE RESONANT FREQUENCY
AND THE BUNCH REPETITION FREQUENCY
V.A. Balakirev, I.N. Onishchenko, A.P. Tolstoluzhsky
National Science Center “Kharkov Institute of Physics and Technology”, Kharkov, Ukraine
Excitation of Cerenkov wakefield oscillations in dielectric cavity with finite value of Q-factor in the presence of
detuning between the bunch repetition frequency and the resonant frequency of the excited oscillations is
investigated. It is shown that the picture of wake oscillations excitation is determined by the ratio between the value
of the Q -factor and frequency detuning parameter / . For the high Q -factor dielectric cavity /Q
picture of wake oscillations excitation is the same as in the cavity without ohmic losses. If the opposite condition is
satisfied, the process of wakefield excitation occurs almost as well as in the case of resonant excitation. Linear
growth of the wakefield amplitude at initial stage reaches its saturation level.
PACS: 41.75.Jv, 41.75.Lx, 41.75.Ht, 96.50.Pw
INTRODUCTION
In paper [1] process of excitation of wakefield
oscillations in planar dielectric cavity with a finite
Q-factor by a sequence of relativistic electron bunches
in conditions of exact resonance between the sequence
bunches and one of the cavity modes is investigated. In
this paper it is shown that the accounting of the Q-factor
leads to a restriction of the resonance oscillations
amplitude. Especially strong influence of Q-factor is
shown in the case of a long sequence (the order of
several hundred or even thousands of low-current
bunches). In the excitation process of resonant
oscillation involving only a finite number of bunches (in
order /N Q ) located in the leading front of the
chain. The remaining bunches contribution to the
amplitude of the resonant oscillation is not given, i.e.
oscillation amplitude saturates. As is known [2], by
introducing a detuning between the frequency of the
excited oscillations and the repetition frequency of
bunches in the dielectric cavity self-acceleration mode
can be realized. In this case, bunches adjacent to the
leading front will transfer its energy to excite
oscillations, and bunches near the back front will gain
energy. The first part of bunches with numbers
/ 2 1,m where is the frequency detuning,
will lose their energy. In turn bunches with numbers
/ / 2m will be accelerated. Then the
process according to the value of detuning and the total
number of bunches in the sequence can be repeated
periodically. The above considerations are valid for the
dielectric cavity without ohmic losses ( Q ).
Meanwhile the accounting of Q-factor of the dielectric
cavity, as in the resonance case may significantly
change picture of wakefield excitation in the dielectric
cavity in the presence of the frequency detuning and
even disrupt auto-acceleration regime when Q-factor of
dielectric cavity is low. As the estimates show, Q-factor
will not influence on the process of auto-acceleration of
bunches sequence when the requirement for Q-factor
values /Q is satisfied. If this condition on the
Q-factor of the dielectric cavity is not satisfied, then the
process of auto-acceleration is disrupted, as in this case,
the amplitude will saturate at low level and cannot be
formed beating oscillations.
In this paper detailed picture of the wakefield
excitation of oscillations in the dielectric cavity with
finite Q-factor by sequence of relativistic electron
bunches in the presence of detuning between the
repetition frequency of bunches and the resonance
frequency of oscillation is presented.
1. STATEMENT OF PROBLEM.
BASIC EXPRESSIONS
Let’s 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 losses determined by Q-factor,
where
1 2/Q ,
1 2, is the real and imaginary part
of permittivity, respectively. On the left end of the
cavity in its volume injected periodic sequence of
electron bunches with arbitrary longitudinal and
transverse profiles of the electron density. The repetition
frequency of bunches
b is different from the
frequency of oscillations
mn in the value of detuning
mn mn b .
Let’s determine wakefield in approximation of given
motion of a single bunch in the dielectric cavity with
Q-factor. The problem will be solved in a standard way.
Firstly we find wakefield of elementary charge, having
the form of a thin ring with charge
bdQ . 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
( , ) / / 2b
b b
b b
Q
dQ r t R r r T t t r dr dt
v t
, (2)
ISSN 1562-6016. ВАНТ. 2015. №1(95) 123
where
bQ 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 condition
1
0
( ) 1,R x dx
1
0
( ) 1T d .
Elementary charge is within the volume of the cavity in
the time interval
0 0 0/t L v t t ,
0/L v is the passing
time of elementary charge through cavity, L is cavity
length. After determine field of the elementary ring
bunch (1)
0 0 0( , , , , )ZGE r t r z t t we determine 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 . (3)
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 2
1 00 1
8 ( 1) ( / )
( ) cos( )
( / )
b n
zw n m m m
n mb n
Q c J r a
E S t k z
v a Lt J r a
,(4)
where
0 0 /v c , a is cavity radius,
1
0
0
( ) ( )b
n n
r
R x J x xdx
a
, (5)
1
0 0 0
0
( ) / ( )m b mnS t T t t Z t t dt , (6)
0 0
0
0 0 02 2
( / )
0 0 0
( )
0 0 0
1
( ) ( / )
sin ( ) ( 1) sin ( / )
( ) sin ( ) sin ( ) ,
mn
mn
mn
mn m
t t L vm
m m mn mn
t t
m m mn mn
Z t t t t L v
t t e t t L v
t t t t e 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, / 2mn mn Q is damping decrement oscillation
with indexes ,m n ,
1, 0,
( )
0, 0
t
t
t
is Heaviside unit function,
1/ 2 for 0m and 1 for 1m .
In the case of the chain of the N bunches wakefield
is the sum of wakefields as bunches which are inside at
the current time in the cavity volume and bunches
passed through the cavity. We choose a particular form
of profile bunches. We assume that the transverse
density profile has a Gaussian shape
2
222
0 / (1/ ) b
r
r
b bR r r r e
,
and longitudinal profile has rectangular form
0
0
0 0
1, 1 / 0
/
0, / 0, / 1
b
b
b b
t t
T t t
t t t t
.
For such model of the bunch profile, the expression for
wakefield of a single bunch has the form
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 cosmntm m
w n m mn
n m mn m b
k z
E E F r t e t
t
,
where
2
1
20
2
1
( / )
( )
( / )
n br
n a
n
n
J r a
F r e
J r a
,
2
0
0 2 2
0
8 ( 1)b bQ ct
E
a L
,
describes the field, excited by a bunch at transition the
entrance of the cavity 0bt t .
Second term
( )
2 0 2 2 2
1 0
cos ( ) cos )
cos( )
( ) cos ( )
cos
mn b
mn
m b m
t tm m
w n mn b
n m mn m b t
mn
t t t
k z
E E F r e t t
t
e t
describes the wakefield excited by a bunch at its
propagation inside 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 [2, 3].
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 ( )
mn mn b
mn b
m m
w n
n m mn m b
t t t
m b mn mn b
t tm
mn b
k z
E E F r
t
t t e t e t t
e t t
And finally, the fourth term describes the field in the
cavity after the bunch left cavity
0/ bt L v t
0
0
4 0 ( )2 2 2
1 0
( / )
0
( / )
0
coscos( )
( )
cos ( )
cos ( / )
( 1) .
cos ( / )
mn
mn b
mn
mn b
t
mnm m
w n t t
n m mn m b mn b
t L v
mnm
t t L v
mn b
e tk z
E E F r
t e t t
e t L v
e t L v t
2. WAKEFIELD EXCITATION
IN DIELECTRIC CAVITY WITH FINITE
Q-FACTOR BY SINGLE ELECTRON
BUNCH
At the beginning we numerically consider the
dynamics of wakefield excitation in dielectric cavity
with finite Q-factor by a single bunch with density
profile indicated in the previous section. Numerical
calculations were performed for the following
parameters of the dielectric cavity and the electron
bunch: length of the cavity is 63.85 cmL , its radius
is 3.92 cma , dielectric permittivity is 2.1 , value
of characteristic radius of bunch is / 0.25br a , bunch
duration is
1/ 5 / 32,bt T
1 11/T f is frequency
124 ISSN 1562-6016. ВАНТ. 2015. №1(95)
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 0.32bQ nC .
0 14 28 42 56 70 84 98 112 126 140
0.2
0.1
0
0.1
0.2
t/T1
E
z
,
k
V
/c
m
Fig. 1,a. The dependence of the field amplitude at the
cavity output end in the case of single bunch, Q
0 14 28 42 56 70 84 98 112 126 140
0.2
0.1
0
0.1
0.2
t/T1
E
z
,
k
V
/c
m
Fig. 1,b. The dependence of the field amplitude at the
cavity output end in the case of single bunch, 200Q
In Fig. 1,a dependence on the wake electric field on
time at the output end of the dielectric cavity with a
large observation time / 2 126 without ohmic
losses is presented. It is shown dispersive spreading of
the circulating pulse and its monochromatization. Note
that increasing the duration of the bunch while keeping
the total charge leads to reduction amplitude of the
wakefield. This result is understandable, since the
increasing in the duration of bunch degrades coherence
radiation wakefield by bunch.
The time of flight through the cavity of the bunch is
/ 2 6transit . Group front passes through the cavity
length over time / 2 12.6g . After bunch left cavity
Cerenkov radiation pulse propagates with the group
velocity. Multiple reflections and dispersive spreading
of the wave packet leads to the decomposition of the
field at the output of the cavity in the pulse sequence.
In Fig. 1,b the dependence of wake electric field
from time to time at the output end dielectric cavity at
Q-factor value 3200,( / 2.5 10 )Q is presented.
Clearly that circulation of pulse in the volume of
dielectric cavity is accompanied by attenuation of its
amplitude.
3. WAKEFIELD EXCITATION IN THE
DIELECTRIC CAVITY WITH OHMIC
LOSSES BY SEQUENCE OF ELECTRON
BUNCHES
In this section the picture excitation of the wakefield
oscillations in dielectric cavity with the finite Q-factor
by sequence of relativistic electron bunches in the
presence of detuning between the repetition frequency
bunches and the resonance frequency of oscillations is
presented. Let’s consider effect of influence of the finite
values Q-factor on wakefield excitation in the dielectric
cavity by resonance sequence bunches when the
repetition frequency of bunches coincides with
frequency of synchronous eigen oscillation of cavity. In
Figs. 2a, b the dependences of the Cherenkov wakefield
field at the exit of the cavity are presented in the case of
the sequence of 100 bunches. The cavity length is
6L 63.85 cm, is wavelength, its radius is equal
to 3.922a cm , the dielectric constant is 2.1 .
Parameters of each bunch are the same as in the
previous section. Fig. 2,a corresponds to the Q and
Fig. 2,b corresponds to the 200Q .
0 14 28 42 56 70 84 98 112 126 140
10
5
0
5
10
t/T1
E
z
,
k
V
/c
m
Fig. 2,a. Dependence of the field amplitude at the output
of the cavity in the case of resonance sequence of
bunches, 100N , Q
0 14 28 42 56 70 84 98 112 126 140
4
2
0
2
4
t/T1
E
z
,
k
V
/c
m
Fig. 2,b. Dependence of the field amplitude at the output
of the cavity in the case of resonant sequence of
bunches, 100N , 200Q
In this and in the other case in beginning non-
monotonic growth of the amplitude of the wake field
takes place. Nonmonotonic growth of amplitude is due
to circulation of increasing signal through a feedback
circuit, the nature of which is caused by the reflection of
the signal from the perfectly conducting dielectric
cavity ends. With decreasing Q-factor the maximum
value of the amplitude wakefield also decreases.
Moreover, in the second case after the last bunch
passing some attenuation field is observed.
Let us now consider the case of wakefield excitation
in dielectric cavity with different values Q-factor in the
presence of detuning. The cavity length is
3L 31.925 cm, dielectric permeability is
2.045 , the number of bunches in the chain is 400,
the value of detuning is
3/ 2.5 10 .
For this value of the detuning in the case of the
lossless cavity phase shift of wakefield after the last
bunch is 2 . Figs. 3,a-3,d shows series of curves for
different values Q-factor lying within
4 22 10 1.25 10Q . For high Q-factor dielectric
cavity 42.0 10Q (see Fig. 3,a) picture of the
wakefield excitation is practically identical to the case
of cavity without ohmic losses [2].
ISSN 1562-6016. ВАНТ. 2015. №1(95) 125
Fig. 3,a. Dependence of the field amplitude at the output
of the cavity in the case of nonresonant sequence of
bunches, 400N , 2000Q , value of detuning is
32.5 10
0 50 100 150 200 250 300 350 400 450 500 550 600
4
2
0
2
4
t/T1
E
z
,
k
V
/c
m
Fig. 3,b. Dependence of the field amplitude at the output
of the cavity in the case of nonresonant sequence of
bunches, 400N , 1250Q , value of detuning is
3/ 2.5 10
This case is intermediate, since the value of the
detuning parameter
3/ 1.2 10 is close to the
value of Q-factor ( 31.25 10Q ). The picture of
wakefield excitation has undergone a qualitative
change. After the non-monotonic growth the wakefield
amplitude relatively quickly reaches its maximum
value. And the maximum shifted towards the region
leading front of bunches sequence. The amplitude of the
field decreases slowly until the last bunch. After last
bunch field non-monotonically decreases with higher
rate, compared with the region of bunches.
0 50 100 150 200 250 300 350 400 450 500 550 600
2
1
0
1
2
t/T1
E
z
,
k
V
/c
m
Fig. 3,c. Dependence of the field amplitude at the output
of the cavity in the case of nonresonant sequence of
bunches, 400N , 125Q , value of detuning is
3/ 2.5 10
0 50 100 150 200 250 300 350 400 450 500 550 600
2
1
0
1
2
t/T1
E
z
,
k
V
/c
m
Fig. 3,d. Dependence of the field amplitude at the output
of the cavity in the case of nonresonant sequence of
bunches, 200N , 125Q , value of detuning is
3/ 5 10
In Fig. 3,b dependence of the wakefield amplitude on
time for value of Q-factor 31.25 10Q is presented.
The picture of wakefield excitation practically does not
differ from the case of resonant excitation [1]. After the
non-monotonic growth amplitude reaches stationary
constant value. Of 400 bunches at such value of
Q-factor in process of the wakefield excitation
participates only the first 100 bunches. With a constant
value of amplitude decrease to almost 3.8 times
compared with the case of high Q-factor cavity (see Fig.
3,a). After the last bunch wakefield amplitude non-
monotonically decreases to zero (see Figs. 3,c; 3,d).
Thus, in this paper excitation of Cerenkov wakefield
oscillations in dielectric cavity with finite value of Q-
factor in the presence of detuning between the repetition
frequency of bunches in the chain and the frequency of
the excited oscillations is investigated. It is shown that
the picture of wake oscillations excitation is determined
by the ratio between the value of the Q -factor and
frequency detuning parameter / . For the high
Q -factor dielectric cavity /Q picture of
wake oscillations excitation is the same as in the cavity
without ohmic losses. If the opposite condition is
satisfied, the process of wakefield excitation occurs
almost as well as in the case of resonant excitation.
Finally, when both parameters are close in value
~ /Q , the intermediate case is realized (see
Fig. 3,b).
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. I.N. Onishchenko, G.V. Sotnikov, T.C. Marshal.
Amplitudes and Spectra of Wake Fields in a Planar
Dielectric Cavity with Finite Q-Factor // 12th Advanced
Accelerator Concepts Workshop, Lake Geneva,
Wisconsin (USA), 10-15 July 2006: AIP Conf.
Proceedings / Editors: Manoel Conde and Catherine
Eyberger, v. 877, p. 866-872.
2. V.A. Balakirev, I.N. Onishchenko,
A.P. Tolstoluzhsky. Wakefield Excitation and Electron
Acceleration at Detuning Bunch Repetition Frequency
and Frequency of Eigen Principal Mode of Wakefield //
Problems of Atomic Science and Technology. Ser.
“Plasma Electronics and New Acceleration Methods”.
2013, № 6, p. 80-83.
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
(in Russian).
Article received 26.11.2014
0 50 100 150 200 250 300 350 400 450 500 550 600
7.5
3.75
0
3.75
7.5
t/T1
E
z
,
k
V
/c
m
126 ISSN 1562-6016. ВАНТ. 2015. №1(95)
ВЛИЯНИЕ КОНЕЧНОГО ЗНАЧЕНИЯ ДОБРОТНОСТИ НА ВОЗБУЖДЕНИЕ КИЛЬВАТЕРНЫХ
КОЛЕБАНИЙ В ДИЭЛЕКТРИЧЕСКОМ РЕЗОНАТОРЕ ПОСЛЕДОВАТЕЛЬНОСТЬЮ
РЕЛЯТИВИСТСКИХ ЭЛЕКТРОННЫХ СГУСТКОВ ПРИ НАЛИЧИИ РАССТРОЙКИ МЕЖДУ
РЕЗОНАНСНОЙ ЧАСТОТОЙ И ЧАСТОТОЙ СЛЕДОВАНИЯ СГУСТКОВ
В.А. Балакирев, И.Н. Онищенко, А.П. Толстолужский
Изучен процесс возбуждения кильватерных колебаний в диэлектрическом резонаторе с конечным
значением добротности Q при наличии расстройки между частотой следования сгустков и частотой
резонансного колебания. Показано, что картина возбуждения кильватерных колебаний определяется
соотношением между значением добротности Q и параметром частотной расстройки / . В случае
высокой добротности диэлектрического резонатора /Q картина возбуждения кильватерных
колебаний такая же, как и в резонаторе без омических потерь. В диэлектрическом резонаторе формируется
биение кильватерного поля. Если выполнено противоположное условие, картина возбуждения кильватерных
колебаний практически не отличается от случая резонансного возбуждения. После начального линейного
роста амплитуды имеет место ее насыщение на постоянном уровне.
ВПЛИВ СКІНЧЕННОЇ ВЕЛИЧИНИ ДОБРОТНОСТІ НА ЗБУДЖЕННЯ КІЛЬВАТЕРНИХ
КОЛИВАНЬ У ДІЕЛЕКТРИЧНОМУ РЕЗОНАТОРІ ПОСЛІДОВНІСТЮ РЕЛЯТИВІСТСЬКИХ
ЕЛЕКТРОННИХ ЗГУСТКІВ ЗА НАЯВНОСТІ РОЗСТРОЙКИ МІЖ РЕЗОНАНСНОЮ ЧАСТОТОЮ
І ЧАСТОТОЮ СЛІДУВАННЯ ЗГУСТКІВ
В.А. Балакірєв, І.М. Оніщенко, О.П. Толстолужський
Вивчено процес збудження кільватерних коливань у діелектричному резонаторі із скінченним значенням
добротності Q при наявності розстройки між частотою проходження згустків і частотою резонансного
коливання. Показано, що картина збудження кільватерних коливань визначається співвідношенням між
значенням добротності Q й параметром частотної розстройки / . У випадку високої добротності
діелектричного резонатора /Q картина збудження кільватерних коливань така ж, як і в резонаторі
без омічних втрат. У діелектричному резонаторі формується биття кільватерного поля. Якщо виконана
протилежна умова, картина збудження кільватерних коливань практично не відрізняється від випадку
резонансного збудження. Після початкового лінійного росту амплітуди має місце її насичення на
постійному рівні.
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| id | nasplib_isofts_kiev_ua-123456789-82111 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1562-6016 |
| language | English |
| last_indexed | 2025-12-07T19:01:56Z |
| publishDate | 2015 |
| publisher | Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
| record_format | dspace |
| spelling | Balakirev, V.A. Onishchenko, I.N. Tolstoluzhsky, A.P. 2015-05-25T09:39:02Z 2015-05-25T09:39:02Z 2015 Influence of the finite q-factor on excitation of wakefield oscillations in dielectric cavity by a sequence of relativistic electron bunches in the presence of detuning between the resonant frequency and the bunch repetition frequency/ V.A. Balakirev, I.N. Onishchenko, A.P. Tolstoluzhsky // Вопросы атомной науки и техники. — 2015. — № 1. — С. 122-126. — Бібліогр.: 3 назв. — англ. 1562-6016 PACS: 41.75.Jv, 41.75.Lx, 41.75.Ht, 96.50.Pw https://nasplib.isofts.kiev.ua/handle/123456789/82111 Excitation of Cerenkov wakefield oscillations in dielectric cavity with finite value of Q-factor in the presence of detuning between the bunch repetition frequency and the resonant frequency of the excited oscillations is investigated. It is shown that the picture of wake oscillations excitation is determined by the ratio between the value of the Q-factor and frequency detuning parameter πω/δω. For the high Q-factor dielectric cavity Q >>πω/δω picture of wake oscillations excitation is the same as in the cavity without ohmic losses. If the opposite condition is satisfied, the process of wakefield excitation occurs almost as well as in the case of resonant excitation. Linear growth of the wakefield amplitude at initial stage reaches its saturation level. Изучен процесс возбуждения кильватерных колебаний в диэлектрическом резонаторе с конечным значением добротности Q при наличии расстройки между частотой следования сгустков и частотой резонансного колебания. Показано, что картина возбуждения кильватерных колебаний определяется соотношением между значением добротности Q и параметром частотной расстройки πω/δω. В случае высокой добротности диэлектрического резонатора Q >>πω/δω картина возбуждения кильватерных колебаний такая же, как и в резонаторе без омических потерь. В диэлектрическом резонаторе формируется биение кильватерного поля. Если выполнено противоположное условие, картина возбуждения кильватерных колебаний практически не отличается от случая резонансного возбуждения. После начального линейного роста амплитуды имеет место ее насыщение на постоянном уровне. Вивчено процес збудження кільватерних коливань у діелектричному резонаторі із скінченним значенням добротності Q при наявності розстройки між частотою проходження згустків і частотою резонансного коливання. Показано, що картина збудження кільватерних коливань визначається співвідношенням між значенням добротності Q й параметром частотної розстройки πω/δω. У випадку високої добротності діелектричного резонатора Q >>πω/δω картина збудження кільватерних коливань така ж, як і в резонаторі без омічних втрат. У діелектричному резонаторі формується биття кільватерного поля. Якщо виконана протилежна умова, картина збудження кільватерних коливань практично не відрізняється від випадку резонансного збудження. Після початкового лінійного росту амплітуди має місце її насичення на постійному рівні. 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 Influence of the finite Q-factor on excitation of wakefield oscillations in dielectric cavity by a sequence of relativistic electron bunches in the presence of detuning between the resonant frequency and the bunch repetition frequency Влияние конечного значения добротности на возбуждение кильватерных колебаний в диэлектрическом резонаторе последовательностью релятивистских электронных сгустков при наличии расстройки между резонансной частотой и частотой следования сгустков Вплив скінченної величини добротності на збудження кільватерних коливань у діелектричному резонаторі послідовністю релятивістських електронних згустків за наявності розстройки між резонансною частотою і частотою слідування згустків Article published earlier |
| spellingShingle | Influence of the finite Q-factor on excitation of wakefield oscillations in dielectric cavity by a sequence of relativistic electron bunches in the presence of detuning between the resonant frequency and the bunch repetition frequency Balakirev, V.A. Onishchenko, I.N. Tolstoluzhsky, A.P. Плазменная электроника |
| title | Influence of the finite Q-factor on excitation of wakefield oscillations in dielectric cavity by a sequence of relativistic electron bunches in the presence of detuning between the resonant frequency and the bunch repetition frequency |
| title_alt | Влияние конечного значения добротности на возбуждение кильватерных колебаний в диэлектрическом резонаторе последовательностью релятивистских электронных сгустков при наличии расстройки между резонансной частотой и частотой следования сгустков Вплив скінченної величини добротності на збудження кільватерних коливань у діелектричному резонаторі послідовністю релятивістських електронних згустків за наявності розстройки між резонансною частотою і частотою слідування згустків |
| title_full | Influence of the finite Q-factor on excitation of wakefield oscillations in dielectric cavity by a sequence of relativistic electron bunches in the presence of detuning between the resonant frequency and the bunch repetition frequency |
| title_fullStr | Influence of the finite Q-factor on excitation of wakefield oscillations in dielectric cavity by a sequence of relativistic electron bunches in the presence of detuning between the resonant frequency and the bunch repetition frequency |
| title_full_unstemmed | Influence of the finite Q-factor on excitation of wakefield oscillations in dielectric cavity by a sequence of relativistic electron bunches in the presence of detuning between the resonant frequency and the bunch repetition frequency |
| title_short | Influence of the finite Q-factor on excitation of wakefield oscillations in dielectric cavity by a sequence of relativistic electron bunches in the presence of detuning between the resonant frequency and the bunch repetition frequency |
| title_sort | influence of the finite q-factor on excitation of wakefield oscillations in dielectric cavity by a sequence of relativistic electron bunches in the presence of detuning between the resonant frequency and the bunch repetition frequency |
| topic | Плазменная электроника |
| topic_facet | Плазменная электроника |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/82111 |
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