Wakefield spectra in the plasma-dielectric accelerator when changing the plasma density
The analysis of the changes in the spectra of a wake field excited in a cylindrical plasma-dielectric waveguide by relativistic electron bunch is carried out. Three variants of structures are considered: the parameters of the dielectric structure and bunches are fixed; inner or outer radius of the d...
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Національний науковий центр «Харківський фізико-технічний інститут» НАН України
2015
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| Zitieren: | Wakefield spectra in the plasma-dielectric accelerator when changing the plasma density / R.R. Kniaziev, P.I. Markov, I.N. Onishchenko, G.V. Sotnikov // Вопросы атомной науки и техники. — 2015. — № 4. — С. 105-110. — Бібліогр.: 12 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1859604121240207360 |
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| author | Kniaziev, R.R. Markov, P.I. Onishchenko, I.N. Sotnikov, G.V. |
| author_facet | Kniaziev, R.R. Markov, P.I. Onishchenko, I.N. Sotnikov, G.V. |
| citation_txt | Wakefield spectra in the plasma-dielectric accelerator when changing the plasma density / R.R. Kniaziev, P.I. Markov, I.N. Onishchenko, G.V. Sotnikov // Вопросы атомной науки и техники. — 2015. — № 4. — С. 105-110. — Бібліогр.: 12 назв. — англ. |
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| container_title | Вопросы атомной науки и техники |
| description | The analysis of the changes in the spectra of a wake field excited in a cylindrical plasma-dielectric waveguide by relativistic electron bunch is carried out. Three variants of structures are considered: the parameters of the dielectric structure and bunches are fixed; inner or outer radius of the dielectric tube is changed, so that the frequency of the first radial mode coincides with the frequency of the plasma wave. The latter two options are necessary in the case of a regular sequence of bunches to increase the amplitude of the wakefield. It is shown that in case of changes in the outer radius an increase in amplitude of the dielectric wave is due to the transformation of the multimode dielectric wave in a monochromatic wave, with the first harmonic, synchronous with the sequence of bunches.
Проведений аналіз зміни спектрів кільватерного поля, збуджуваного в циліндричному плазмово-діелектричному хвилеводі релятивістськими електронними згустками. Розглянуто три варіанти структур: параметри діелектричної структури й згустків фіксовані; внутрішній або зовнішній радіуси діелектричної трубки змінюються так, що частота першої радіальної моди збігається із частотою плазмової хвилі. Останні два варіанти необхідні у випадку використання регулярної послідовності згустків для збільшення амплітуди кільватерного поля. Показано, що у випадку зміни зовнішнього радіуса ріст амплітуди діелектричної хвилі пов'язаний із трансформацією багатомодового спектра діелектричної хвилі в одномодовий з першою гармонікою, яка синхронна з послідовністю згустків.
Проведен анализ изменения спектров кильватерного поля, возбуждаемого в цилиндрическом плазменно-диэлектрическом волноводе релятивистскими электронными сгустками. Рассмотрены три варианта структур: параметры диэлектрической структуры и сгустков фиксированы; внутренний или внешний радиусы диэлектрической трубки изменяются так, что частота первой радиальной моды совпадает с частотой плазменной волны. Последние два варианта необходимы в случае использования регулярной последовательности сгустков для увеличения амплитуды кильватерного поля. Показано, что в случае изменения внешнего радиуса рост амплитуды диэлектрической волны связан с трансформацией многомодового спектра диэлектрической волны в одномодовый с первой гармоникой, синхронной с последовательностью сгустков.
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ISSN 1562-6016. ВАНТ. 2015. №4(98) 105
WAKEFIELD SPECTRA IN THE PLASMA-DIELECTRIC
ACCELERATOR WHEN CHANGING THE PLASMA DENSITY
R.R. Kniaziev1,2, P.I. Markov2, I.N. Onishchenko2, G.V. Sotnikov2
1V.N. Karazin Kharkiv National University, Kharkov, Ukraine;
2National Science Center “Kharkov Institute of Physics and Technology”, Kharkov, Ukraine
E-mail: sotnikov@kipt.kharkov.ua
The analysis of the changes in the spectra of a wake field excited in a cylindrical plasma-dielectric waveguide by
relativistic electron bunch is carried out. Three variants of structures are considered: the parameters of the dielectric
structure and bunches are fixed; inner or outer radius of the dielectric tube is changed, so that the frequency of the
first radial mode coincides with the frequency of the plasma wave. The latter two options are necessary in the case
of a regular sequence of bunches to increase the amplitude of the wakefield. It is shown that in case of changes in
the outer radius an increase in amplitude of the dielectric wave is due to the transformation of the multimode dielec-
tric wave in a monochromatic wave, with the first harmonic, synchronous with the sequence of bunches.
PACS: 41.75.Ht, 41.75.Lx, 41.75.Jv, 96.50.Pw
INTRODUCTION
Using plasma as an element of accelerating structure
is perspective, rapidly developing direction of wakefield
acceleration methods [1]. Plasma provides not only gi-
ant accelerating fields, which are unattainable in con-
ventional accelerators, but also give an ability to focus
accelerated bunch [2, 3]. If we use another drive bunch
of electrons for wakefield excitation, plasma will focus
this bunch too. But the area of the focusing phase lim-
ited to quarter length of plasma wave. At the boundaries
of this interval accelerating field or focusing field turn
to zero, so real accelerated bunches must have signifi-
cantly smaller length than quarter length of excited
wave.
Another type of wakefield accelerator structures, di-
electric wakefield accelerator (DWA), also allows to
receive the accelerating gradients, surpassing those in
traditional accelerators [4 - 6]. Although these gradients
are inferior than accelerating gradients in plasma wake-
field structures, but DWA has it's own advantages, asso-
ciated with the simplicity of manufacture, stable operat-
ing, repeatable results etc. [7]. For focusing accelerated
bunches in DWA were suggested to fill drift channel by
isotropic plasma with a certain density [8, 9]. In such
wakefield accelerator structure acceleration is produced
by a longitudinal electric field of dielectric wave, and
focusing − by transverse field of a plasma wave.
In case, considered in the papers [8, 9], the plasma
density was small, so the spatial period of the plasma
wave was bigger than wavelength of any dielectric
mode. Possibilities of increasing the amplitude of the
accelerating field by increasing longitudinal electric
field of plasma wave with increasing density of the
plasma had been analyzed by us1.
Main results of these investigations are the next. A
case without frequency adjustment of bunch repetition
and the eigen frequencies of the structure was consid-
ered. Also were reviewed cases with this frequency ad-
justment, when changing the plasma density, synchro-
nously changes frequency of the first radial mode of
dielectric wave.
1 The results will be published somewhere: R.R. Kniaziev, I.N.
Onishchenko, G.V. Sotnikov. Wakefield generation when filling
dielectric structure with a plasma.
It turned out, that the amplitude of the dielectric wave
with increasing plasma density behaves differently, de-
pending on the method of the first radial mode dielectric
wave frequency adjustment, by varying the outer radius
or by varying the inner radius of dielectric tube.
The observed behavior of the total field and dielec-
tric wave field is qualitatively different from the behav-
ior of wakefield of the plasma density in the case of a
dielectric waveguide with magnetized plasma in the
drift channel [10, 11], where the amplitude of the wake
field increases with increasing of plasma density.
In order to understand the behavior of the amplitude
of total Wakefield and its components from plasma den-
sity we continue research begun before.
Research results of depending spectral characteris-
tics of accelerating field, excited in the plasma wake-
field dielectric structure, from the plasma density are,
presented in this paper.
1. STATEMENT OF THE PROBLEM
Let there beam et a waveguide with radius b , in
which is inserted the dielectric tube with inner radius a ,
and its outer radius coincides with the radius of the met-
al waveguide. The dielectric constant of the tube mate-
rial is .ε Dielectric tube channel (drift channel) is com-
pletely filled with an isotropic plasma with density pn .
In drift channel travels regular sequence of bN electron
bunches of cylindrical shape with uniform distribution
of the charge density inside each bunch. The length of a
single bunch is bL , radius the total charge for each
bunch is 0Q . Leading bunches move uniform rectilinear,
and they excite wake field, which then accelerates test
bunches (accelerated bunches). All such system we will
call plasma-dielectric wakefield accelerator (PDWA).
2. EXPRESSIONS FOR THE FIELDS
Current density, produced by electron bunches with
uniform density distribution inside them, looks as:
{ }0
1
( ) [ ( 1) ] [ ( 1) ] ,
bN
b b
i
j zQ r r i T i Tτ τ τ
=
= Q − Q − − −Q − − −∑
(1)
where 0/t z vτ = − ; 0/b bL vτ = ; ( )τQ is Heaviside
function; T is the repetition period of bunches; 0v is
ISSN 1562-6016. ВАНТ. 2015. №4(98) 106
longitudinal velocity of bunch electrons; z is the unit
vector along the axis of the waveguide.
Solving Maxwell's equations with the source like
(1), we obtain expressions for wakefield in plasma and
dielectric. Further we are interested only in the longitu-
dinal component of wakefield zE in drift channel. It
can be shown as [8, 9]:
[ ]0
||2
1
4
( ) ( ) ( 1)
bN
s s
z s b z
i s
Q
E R r e r i T
a
τ
=
= − Ψ − − −∑∑
[ ]0
||
1
4
( ) ( 1) .
bN
p p
z
ib b
Q
e r i T
r L
τ
=
− Ψ − −∑ (2)
In equation (2) functions , ( )p s
ze r , describe the trans-
verse field structure, and function ,
|| ( )p s τΨ , describe the
longitudinal structure of a field:
1/2
0
0
( )
( )
'( ) ( )
s
ps
z s
s s p
I rae r
D I a
κ
ω ω κ
=
, (3)
0
1
0
1
0
0
( )1 ( , ),
( )
( )
( )
( , ),
( )
p
p b p b
p b pp
z
p
p p b b
p
I k r
k r k a r r
k r I k a
e r
I k r
k a k r r r a
I k a
− ∆ <
=
∆ < <
, (4)
,
|| ,
,
1( ) sin( ) ( )p s
p s
p s b
τ ω τ τ
ω τ
Ψ = Q −
,sin[ ( )] ( ) ,p s b bω τ τ τ τ − − Q − (5)
designation left in (2)-(5) are:
2( ) ( )s
s b z bs
p b
R r e r
rκ
= , 0/p pk vω= , 0 0 /v cβ = ,
1/22
0 01 ( ) /s
p p s s vκ β ε ω ω = − , 2 2( ) 1 /p pε ω ω ω= − ,
2 24p pe n mω π= , '( ) ( ) /D dD dω ω ω= ,
0 0( , ) ( ) ( ) ( 1) ( ) ( )n
n n nx y I x K y K x I y∆ = − − ,
where -e, m are charge, mass of electrons; nI and nK -
modified Bessel and Macdonald functions n-th order.
Eigen frequencies sω of dielectric waves are deter-
mined by solving the dispersion equation:
( )
1 1
0 0
( ) ( ) ( , )( ) 0
( ) ,
s s s
p s p d d
s s s s s s
p p d d d
I a F a bD
I a F a b
ε ω κ κ κεω
κ κ κ κ κ
≡ + = , (6)
where ( )1/22
0 01d s vκ β ε ω= − ,
[ ]0 0( , ) ( 1) ( ) ( ) ( ) ( )n
n n nF x y J x Y y Y x J y= − − ; nJ and nY -
Bessel and Weber functions n-th order.
As we can see from (2), the longitudinal electric
field consists of two parts. The first amount describes
the wake field of dielectric waves, another – wake field
of plasma wave. They were both excited by a relativistic
electron bunch. By varying the density of the plasma the
ratio between the amplitudes of plasma and dielectric
waves can be changed. The excitation the two types of
waves in isotropic plasma is the significant difference
from case of wakefield excitation in a magnetized plas-
ma [10, 11], where for excitation of plasma wave by
electron bunch an upper limit on its energy exists. But
such bunches are not of interest for the given accelerator
scheme, so we can assume, that relativistic electron
bunches do not excite plasma wave in a magnetized
plasma waveguide.
3. NUMERICAL ANALYSIS
OF WAKEFIELD SPECTRUM
To investigate the dependence of the amplitude of the
longitudinal electric field in PDWA as the initial param-
eters of dielectric structure and bunches parameters,
typical for the experimental apparatus “Almaz-2”were
taken [12]: 1.1a = cm, 4.3b = cm, 2.1ε = , 1.0br = cm,
1.7bL = cm, 0 0.32Q = − nC, energy electron bunch-
es 5bU = MeV. For such parameters the eigen frequency
of the first radial mode of vacuum structure, defined by
the equation (3), 1 1 / 2 2710f ω π= = MHz.
With the increase of the plasma density the resonant
frequency of the first radial mode dielectric wave in-
creases, and if fix the frequency of bunch repetition,
then synchronicity of bunches effect on structure will
deteriorate, and the amplitude of the total wakefield will
be reduced. Under total field we understand the sum of
plasma wakefield and the dielectric wakefield. To pre-
vent violations of synchronicity it was proposed to
change the dimensions of the structure so the resonant
frequency of the Cherenkov the first radial mode dielec-
tric wave was equal to the plasma frequency. The repeti-
tion frequency of bunches adjust to these frequencies.
Fig. 1. Dependence of wakefield amplitude in PDWA
with changing outer radius from plasma density
for different numbers of bunches
in a sequence ( bN 1,4,11,21= ): total field (a);
dielectric wave field (b). For comparison open symbols
show the field of the first radial mode of dielectric wave
a
b
ISSN 1562-6016. ВАНТ. 2015. №4(98) 107
Fig. 1 shows the dependence of the amplitude of the
axial force (the maximum value of the longitudinal
force behind bunch on the axis of the drift channel)
z zF eE= − , acting on a test electron, from the density of
the plasma for different numbers of bunches in the se-
quence: one bunch, 4, 11 and 21. Fig. 1,a corresponds to
the total wake field, Fig. 1,b – dielectric wave (first
double sum in equation (2)). The values of the outer
radius of the waveguide at different plasma densities are
given in Table.
Outer radius b of dielectric tube in case adjusting
the first radial mode dielectric wave to frequency
of plasma wave
np, cm-3
ωp/2π, MHz b, cm
1010 897.9 12.406
105 10⋅ 2008 5.815
1110 2839 4.31
112 10⋅ 4015 3.281
115 10⋅ 6349 2.4115
1210 8979 1.997
125 10⋅ 20080 1.479
1310 28390 1.3638
According to Fig. 1,b, for bunch sequences the total
field increases with increasing of plasma density, reach-
es its maximum, and then decreases. Maximum of ac-
celerating field if 12~ 10pn cm-3 is due to plasma wave
field maximum [9]. The increase of the total field over a
range of plasma densities 113 10pn < ⋅ cm-3 related as
with increasing plasma wave field, and also with in-
creasing dielectric wave field (Fig. 2,b). In same time,
for a single bunch increasing of dielectric wave ampli-
tude on the entire range of plasma densities is not seen
(see black solid line on Fig. 1,b). Dielectric wave ampli-
tude is almost constant at low plasma densi-
ties 112 10pn ≤ ⋅ cm-3, then decreases with further in-
crease of the plasma density. As shown by numerical
analysis so different behavior of the amplitude of the
dielectric wave in the case of structure excitation by a
single bunch or by bunches sequence is due to changing
spectral characteristics of excited wakefield. On Fig. 1,b
amplitude value of the first radial mode of dielectric
wave at different plasma densities are shown by open
symbols. For a single bunch the dielectric wakefield
increases with increasing of plasma density from zero
and reaches its maximum in range np=(2…5)·1011 cm-3.
Bunches, injected in PDWA, with a repetition rate equal
the frequency of a first radial mode, will only reinforce
this resonance mode. So the more bunches are in the
chain, the more precisely the amplitude of the total field
dielectric wave will approach the resonant radial mode
field. Open symbols on Fig. 1,b demonstrate this clearly.
Fig. 2 shows the spectral characteristics of a total
wakefield at different plasma densities. For the low
plasma density, 1010pn = cm-3 (which corresponds to the
outer radius of the waveguide 12.4 cm), spectrum of
wakefield is multimode. 5-th harmonic dielectric wave
has maximum amplitude, amplitude of 1st harmonic is
small and comparable in magnitude with the amplitude
of the plasma wave.
Fig. 2. Amplitudes of the wakefield harmonics
for different plasma densities: np=1010 cm-3 (a);
np=2·1011 cm-3 (b); np=1012cm-3 (c); np=1013 cm-3 (d).
Light green squares mark dielectric waves amplitudes
(right scale), black – plasma wave amplitude (left
scale). The outer radius of the dielectric tube
is changed in accordance with the Table
Note that due to the slow decay of the harmonic am-
plitudes with high number in the calculation of the total
field we used 30 harmonic of dielectric wave. With the
increase of the plasma density the spectrum of the excit-
ed oscillations is narrowed (in a relative meaning) and
shifted to lower harmonic numbers. For example, for the
density 112 10pn = ⋅ cm-3 (see Fig. 2,b) the first harmonic
becomes dominant and major contribution to the total
field make plasma wave and first and second radial
modes of dielectric wave. When the plasma density is
a
b
c
d
ISSN 1562-6016. ВАНТ. 2015. №4(98) 108
1210pn = cm-3 (see Fig. 2,с), when the maximum of the
total of the accelerating field, plasma wave becomes the
predominant, in dielectric modes notable importance
has only the first mode of dielectric wave. And if the
plasma density is 1310pn = cm-3 (see Fig. 2,d) in the
spectrum of the total field is presented only plasma
wave.
0 20 40 60 80 100
-20
-10
0
10
20
Langmuir
Dielectric
Total
Fz
(k
eV
/m
)
ξ=v0τ, cm
a)
0 20 40 60 80 100
-20
-10
0
10
20
Langmuir
Dielectric
Total
Fz
(k
eV
/m
)
ξ=v0τ, cm
a)
0 10 20 30 40
-40
-30
-20
-10
0
10
20
30
40
b)
Fz
, k
eV
/m
ξ=v0τ, cm
Langmuir Dielectric Total
0 10 20 30 40
-40
-30
-20
-10
0
10
20
30
40
b)
Fz
, k
eV
/m
ξ=v0τ, cm
Langmuir Dielectric Total
0 5 10 15 20 25
-60
-40
-20
0
20
40
60
c)
Fz
, k
eV
/m
ξ=v0τ, cm
Langmuir Dielectric Total
0 5 10 15 20 25
-60
-40
-20
0
20
40
60
c)
Fz
, k
eV
/m
ξ=v0τ, cm
Langmuir Dielectric Total
0 2 4 6 8 10
-20
-10
0
10
20 d)
Fz
, k
eV
/m
ξ=v0τ, cm
Langmuir Dielectric Total
0 2 4 6 8 10
-20
-10
0
10
20 d)
Fz
, k
eV
/m
ξ=v0τ, cm
Langmuir Dielectric Total
Fig. 3. The time dependence of wakefield for the
same plasma densities, that on Fig. 2. Line ‘Total’
notes the total field, ‘Dielectric’ - dielectric wave
field, ‘Langmuir’ - plasma wave field
The axial wakefield structure for the same plasma
densities, as for Fig. 2 the spectral characteristics are
given, is shown in Fig. 3. When the plasma density
1010pn = cm-3 distribution has “spiking” character, the
amplitude of plasma wave is very small. But when the
density reaches 112 10pn = ⋅ cm-3 the plasma wave ampli-
tude coincides with dielectric wave amplitude. When
the plasma density 1210pn = cm-3 amplitude of plasma
wave much higher than dielectric waves amplitude, axi-
al distribution of which is already close to monochro-
matic. When the plasma density 1310pn = cm-3 only
plasma wave is excited.
Here is the spectra wakefield for the other two op-
tions PDWA, wakefield amplitude are investigated in
[10]. In Fig. 4 is shown the spectra wakefield for case
when frequency of the first radial mode is adjusted to
the repetition frequency of bunches by changing inner
radius of dielectric tube. With increasing plasma density
the radius of the drift of the channel should be in-
creased, so with increasing plasma density dielectric
wave amplitude decreases rapidly and the total field is
mainly determined by the field of a plasma wave.
This trend is clearly confirmed by comparing the
spectra of wakefield, shown on Figs. 4,а,b for two char-
acteristic plasma densities: np=1011 and 5·1011 cm-3.
Fig. 4. The amplitudes of the wakefield harmonics for
plasma densities np=1011 cm-3 (a) and np=5·1011 cm-3 (b)
in the case of changing the inner radius of dielectric
sleeve; inner radius a=1.085 and 3.094 cm. Blue rec-
tangles mark the dielectric wave amplitude (right
scale); black – plasma wave amplitude (left scale)
Distribution of wake field behind a bunch of two
plasma densities, which oscillation spectrum is shown in
Fig. 4, is shown in Fig. 5. For relatively low plasma
density 1110pn = cm-3 plasma wave amplitude and die-
lectric wave field amplitude same order. Although the
total field has irregular behavior, but the period of plas-
ma wave is approximately equal to period of the dielec-
b
a
c
d
a
b
ISSN 1562-6016. ВАНТ. 2015. №4(98) 109
tric wavefield. When using a sequence of bunches they
will be amplified synchronous.
0 10 20 30 40 50
-30
-20
-10
0
10
20
30
Langmuir Dielectric Total
Fz
, k
eV
/m
ξ=v0τ, cm
a)
0 10 20 30 40 50
-30
-20
-10
0
10
20
30
Langmuir Dielectric Total
Fz
, k
eV
/m
ξ=v0τ, cm
a)
0 10 20 30 40 50
-60
-40
-20
0
20
40
60
ξ=v0τ, cm
Langmuir Total Dielectric
Fz
, k
eV
/m
b)
-0.08
-0.06
-0.04
-0.02
0.00
0.02
0.04
0.06
0.08
Fz
, k
eV
/m
0 10 20 30 40 50
-60
-40
-20
0
20
40
60
ξ=v0τ, cm
Langmuir Total Dielectric
Fz
, k
eV
/m
b)
-0.08
-0.06
-0.04
-0.02
0.00
0.02
0.04
0.06
0.08
Fz
, k
eV
/m
Fig. 5. The time dependence of wakefield for the case
of change in the radius of the drift channel. The plasma
density and radius of the channel as shown in caption
of Fig. 4
Third variant of PDWA – without the use of any
method of adjusting the eigen frequencies. The parame-
ters of the dielectric structure and the bunch are fixed,
only plasma density is changed. In Fig. 6 are given axial
distributions of the total field and its components (see
designation as in Fig. 3) for three values of the density
of the plasma. As it follows from Fig. 6,b for plasma
density 1110pn = cm3 plasma and dielectric waves are
same, that increases the amplitude of the total field.
When the plasma density is 1210pn = cm3 the longitudi-
nal structure of the field is almost entirely determined
by the plasma wave.
Work supported in part by NAS of Ukraine program
"Perspective investigations on plasma physics, con-
trolled thermonuclear fusion and plasma technologies",
Project P-1/63-2015 "Development of physical princi-
ples of plasma-dielectric wakefield accelerator".
0 10 20 30 40 50
-30
-20
-10
0
10
20
30 Langmuir Dielectric Total
Fz
, k
eV
/m
ξ=v0τ, cm
a)
0 10 20 30 40 50
-30
-20
-10
0
10
20
30 Langmuir Dielectric Total
Fz
, k
eV
/m
ξ=v0τ, cm
a)
0 10 20 30 40 50
-30
-20
-10
0
10
20
30
Langmuir Dielectric Total
Fz
, k
eV
/m
ξ=v0τ, cm
b)
0 10 20 30 40 50
-30
-20
-10
0
10
20
30
Langmuir Dielectric Total
Fz
, k
eV
/m
ξ=v0τ, cm
b)
0 5 10 15 20 25 30
-40
-20
0
20
40
Langmuir Dielectric Total
Fz
, k
eV
/m
ξ=v0τ, cm
c
0 5 10 15 20 25 30
-40
-20
0
20
40
Langmuir Dielectric Total
Fz
, k
eV
/m
ξ=v0τ, cm
c
Fig. 6. The time dependence of wakefield in the case
with fixed parameters PDWA except plasma density:
np=1010 cm-3 (a); np=1011 cm-3 (b); np=1012 cm-3 (с)
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Article received 03.06.2015
СПЕКТРЫ КИЛЬВАТЕРНОГО ПОЛЯ В ПЛАЗМЕННО-ДИЭЛЕКТРИЧЕСКОМ УСКОРИТЕЛЕ
ПРИ ИЗМЕНЕНИИ ПЛОТНОСТИ ПЛАЗМЫ
Р.Р. Князев, П.И. Марков, И.Н. Онищенко, Г.В. Сотников
Проведен анализ изменения спектров кильватерного поля, возбуждаемого в цилиндрическом плазменно-
диэлектрическом волноводе релятивистскими электронными сгустками. Рассмотрены три варианта струк-
тур: параметры диэлектрической структуры и сгустков фиксированы; внутренний или внешний радиусы
диэлектрической трубки изменяются так, что частота первой радиальной моды совпадает с частотой плаз-
менной волны. Последние два варианта необходимы в случае использования регулярной последовательно-
сти сгустков для увеличения амплитуды кильватерного поля. Показано, что в случае изменения внешнего
радиуса рост амплитуды диэлектрической волны связан с трансформацией многомодового спектра диэлек-
трической волны в одномодовый с первой гармоникой, синхронной с последовательностью сгустков.
СПЕКТРИ КІЛЬВАТЕРНОГО ПОЛЯ В ПЛАЗМОВО-ДІЕЛЕКТРИЧНОМУ ПРИСКОРЮВАЧІ
ПРИ ЗМІНІ ГУСТИНИ ПЛАЗМИ
Р.Р. Князєв, П.І. Марков, І.М. Онiщенко, Г.В. Сотнiков
Проведений аналіз зміни спектрів кільватерного поля, збуджуваного в циліндричному плазмово-
діелектричному хвилеводі релятивістськими електронними згустками. Розглянуто три варіанти структур:
параметри діелектричної структури й згустків фіксовані; внутрішній або зовнішній радіуси діелектричної
трубки змінюються так, що частота першої радіальної моди збігається із частотою плазмової хвилі. Останні
два варіанти необхідні у випадку використання регулярної послідовності згустків для збільшення амплітуди
кільватерного поля. Показано, що у випадку зміни зовнішнього радіуса ріст амплітуди діелектричної хвилі
пов'язаний із трансформацією багатомодового спектра діелектричної хвилі в одномодовий з першою гармо-
нікою, яка синхронна з послідовністю згустків.
INTRODUCTION
1. Statement of the problem
2. Expressions for the fields
3. Numerical analysis
of WAKEFIELD spectrum
references
сПеКТРЫ КИЛЬВАТЕРНОГО поля в плазменно-диэлектрическом ускорителе ПРИ Изменении плотности плазмы
спектри КІЛЬВАТЕРНОГО поля в плазмоВО-діелектричному прискорювачі ПРИ Зміні ГУСТИНИ плазми
|
| id | nasplib_isofts_kiev_ua-123456789-112190 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1562-6016 |
| language | English |
| last_indexed | 2025-11-28T02:09:00Z |
| publishDate | 2015 |
| publisher | Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
| record_format | dspace |
| spelling | Kniaziev, R.R. Markov, P.I. Onishchenko, I.N. Sotnikov, G.V. 2017-01-17T20:26:51Z 2017-01-17T20:26:51Z 2015 Wakefield spectra in the plasma-dielectric accelerator when changing the plasma density / R.R. Kniaziev, P.I. Markov, I.N. Onishchenko, G.V. Sotnikov // Вопросы атомной науки и техники. — 2015. — № 4. — С. 105-110. — Бібліогр.: 12 назв. — англ. 1562-6016 PACS: 41.75.Ht, 41.75.Lx, 41.75.Jv, 96.50.Pw https://nasplib.isofts.kiev.ua/handle/123456789/112190 The analysis of the changes in the spectra of a wake field excited in a cylindrical plasma-dielectric waveguide by relativistic electron bunch is carried out. Three variants of structures are considered: the parameters of the dielectric structure and bunches are fixed; inner or outer radius of the dielectric tube is changed, so that the frequency of the first radial mode coincides with the frequency of the plasma wave. The latter two options are necessary in the case of a regular sequence of bunches to increase the amplitude of the wakefield. It is shown that in case of changes in the outer radius an increase in amplitude of the dielectric wave is due to the transformation of the multimode dielectric wave in a monochromatic wave, with the first harmonic, synchronous with the sequence of bunches. Проведений аналіз зміни спектрів кільватерного поля, збуджуваного в циліндричному плазмово-діелектричному хвилеводі релятивістськими електронними згустками. Розглянуто три варіанти структур: параметри діелектричної структури й згустків фіксовані; внутрішній або зовнішній радіуси діелектричної трубки змінюються так, що частота першої радіальної моди збігається із частотою плазмової хвилі. Останні два варіанти необхідні у випадку використання регулярної послідовності згустків для збільшення амплітуди кільватерного поля. Показано, що у випадку зміни зовнішнього радіуса ріст амплітуди діелектричної хвилі пов'язаний із трансформацією багатомодового спектра діелектричної хвилі в одномодовий з першою гармонікою, яка синхронна з послідовністю згустків. Проведен анализ изменения спектров кильватерного поля, возбуждаемого в цилиндрическом плазменно-диэлектрическом волноводе релятивистскими электронными сгустками. Рассмотрены три варианта структур: параметры диэлектрической структуры и сгустков фиксированы; внутренний или внешний радиусы диэлектрической трубки изменяются так, что частота первой радиальной моды совпадает с частотой плазменной волны. Последние два варианта необходимы в случае использования регулярной последовательности сгустков для увеличения амплитуды кильватерного поля. Показано, что в случае изменения внешнего радиуса рост амплитуды диэлектрической волны связан с трансформацией многомодового спектра диэлектрической волны в одномодовый с первой гармоникой, синхронной с последовательностью сгустков. Work supported in part by NAS of Ukraine program "Perspective investigations on plasma physics, controlled thermonuclear fusion and plasma technologies", Project P-1/63-2015 "Development of physical principles of plasma-dielectric wakefield accelerator" en Національний науковий центр «Харківський фізико-технічний інститут» НАН України Вопросы атомной науки и техники Новые методы ускорения заряженных частиц Wakefield spectra in the plasma-dielectric accelerator when changing the plasma density Спектри кільватерного поля в плазмово-діелектричному прискорювачі при зміні густини плазми Спектры кильватерного поля в плазменно-диэлектрическом ускорителе при изменении плотности плазмы Article published earlier |
| spellingShingle | Wakefield spectra in the plasma-dielectric accelerator when changing the plasma density Kniaziev, R.R. Markov, P.I. Onishchenko, I.N. Sotnikov, G.V. Новые методы ускорения заряженных частиц |
| title | Wakefield spectra in the plasma-dielectric accelerator when changing the plasma density |
| title_alt | Спектри кільватерного поля в плазмово-діелектричному прискорювачі при зміні густини плазми Спектры кильватерного поля в плазменно-диэлектрическом ускорителе при изменении плотности плазмы |
| title_full | Wakefield spectra in the plasma-dielectric accelerator when changing the plasma density |
| title_fullStr | Wakefield spectra in the plasma-dielectric accelerator when changing the plasma density |
| title_full_unstemmed | Wakefield spectra in the plasma-dielectric accelerator when changing the plasma density |
| title_short | Wakefield spectra in the plasma-dielectric accelerator when changing the plasma density |
| title_sort | wakefield spectra in the plasma-dielectric accelerator when changing the plasma density |
| topic | Новые методы ускорения заряженных частиц |
| topic_facet | Новые методы ускорения заряженных частиц |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/112190 |
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