Theoretical studies of the resonator concept of dielectric wakewield accelerator
Theoretical studies and numerical simulation of wakefield excitation in planar dielectric resonator by regular sequence of relativistic electron bunches are carried out. It is shown, that in resonator case at conservation of field peaking, i.e. maintenance of multimode condition, the number of bun...
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Національний науковий центр «Харківський фізико-технічний інститут» НАН України
2006
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| Цитувати: | Theoretical studies of the resonator concept of dielectric wakewield accelerator / N.I. Onishchenko, G.V. Sotnikov // Вопросы атомной науки и техники. — 2006. — № 5. — С. 203-207. — Бібліогр.: 9 назв. — англ. |
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Onishchenko, N.I. Sotnikov, G.V. 2015-05-12T20:03:38Z 2015-05-12T20:03:38Z 2006 Theoretical studies of the resonator concept of dielectric wakewield accelerator / N.I. Onishchenko, G.V. Sotnikov // Вопросы атомной науки и техники. — 2006. — № 5. — С. 203-207. — Бібліогр.: 9 назв. — англ. 1562-6016 PACS: 41.60.-m https://nasplib.isofts.kiev.ua/handle/123456789/81182 Theoretical studies and numerical simulation of wakefield excitation in planar dielectric resonator by regular sequence of relativistic electron bunches are carried out. It is shown, that in resonator case at conservation of field peaking, i.e. maintenance of multimode condition, the number of bunches, participating in wakefield summing, is increased. As a result the amplitude of the field, used for charged particle acceleration, essentially increases in comparison with a section of the dielectric waveguide of the same length. Thus, legitimacy of the resonator concept for wakefield method of charged particle acceleration is proved. Numerical calculations are carried out for planned experiment on accelerator "Almaz-2" on wakefield excitation in the rectangular dielectric resonator by a sequence of bunches with charge 0.32 nC and energy 4 MeV each. Проведено теоретическое исследование и численное моделирование возбуждения кильватерного поля в плоском диэлектрическом резонаторе регулярной последовательностью сгустков релятивистских электронов. Показано, что в резонаторном случае при сохранении пикирования поля, т.е. многомодового режима, увеличивается количество сгустков, участвующих в суммировании кильватерного поля. В результате амплитуда поля, используемая для ускорения заряженных частиц, существенно возрастает по сравнению с отрезком диэлектрического волновода такой же длины. Таким образом, в работе доказана правомерность резонаторной концепции для кильватерного метода ускорения заряженных частиц. Численные расчеты выполнены для планируемого эксперимента на ускорителе “Алмаз-2” по возбуждению кильватерного поля в прямоугольном диэлектрическом резонаторе последовательностью сгустков с зарядом 0.32 нК и энергией 4 МэВ каждый. Проведено теоретичне дослідження та чисельне моделювання збудження кільватерного поля у плоскому діелектричному резонаторі регулярною послідовністю згустків релятивістських електронів. Показано, що у резонаторному випадку при збереженні пікірування поля, тобто багатомодового режиму, збільшується кількість згустків, що приймають участь у підсумовуванні кільватерного поля. В результаті амплітуда поля, що використовується для прискорення заряджених часток, істотно зростає у порівнянні з відрізком діелектричного хвилеводу такої самої довжини. Таким чином, у роботі доведена правомірність резонаторної концепції для кільватерного методу прискорення заряджених часток. Чисельні розрахунки виконані для запланованого експерименту на прискорювачі “Алмаз-2” по збудженню кільватерного поля у прямокутному діелектричному резонаторі послідовністю згустків з зарядом 0.32 нК та енергією 4 МеВ кожний. The study is supported in part by CRDF Grant No. UP2-2569-KH-04. en Національний науковий центр «Харківський фізико-технічний інститут» НАН України Вопросы атомной науки и техники Новые методы ускорения Theoretical studies of the resonator concept of dielectric wakewield accelerator Теоретические исследования резонаторной концепции ускорителя на кильватерных полях в диэлектрике Теоретичнi дослiдження резонаторної концепцiї прискорювача на кільватерних хвилях у дієлектрику Article published earlier |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| title |
Theoretical studies of the resonator concept of dielectric wakewield accelerator |
| spellingShingle |
Theoretical studies of the resonator concept of dielectric wakewield accelerator Onishchenko, N.I. Sotnikov, G.V. Новые методы ускорения |
| title_short |
Theoretical studies of the resonator concept of dielectric wakewield accelerator |
| title_full |
Theoretical studies of the resonator concept of dielectric wakewield accelerator |
| title_fullStr |
Theoretical studies of the resonator concept of dielectric wakewield accelerator |
| title_full_unstemmed |
Theoretical studies of the resonator concept of dielectric wakewield accelerator |
| title_sort |
theoretical studies of the resonator concept of dielectric wakewield accelerator |
| author |
Onishchenko, N.I. Sotnikov, G.V. |
| author_facet |
Onishchenko, N.I. Sotnikov, G.V. |
| topic |
Новые методы ускорения |
| topic_facet |
Новые методы ускорения |
| publishDate |
2006 |
| language |
English |
| container_title |
Вопросы атомной науки и техники |
| publisher |
Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
| format |
Article |
| title_alt |
Теоретические исследования резонаторной концепции ускорителя на кильватерных полях в диэлектрике Теоретичнi дослiдження резонаторної концепцiї прискорювача на кільватерних хвилях у дієлектрику |
| description |
Theoretical studies and numerical simulation of wakefield excitation in planar dielectric resonator by regular
sequence of relativistic electron bunches are carried out. It is shown, that in resonator case at conservation of field
peaking, i.e. maintenance of multimode condition, the number of bunches, participating in wakefield summing, is
increased. As a result the amplitude of the field, used for charged particle acceleration, essentially increases in
comparison with a section of the dielectric waveguide of the same length. Thus, legitimacy of the resonator concept
for wakefield method of charged particle acceleration is proved. Numerical calculations are carried out for planned
experiment on accelerator "Almaz-2" on wakefield excitation in the rectangular dielectric resonator by a sequence of
bunches with charge 0.32 nC and energy 4 MeV each.
Проведено теоретическое исследование и численное моделирование возбуждения кильватерного поля в
плоском диэлектрическом резонаторе регулярной последовательностью сгустков релятивистских
электронов. Показано, что в резонаторном случае при сохранении пикирования поля, т.е. многомодового
режима, увеличивается количество сгустков, участвующих в суммировании кильватерного поля. В
результате амплитуда поля, используемая для ускорения заряженных частиц, существенно возрастает по
сравнению с отрезком диэлектрического волновода такой же длины. Таким образом, в работе доказана
правомерность резонаторной концепции для кильватерного метода ускорения заряженных частиц.
Численные расчеты выполнены для планируемого эксперимента на ускорителе “Алмаз-2” по возбуждению
кильватерного поля в прямоугольном диэлектрическом резонаторе последовательностью сгустков с зарядом
0.32 нК и энергией 4 МэВ каждый.
Проведено теоретичне дослідження та чисельне моделювання збудження кільватерного поля у плоскому
діелектричному резонаторі регулярною послідовністю згустків релятивістських електронів. Показано, що у
резонаторному випадку при збереженні пікірування поля, тобто багатомодового режиму, збільшується
кількість згустків, що приймають участь у підсумовуванні кільватерного поля. В результаті амплітуда поля,
що використовується для прискорення заряджених часток, істотно зростає у порівнянні з відрізком
діелектричного хвилеводу такої самої довжини. Таким чином, у роботі доведена правомірність резонаторної
концепції для кільватерного методу прискорення заряджених часток. Чисельні розрахунки виконані для
запланованого експерименту на прискорювачі “Алмаз-2” по збудженню кільватерного поля у прямокутному
діелектричному резонаторі послідовністю згустків з зарядом 0.32 нК та енергією 4 МеВ кожний.
|
| issn |
1562-6016 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/81182 |
| citation_txt |
Theoretical studies of the resonator concept of dielectric wakewield accelerator / N.I. Onishchenko, G.V. Sotnikov // Вопросы атомной науки и техники. — 2006. — № 5. — С. 203-207. — Бібліогр.: 9 назв. — англ. |
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| first_indexed |
2025-11-24T03:46:47Z |
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2025-11-24T03:46:47Z |
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| fulltext |
___________________________________________________________
ВОПРОСЫ АТОМНОЙ НАУКИ И ТЕХНИКИ. 2006. № 5.
Серия: Плазменная электроника и новые методы ускорения (5), с.203-207. 203
THEORETICAL STUDIES
OF THE RESONATOR CONCEPT OF DIELECTRIC
WAKEWIELD ACCELERATOR
N.I. Onishchenko, G.V. Sotnikov
National Science Center “Kharkov Institute of Physics and Technology”
Kharkov, Ukraine
E-mail: sotnikov@kipt.kharkov.ua
Theoretical studies and numerical simulation of wakefield excitation in planar dielectric resonator by regular
sequence of relativistic electron bunches are carried out. It is shown, that in resonator case at conservation of field
peaking, i.e. maintenance of multimode condition, the number of bunches, participating in wakefield summing, is
increased. As a result the amplitude of the field, used for charged particle acceleration, essentially increases in
comparison with a section of the dielectric waveguide of the same length. Thus, legitimacy of the resonator concept
for wakefield method of charged particle acceleration is proved. Numerical calculations are carried out for planned
experiment on accelerator "Almaz-2" on wakefield excitation in the rectangular dielectric resonator by a sequence of
bunches with charge 0.32 nC and energy 4 MeV each.
PACS: 41.60.-m
1. INTRODUCTION
Is dielectric wakefield accelerator (DWA) a tribute
to the modern style, does it arouse academic interest or
can it compete with other new and traditional methods
of acceleration? In favour of positive answer to the last
question it can be said, that numerous theoretical
investigations of acceleration with use of wakefields in
dielectric structures pass in a stage of the experimental
realization [1-3].
Acceleration with use of wakefields in dielectric
structures is one of varieties of two-beam methods of
acceleration in which for creating of intensive
longitudinal electrical field the high-current beam (or a
beam called driving) is used. Thus the necessity for use
of external source of microwave field takes out. The
second beam (or the beam called driven) is accelerated
in the field of the first beam. For experiments in
Brookhaven National Laboratory (BNL) [1] for
excitation of accelerating field the sequence of
supershort (with duration of 3.5 fs) electron bunches
with energy 500 MeV is used, and in experiments in
Argonne National Laboratory (ANL) [3] − the sequence
of short (with duration of 6.7 ps) electron bunches with
energy 15 MeV is used.
The attractiveness of dielectric wakefield accelerator
consists of the following:
• simplicity of its prototype creation (section of
waveguide) and of the further testing of main
principles;
• stability and easy controllability of slowing medium
parameters;
• possibility of sectioning with the purpose of
reaching high energies of accelerated particles.
The only essential weakness of DWA is the
possibility of breakdown on dielectric surface. Use of
ceramic structures [2] allows to increase considerably
breakdown thresholds and to reach electric field
strengths not below, than in traditional accelerators.
Other possibility of breakdown effect diminution is use
of dielectric structures and electron bunches with
micron sizes [1].
DWA can work in single-mode [2,3] or multimode
[4] conditions. Such classification is connected with
number of harmonics participating in complete
electromagnetic field forming. The electron bunch,
passing through dielectric structure, excites a set of
harmonics relevant to transversal modes of natural
oscillations of the structure. Therefore at use of
sequence of bunches in the first case for supporting of
effectiveness of the accelerator it is necessary to
suppress "parasitic" (not relevant to operation mode)
oscillations, and in the second case it is necessary to
choose the parameters of slowing structure so that to
provide equidistance of resonant with bunch
eigenfrequencies of structure. At that bunch repetition
rate should be multiple to wave length of principal
mode.
Wakefield strengths in multimode regime of DWA
are much higher than fields in single-mode regime.
However at use of cylindrical waveguide with partial
dielectric filling as dielectric structure realization of
multimode regime faces difficulties of maintenance of
excited frequency equidistance.
In the present work we investigate multimode
excitation of wakefields by a sequence of electron
bunches in the planar dielectric resonator. The need for
resonator concept of DWA originates in connection
with necessity of elimination of undesirable effect of
removal of wakefield with group velocity of excited
waves from waveguide dielectric structure [5]. The first
outcomes of theoretical examinations [6] and numerical
calculations with numerical PIC code KARAT [7],
carried out for cylindrical geometry of the dielectric
resonator, showed, that strong restriction on maximum
number of bunches which give the contribution to
growth of amplitude of the field, can be removed in
resonator concept of DWA. In an optimal condition
excitation of dielectric resonator by a sequence of
bunches is similar to excitation of resonator by mode-
locked laser equipped with an “optical switch”. At the
moment when reflected from the output of the resonator
short laser impulse comes to the input, the optical
switch injects the next impulse into the resonator. But,
mailto:sotnikov@kipt.kharkov.ua
as mentioned above, in cylindrical geometry it is
difficult to realize multimode condition of DWA
operation. Below, in planar geometry, we will consider
the possibility of combination of resonator advantage
with already available advantages of DWA, namely,
with multimode regime and use of great number of
bunches.
2. WAKEFIELD IN THE PLANAR
DIELECTRIC RESONATOR
Let's obtain the expression for longitudinal electric
field excited by a sequence of bunches in the dielectric
resonator. Let the planar metal resonator has a cross size
( ) and its length is equal a / 2 / 2a x a− ≤ ≤ L . The
wave guide is filled by the homogeneous dielectric with
permittivity ε . Along the axis of waveguide there is a
drift channel which sizes are small in comparison with
cross size of the resonator, that allows to neglect shift of
its eigenfrequencies in comparison with the complete
filling by dielectric. We will suppose, that
monoenergetic thin electron bunches are injected into
the input of resonator and then move with a
stationary velocity along the axis. The distribution of
current density of a single bunch have the form of:
0z =
0v
(1) ( ) ( )0 0 0
0 0 0
/
[ ( ) ( / )]/ ,
z b i
i i
j Q x x t t z v
t t t t L v v
δ δ
θ θ
= − − − ×
− − − − 0
where – a charge of a bunch per length unit in
direction, – the time of i
bQ
y 0it − th bunch injection into
the wave guide, 0x – cross coordinate of a bunch, ( )tθ −
Heaviside function.
Having solved the wave equation taking into account
vanishing of tangential components of electric field on
metal walls of the resonator, we will receive the
expression for longitudinal electric field:
]
2 2 2
0 10 2 2
0 1 0
2 2 2
0 0
2 2 2 2 2 2
0 0
0 0 0
cos( ) /
/sin ( ) sin ( ) ( )
/( 1) sin ( / )
sin ( / ) ( /
bN
l ml l
z l
i m l ml l ml
l l
ml i l i i
l
l ml l l l
ml i
ml l
l i i
k z k cE E
k ct t t t t t
k c k ct t L v
t t L v t t L
ω εδ ω
ω ω ω
ω εω ω θ
ω 0
/ω ε ω εω
ω ω
ω θ
∞ ∞
= = =
⎧⎡ −⎪= ×⎨⎢− ⎪⎣⎩
⎤−
− − − − −⎥
⎦
⎡ − −
− − − − ×⎢
⎣
− − − −
∑∑∑
}0 0) ( , ),mv G x x
8 /bE Q v aL
(2)
where
0 0 10π εω= − 0l lk vω = /m m aκ π= /lk l Lπ= ;
function lδ is equal 1 if and is equal 2 if 0l = 0l ≠ ;
,
− the number of bunches in a sequence.
Eigenfrequencies of the resonator and Cherenkov
frequencies are defined by expressions:
0 0( , ) sin[ ( / 2)]sin[ ( / 2)]m m mG x x x a x aκ κ= + + /m m aκ π=
bN
(3) 2 2 2 2
0( ) / ,ml m l l lk c k vω κ ε ω= + =
Apparently from (2) the complete field consists of
the field of space charge (relevant to frequencies lω )
and of the fields, excited by a bunch in the resonator on
frequencies mlω . After leaving of all particles the
resonator ( ) the field of space charge
disappears, and expression for longitudinal electric field
gets the form:
0 /Nbt t L v> +
2 2
0 10 2 2
0 1 0
0 0 0
cos( ) /
sin ( ) ( 1) sin ( / ) ( , ),
bN
l m
z l
i m l ml l ml
l
ml i ml i m
k z cE E
t t t t L v G x x
κ εδ ω
ω ω ω
ω ω
∞ ∞
= = =
= ×
−
⎡ ⎤− − − − −⎣ ⎦
∑∑∑
0
(4)
Let's note, that at realization of the condition
ml lω ω= (5)
the relevant items in the sum (4) become dominant. The
indicated condition is nothing else than as condition of
Cherenkov radiation in slowing medium. Then these
resonant items can be treated as Cherenkov field,
accumulated in dielectric resonator, and the rest of the
field as a field of transition radiation on both
boundaries. We should note, that radiation of a charged
particle in the vacuum rectangular resonator was
considered first in paper [8], and in the cylindrical
vacuum resonator in paper [9]. In these cases the
requirement of Cherenkov radiation is not fulfilled. For
our studies namely the resonant case is of interest.
Because of discreteness on longitudinal wave
numbers of oscillation spectrum, the resonant
condition at optional sizes of resonator, permittivity and
energy of bunch can be fulfilled only approximately and
only for a finite number of harmonics. Taking into
account, that we want to implement a multimode
condition of DWA, it makes sense to find the relation
between sizes from the resonant requirement. Let the
resonant condition is fulfilled for harmonic
lk
1m = , l N= . Then from (3),(5) we obtain
2
0 0 01, /L Na v cβ ε β= − = (6)
i.e. the length of the resonator should be multiple half-
integer of wave lengths of the basic resonant harmonic.
The condition of equidistance is fulfilled automatically
for harmonics l Nm= ( 1,2,m = K ), thus, multimode
operation regime of DWA is provided.
For supporting of coherent summing of fields in the
resonator it is necessary, that the resonant frequency
1Nω was multiple to frequency of bunch following. In
the case when bunches are injected on every period of
first harmonic with frequency 1Nf ω= of the wave, this
condition sets the cross size of the dielectric resonator
2
0 0/ 2 1a v f β ε= − (7)
Conditions (6) and (7) are the basis of the resonator
concept of dielectric wakefield accelerator. In such
resonator it is provided:
1. multimode regime of field excitation;
2. coherent summing of fields from bunches of
sequence.
Let's explain written above at discussion of
expression (4) and relations (6),(7) by graphic example.
In Fig.1 dispersion dependencies of dielectric
resonator ( 2.1ε = ), excited by a sequence of electron
bunches with energies 4 MeV , frequency of bunch
repetition 2.85f GHz= are presented. The cross size,
chosen according to condition (7), is equal
5,045a cm= , and
0
204
Fig.1. Eigenfrequencies of the dielectric resonator for
. First 9 cross harmonics of the resonator are
presented. Pentagons show Cherenkov frequencies of
the bunch
3N =
longitudinal size − according to requirement (6), is
equal 15,677L cm= (at that third longitudinal harmonic
is chosen as resonant, ). The horizontal grid on
fig.1 is lined with interval, equal to frequency of bunch
repetition, and vertical grid − with interval, equal to the
number of longitudinal resonant harmonic. As Fig.1
illustrates, cross points of Cherenkov frequencies
(pentagons) and eigenfrequencies of the resonator are
multiple to the frequency of bunch repetition.
3N =
3. NUMERICAL CALCULATIONS
Let bunches have rectangular shape and their
longitudinal size is , cross size is
(
bL ba
0/ 2 / 2ba x ab− ≤ ≤ ). Wakefield from a sequence of
bunches of finite sizes is obtained by integration of
expression (2) by time of injection and by cross
positions
0it
0x of microbunches:
[ ] [ ] [
[ ]
]
[ ]
2
0 02 2 2
0 1 0
2
0 0 02
cos( ) ( ) 1 cos ( / ) 1 cos ( / ) ( ) 1 cos
( / ) 1 cos ( / ) ( 1) ( ) 1 cos ( / ) 1 cos (
bN
l m
z b l i ml i i b ml i b i l i
i m l ml l ml
l m
i b l i b iL ml iL iL b ml iL b
ml
k zE E t t t L v t L v t t
t L v t L v t t t L v t L
δ θ ω θ ω θ
ω ω ω
θ ω θ ω θ ω
ω
∞ ∞
= = =
⎧ Ω ⎡ ⎤= − − − − − −⎨ ⎣ ⎦− ⎩
Ω
− − − − − − − − − −
∑ ∑ ∑
[ ]
[ ] [ ]}
0
0 0
/ )
( 1) ( ) 1 cos ( 1) ( / ) 1 cos ( / ) ( , , ),l l
iL l iL i b l iL b m b
v
t t t L v t L v G x a aθ ω θ ω
⎡ ⎤
ω− +
+⎣ ⎦
− − − − − − −
(8)
where: , ( 1)it t i T= − − 0/iL it t L v= − ,
, 2 2 2 2
0 0/( 1)m mvκ β εΩ = − 2 2
016 ( 1) /b b bE Q c a LL 2
bβ ε= − − ε
a
,
. 2sin ( / 2)sin( / 2 )cos( / )b
m bG m ma a mxπ π π=
Fig.2. Longitudinal distribution of electric field zE
in the centre of resonator ( ) at time
after injection of 5 bunches. Dashed line
shows the shape and position of bunches
0x =
1,738t =
205
ns
m
Let’s choose the following parameters for numerical
calculations: , , 1,7bL c= 0,1ba a= 10N = ,
, , the rest of parameters −
the same as on Fig.1. In Fig. 2 and Fig.3 distributions of
wakefield for two moments are presented:
101bN = 0.32 /bQ nC= cm
ns1,738t =
(5 bunches are injected into the resonator) and
(the last bunch of sequence is injected
into the resonator).
35,639t = ns
In initial stage of injection (Fig.2) the amplitude of
the field grows from the head of a sequence to the
location of the group wavefront, excited by the first
bunch, and then decreases to the input of the resonator.
Fig.3. The same, that on Fig.2 at instant
35,639t ns= after injection of 101 bunches
Wakefield in the resonator before leaving of the first
bunch qualitatively and quantitatively coincides with the
field in semi-infinite waveguide. The shape of wakefield
impulses and their duration approximately repeats the
shape and duration of bunches. In later times, after all
bunches are injected into the resonator, almost
homogeneous distribution of field amplitude is formed
in it.
In contrast to considered case of the resonator, in the
semi-infinite waveguide increasing from input to output
distribution of field amplitude [5] is formed. At that the
number of bunches working on build up of maximum
amplitude, is much lower, than in the resonator. For the
dielectric waveguide with the same length, cross size
and permittivity, as for the considered resonator this
number is equal 6. From comparison of Fig.2 and Fig.3
it follows, that all bunches of sequence equally
contribute to the forming of amplitude of longitudinal
electric field. I.e. it is possible to excite wakefield in the
resonator with the amplitude considerably exceeding
amplitude of field in the semi-infinite waveguide. At
that the regularity of oscillations is kept.
Fig.4. Time diagram (upwardly) of longitudinal
electric field and its spectral density
(below) in the dielectric resonator after injection of
101 bunches. Parameters are the same, as on Fig.3
( 0, 0zE x z= =
206
)
s
In Fig.4 time diagram of wakefield in the dielectric
resonator (above) after injection of 101st bunch is
presented, last bunch left the resonator at time t n38≈ .
Wakefield at input of the resonator has a shape of
rectangular pulses sequence with period equal to period
of bunch repetition rate. The amplitude of pulses weakly
varies with time. In the bottom part of Fig.4 the
spectrum of longitudinal electric field is presented. It is
seen, that only odd resonant frequencies constitute
wakefield. Non-resonant harmonics almost do not
contribute to amplitude of wakefield.
Fig.5. Time averaged on time ( 50 )
longitudinal distribution of wakefield in the centre
of resonator ( ). Parameters are the same, as
on Fig.4
85ns t ns≤ ≤
0x =
In Fig.5 longitudinal distribution of wakefield
averaged over time is presented. It is seen, that on
average over time, the standing wave is formed after
leaving of all bunches from the resonator. The narrow
peaks, formed by a great number of resonant harmonics,
have mean amplitude approximately and the
distance between them is equal to period of bunch
repetition.
33 /kV cm
For investigation of acceleration of driven bunch
electrons we took an axial bunch with duration and
energy, equal to duration and energy of driving bunches.
In Fig.6 the gain of energy of electrons, accelerated
along the resonator, is shown.
Fig.6. Gain of energy of electrons, accelerated
along the resonator. Parameters of the resonator
and sequence of bunches are the same, as on Fig.4
The gain of energy of at most accelerated electrons
is equal 1,6 MeV, that is approximately equal to half of
energy gain of a particle in the constant field, equal to
half of wakefield amplitude, excited in the resonator. In
Fig.7 the value of longitudinal electric field,
accelerating a particle along the resonator, is presented.
From comparison of Fig.6 and Fig.7 it follows, that
acceleration gradient is equal to mean of wakefield on
particle trajectory. Peaks of wakefield have the shape of
bunches and follow with period twice greater, than
period of wakefield. Such periodicity of field
distribution on particle trajectory is typical for a
resonator system.
Thus, carried out studies showed realizability of the
resonator concept of dielectric wakefield accelerator in
planar geometry.
207
Fig.7. Longitudinal electric field strength on the
trajectory of the most accelerated particle. Parameters
of the resonator and sequence of bunches are the same,
as on Fig.4
4. ACKNOWLEDGMENTS
The study is supported in part by CRDF Grant No.
UP2-2569-KH-04.
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using a dielectric-loaded waveguide // Nucl. Instr.
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P. Schoessow, A.D. Kanareykin. Measurements of
the longitudinal wakefields in a multimode,
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dorenko, G.V. Sotnikov. Excitation of a Wake Field
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v.93. p.33-42.
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dorenko, G.V. Sotnikov. Charged Particles
Accelerated by Wake Fields in a Dielectric
Resonator with Exciting Electron Bunch Channel //
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ТЕОРЕТИЧЕСКИЕ ИССЛЕДОВАНИЯ РЕЗОНАТОРНОЙ КОНЦЕПЦИИ УСКОРИТЕЛЯ
НА КИЛЬВАТЕРНЫХ ПОЛЯХ В ДИЭЛЕКТРИКЕ
Н.И.Онищенко, Г.В.Сотников
Проведено теоретическое исследование и численное моделирование возбуждения кильватерного поля в
плоском диэлектрическом резонаторе регулярной последовательностью сгустков релятивистских
электронов. Показано, что в резонаторном случае при сохранении пикирования поля, т.е. многомодового
режима, увеличивается количество сгустков, участвующих в суммировании кильватерного поля. В
результате амплитуда поля, используемая для ускорения заряженных частиц, существенно возрастает по
сравнению с отрезком диэлектрического волновода такой же длины. Таким образом, в работе доказана
правомерность резонаторной концепции для кильватерного метода ускорения заряженных частиц.
Численные расчеты выполнены для планируемого эксперимента на ускорителе “Алмаз-2” по возбуждению
кильватерного поля в прямоугольном диэлектрическом резонаторе последовательностью сгустков с зарядом
0.32 нК и энергией 4 МэВ каждый.
ТЕОРЕТИЧНI ДОСЛIДЖЕННЯ РЕЗОНАТОРНОЇ КОНЦЕПЦIЇ ПРИСКОРЮВАЧА
НА КІЛЬВАТЕРНИХ ХВИЛЯХ У ДІЄЛЕКТРИКУ
М.І.Онищенко, Г.В.Сотніков
Проведено теоретичне дослідження та чисельне моделювання збудження кільватерного поля у плоскому
діелектричному резонаторі регулярною послідовністю згустків релятивістських електронів. Показано, що у
резонаторному випадку при збереженні пікірування поля, тобто багатомодового режиму, збільшується
кількість згустків, що приймають участь у підсумовуванні кільватерного поля. В результаті амплітуда поля,
що використовується для прискорення заряджених часток, істотно зростає у порівнянні з відрізком
діелектричного хвилеводу такої самої довжини. Таким чином, у роботі доведена правомірність резонаторної
концепції для кільватерного методу прискорення заряджених часток. Чисельні розрахунки виконані для
запланованого експерименту на прискорювачі “Алмаз-2” по збудженню кільватерного поля у прямокутному
діелектричному резонаторі послідовністю згустків з зарядом 0.32 нК та енергією 4 МеВ кожний.
REFERENCES
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