Simulation of wakefields excited by a train of electron bunches in rectangular dielectric waveguide
Wake field excitation by a sequence of electron bunches in rectangular dielectric waveguide of finite length is investigated for acceleration with high gradient electric field. Characteristics of wake field for parameters of planned in NSC KIPT experiments are determined. Досліджені процеси збудженн...
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Національний науковий центр «Харківський фізико-технічний інститут» НАН України
2005
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| Цитувати: | Simulation of wakefields excited by a train of electron bunches in rectangular dielectric waveguide / N.I. Onishchenko, G.V. Sotnikov // Вопросы атомной науки и техники. — 2005. — № 1. — С. 146-148. — Бібліогр.: 9 назв. — англ. |
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Onishchenko, N.I. Sotnikov, G.V. 2015-03-24T08:11:05Z 2015-03-24T08:11:05Z 2005 Simulation of wakefields excited by a train of electron bunches in rectangular dielectric waveguide / N.I. Onishchenko, G.V. Sotnikov // Вопросы атомной науки и техники. — 2005. — № 1. — С. 146-148. — Бібліогр.: 9 назв. — англ. 1562-6016 PACS: 41.60.-m https://nasplib.isofts.kiev.ua/handle/123456789/78946 Wake field excitation by a sequence of electron bunches in rectangular dielectric waveguide of finite length is investigated for acceleration with high gradient electric field. Characteristics of wake field for parameters of planned in NSC KIPT experiments are determined. Досліджені процеси збудження кільватерного поля електронними згустками та їх послідовністю в прямокутних діелектричних хвилеводах скінченої довжини: напів обмеженого хвилеводу та резонаторі. Визначені характеристики кільватерного поля для параметрів запланованого в ННЦ ХФТІ експерименту Исследовано возбуждение кильватерного поля электронными сгустками и их последовательностью в прямоугольных диэлектрических волноводах конечной длины: полу бесконечном волноводе и резонаторе. Определены характеристики кильватерного поля для параметров планируемого в ННЦ ХФТИ эксперимента. The study is supported in part by CRDF Grant No. UP2-2569-KH-04 R en Національний науковий центр «Харківський фізико-технічний інститут» НАН України Вопросы атомной науки и техники Plasma electronics Simulation of wakefields excited by a train of electron bunches in rectangular dielectric waveguide Моделювання збудження кильватерного поля послідовністю електронних згустків в прямокутному діелектричному хвилеводі Моделирование возбуждения кильватерного поля последовательностью электронных сгустков в прямоугольном диэлектрическом волноводе Article published earlier |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine |
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DSpace DC |
| title |
Simulation of wakefields excited by a train of electron bunches in rectangular dielectric waveguide |
| spellingShingle |
Simulation of wakefields excited by a train of electron bunches in rectangular dielectric waveguide Onishchenko, N.I. Sotnikov, G.V. Plasma electronics |
| title_short |
Simulation of wakefields excited by a train of electron bunches in rectangular dielectric waveguide |
| title_full |
Simulation of wakefields excited by a train of electron bunches in rectangular dielectric waveguide |
| title_fullStr |
Simulation of wakefields excited by a train of electron bunches in rectangular dielectric waveguide |
| title_full_unstemmed |
Simulation of wakefields excited by a train of electron bunches in rectangular dielectric waveguide |
| title_sort |
simulation of wakefields excited by a train of electron bunches in rectangular dielectric waveguide |
| author |
Onishchenko, N.I. Sotnikov, G.V. |
| author_facet |
Onishchenko, N.I. Sotnikov, G.V. |
| topic |
Plasma electronics |
| topic_facet |
Plasma electronics |
| publishDate |
2005 |
| language |
English |
| container_title |
Вопросы атомной науки и техники |
| publisher |
Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
| format |
Article |
| title_alt |
Моделювання збудження кильватерного поля послідовністю електронних згустків в прямокутному діелектричному хвилеводі Моделирование возбуждения кильватерного поля последовательностью электронных сгустков в прямоугольном диэлектрическом волноводе |
| description |
Wake field excitation by a sequence of electron bunches in rectangular dielectric waveguide of finite length is investigated for acceleration with high gradient electric field. Characteristics of wake field for parameters of planned in NSC KIPT experiments are determined.
Досліджені процеси збудження кільватерного поля електронними згустками та їх послідовністю в прямокутних діелектричних хвилеводах скінченої довжини: напів обмеженого хвилеводу та резонаторі. Визначені характеристики кільватерного поля для параметрів запланованого в ННЦ ХФТІ експерименту
Исследовано возбуждение кильватерного поля электронными сгустками и их последовательностью в прямоугольных диэлектрических волноводах конечной длины: полу бесконечном волноводе и резонаторе. Определены характеристики кильватерного поля для параметров планируемого в ННЦ ХФТИ эксперимента.
|
| issn |
1562-6016 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/78946 |
| citation_txt |
Simulation of wakefields excited by a train of electron bunches in rectangular dielectric waveguide / N.I. Onishchenko, G.V. Sotnikov // Вопросы атомной науки и техники. — 2005. — № 1. — С. 146-148. — Бібліогр.: 9 назв. — англ. |
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2025-11-24T05:51:15Z |
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2025-11-24T05:51:15Z |
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| fulltext |
SIMULATION OF WAKEFIELDS EXCITED BY A TRAIN OF
ELECTRON BUNCHES IN RECTANGULAR DIELECTRIC WAVEGUIDE
N.I. Onishchenko , G.V. Sotnikov
National Science Center «Kharkov Institute of Physics & Technology»,
61108, Academicheskaya Str.1, Kharkov, Ukraine, e-mail: onish @ kipt . kharkov . ua
Wake field excitation by a sequence of electron bunches in rectangular dielectric waveguide of finite length is inves
tigated for acceleration with high gradient electric field. Characteristics of wake field for parameters of planned in NSC
KIPT experiments are determined.
PACS: 41.60.-m
1. INTRODUCTION
Recently several papers appeared, which are devoted to accel
eration of electrons by wakefield in dielectric filled waveguide
[1-3]. Increased interest to wakefields in dielectric is connect
ed with the fact that short charged bunches excite simultane
ously a great many of radial harmonics of the dielectric
waveguide that leads to compression of wakefields in longitu
dinal direction and to formation of narrow peaks of field on
the axis of system with intensity much greater, than amplitude
of one radial harmonic [4].
In papers [4,5] regular sequences of bunches with
rather small charge, fields from which would sum coher
ently, were offered to use for achieving intensive acceler
ating fields. Experimentally it easier to create such se
quence, than a single bunch with big charge. Neverthe
less, this method faces with the following difficulties.
Firstly, for providing of effective coherent summing
of multimode fields it is necessary to provide equidistance
of the next resonance frequencies of the waveguide [4].
However in the cylindrical waveguide with partial dielec
tric filling the requirement of equidistance of excited fre
quencies is fulfilled only approximately.
Secondly, the pattern of field excitation in the dielec
tric waveguide with finite length qualitatively differs from
the idealized model of infinite waveguide. Good approxi
mation for describing of waveguide of finite length with
out reflections on the output is the semi-infinite waveg
uide. The solution of wake problem in semi-infinite
waveguide has shown, that when driving bunches excite
only traveling forward wave, "removal" of excited oscilla
tions after bunches with group velocity [6] occurs. There
fore in waveguide without reflections at excitation of
wakefield from a sequence of big number of bunches only
a part of this sequence will be effective.
With the purpose to bypass the mentioned difficulties
in Brookhaven [1] and NSC KIPT experiments on excita
tion of wakefields in the rectangular dielectric waveguide
are planed. For theoretical substantiation of planed exper
iments we carried out the research of effects of longitudi
nal finiteness on excitation of wakefields.
2. WAKEFIELD IN THE SEMIINFINITE
RECTANGULAR DIELECTRIC WAVEGUIDE
Let's consider a rectangular metal waveguide with
width b ( 0 x bЈ Ј ) and height d ( 0 y dЈ Ј ). The
waveguide is filled by homogeneous dielectric with per
mittivity ε . In longitudinal direction the waveguide occu
pies area 0 ≤ z∞ . From the end 0z = it is short-cir
cuited by a metal wall. We suppose, that monoenergetic
point electron bunch moves with constant velocity 0v
along the axis of waveguide to the end face of waveguide.
Distribution of charge density and current density of such
bunch is:
( ) ( ) ( )0 0 0 0 0/ / ,b L zQ x x y y t t z v v j vρ δ δ δ ρ= − − − − = ,
where bQ is bunch charge, 0t is time of bunch arrival to
the waveguide, 0 0,x y are transverse coordinates of bunch.
Having solved a wave equation with boundary condi
tions on metal walls of a waveguide we shall obtain ex
pression for a longitudinal electric field as the sum of
Cherenkov radiation cher
zE and the transition radiation
trans
zE [7]:
( )
( ) ( )
0 0 0
0 0 0 0 0 0
, , , , , ,
, , , , , , , , , , , , ,
z
cher trans
z z
E t x y z t x y
E t x y z t x y E t x y z t x y
=
+
( )0 0 0
0 0
,
0 0 0 0 0
, , , , , ,
16 sin sin sin sin
cos[ ( / )] ( / ) ( / ) ,
cher
z
b
k l
kl g
E t x y z t x y
Q k l k lx y x y
bd b d b d
t t z v t t z v t t z v
π π π π π
ε
ω
=
ц ц ц цж ж ж ж− ґз ч з ч з ч з чи и и иш ш ш ш
й щ− − Θ − − − Θ − −л ы
е
( )
( ) ( ){
( ) ( ) ( ) ( )
( ) ( ) ( ) ( )
0 0 0
0 0
,
0 0
2 2
1 2 2 0
1
2 2
0 1 2 2
1
, , , , , ,
16 sin sin sin sin
/ /
1 /
1 ,
trans
z
b
k l
ph gr
m m m
m gr
m
m m m
m
m
E t x y z t x y
Q k l k lx y x y
bd b d b d
t t z v t t z v
r r J y t t z v
J y r r J y
π π π π π
ε
θ θ
θ
Ґ
=
Ґ
−
=
=
ц ц ц цж ж ж ж− ґз ч з ч з ч з чи и и иш ш ш ш
й щ− − − − − ґл ы
− − + − − ґ
ьй щп+ − + эк ъпл ыю
е
е
е
where 2 2 2 2 2
0[( / ) ( / ) ] /( / 1/ )kl k b l b c vω π π ε= + − , 0J - cylin
drical functions, ( )xθ - Heaviside function and
0 0
1
0 0
/ 1 /
, / ,
/ 1 /
ph ph
ph
ph ph
t t z v v v
r v c
t t z v v v
ε
− − −
= =Ч
− + + ,
0 0 2
2 0
0 0
/ 1 /
, /
/ 1 /
ph ph
gr
ph ph
t t z v v v
r v c v
t t z v v v
ε
− − +
= =Ч
− + − .
Vavilov - Cherenkov wakefield with the account of
"damping wave» is nonzero at ( ) ( )0 0 0grt t v z t t v− < −Ј .
Within this area the envelope of cherenkov signal is con
stant. Value grv is group velocity of synchronous with
bunch electromagnetic wave. The plane ( )0
gr
grz t t v= − is
146 Problems of Atomic Science and Technology. 2005. № 1. Series: Plasma Physics (10). P. 146-148
mailto:sotnikov@kipt.kharkov.ua
back front of wakefield. This front moves after a bunch
with group velocity.
The field of transitional radiation exists in area
( )00 phz t t v< −Ј . Value phv is the greatest velocity of elec
tromagnetic signal propagation in the dielectric waveguide,
with this velocity the fastest high-frequency part of transitional
signal – so-called "precursor" is propagated.
For a bunch of finite sizes or for a sequence of bunch
es the expression for wakefield is fulfilled by integration
on transverse coordinates and on moments of entrance of
elementary charges.
In Fig.1-Fig.2 results of calculations for the following pa
rameters are presented: 4.3b cm= ; 8.6d cm= ; the charge of
a single bunch 0.32bQ nC= − ; energy– 4 MeV ; transverse
sizes of a bunch- 0 1.0b cm= 0 1.0d cm= ; 2.83ε = .
0 20 40 60 80 100
-0,6
-0,4
-0,2
0,0
0,2
0,4
0,6
E
z, k
V
/c
m
z, cm
a
0 20 40 60 80 100
-0,6
-0,4
-0,2
0,0
0,2
0,4
0,6
E
z, k
V
/c
m
z, cm
b
Fig. 1. Wakefield excited by a single bunch in the semi-in
finite dielectric waveguide at t=3.29 ns:
(a) - cherenkov field, (b)- full field. The label and dash
line show bunch location
The single bunch excites a plenty of transverse harmon
ics (we consider 50 harmonics on x and 50 harmonics on y
). As frequencies of excited harmonics are not divisible ratio
with the lowest eigen frequency the longitudinal structure of
the field has the irregular character even without taking into
account transitional radiation. Presence of transition radiation
especially complicates the field pattern as it contains the
whole continuous spectrum of frequencies, beginning from a
cut-off frequency. The field excited by a bunch flies out from
a system with a group velocity and near to input of system
the amplitude of the field is close to zero.
When in the semi-infinite waveguide the sequence of
bunches is injected with repetition rate 2886f MHz= ,
which is equal to lowest eigen frequency of structure, the
longitudinal structure of the field qualitatively changes. It
becomes regular with the narrow peaks following with
period of bunch train. I.e. the sequence of bunches "cuts
out" from a spectrum excited by a single bunch only fre
quencies multiple to of bunch repetition rate. And, as fol
lows from comparison of curves on Fig. 2, the transition
field destroys insignificantly regular structure of the field.
"Removal" of excited oscillations with group velocity re
duces in restriction of maximum quantity of bunches
which give the contribution to growth of amplitude of the
field [6,7]. On length of the system 100L cm= this bunch
quantity is 17. Additional injection of bunches will not re
duce in increase of amplitude of the field at given length
of structure.
0 20 40 60 80 100
-4
-2
0
2
4
E z, k
V
/c
m
z, cm
a
0 20 40 60 80 100
-4
-3
-2
-1
0
1
2
3
4
E
z, k
V
/c
m
z, cm
b
Fig. 2. Wakefield excited by a sequence of 17 bunches in
the semi-infinite dielectric waveguide at t=8.43 ns:
(a)- cherenkov field, (b)- full field. Labels and dash lines
show locations of the last 2 bunches of a sequence
3. WAKEFIELD IN RECTANGULAR DIELEC
TRIC RESONATOR
Let's suppose, that output end of waveguide z L= as well
as input end is closed by the metal gride, transparent for
particles. Then the statement of problem of the previous
section passes in determination of the longitudinal electric
field excited by a point electron bunch in the rectangular
dielectric resonator. We will suppose, that the height of
the resonator considerably exceeds its width, therefore we
will neglect dependence of excited fields on coordinate y
. Having solved wave equation with boundary conditions
analogous to the previous section and a source we obtain
expression for longitudinal electric field
] }
2 2 2
0 10 02 2
1 0
2 2 2
0 0
2 2 2
0 0
2 2 2
0 0 0 0
cos( ) / sin[ ( )]
/ sin[ ( )] ( )
/( 1) sin[ ( / )]
/ sin[ ( / )] ( / ) (
l ml l
z l ml
m l ml l ml
l l
l
l
l ml l
ml
ml
l l
l m
l
k z k cE E t t
k c t t t t
k c t t L v
k c t t L v t t L v G
ω εδ ω ω
ω ω ω
ω ε ω θ
ω
ω ε ω
ω
ω ε ω θ
ω
Ґ Ґ
= =
мй −п= − −нк− пло
щ− − − −ъ
ы
й −− − − −к
л
− − − − −
е е
0, ),x x
where 0 0 108 /bE Q v aLπ εω= − , 2 2 2 2[ ] /ml m lk cω κ ε= + , 0l lk vω = ,
/m m bκ π= , /lk l Lπ= ; function lδ is equal 1 if 0l = it is
equal 2 if 0l№ ; 0 0( , ) sin( )sin( )m m mG x x x xκ κ= .
As seen from full field will consist of the field of space
charge (corresponding to frequencies lω ) and the fields, excit
ed by a bunch in the resonator on frequencies mlω . After exit
of particles from the resonator the field of space charge as fol
lows from , disappears. It should be noted, that at the condition
ml lω ω= the corresponding items in the sum become domi
nant. The indicated condition is exactly cherenkov radiation in
delay medium. Then these resonant items may be treated as
147
cherenkov radiation in the dielectric resonator, and the rest of
the field as transition radiation on both boundaries. Let's note,
that radiation of a charged particle in the vacuum rectangular
resonator is first considered in [8], and in the cylindrical vacu
um resonator in [9]. In these cases the condition of cherenkov
radiation is not fulfilled. The resonant case is of interest for our
researches.
a b
Fig. 3. Wakefield excited by a single bunch in the flat di
electric resonator: (a) - at t=3.415ns, (b) – at t=99ns
Let's choose for the calculations parameters of experi
ment for the setup in NSC KIPT: charge of a single bunch
0.32bQ nC= − , energy– 4 MeV , 4.3b cm= , bunch repeti
tion rate 2850 MHz , 2.509ε = , 104.51L cm= . For such
sizes the resonant condition is fulfilled for numbers of
longitudinal and transverse harmonics at ratio 5=l m .
On fig.3-fig.4 outcomes of calculations are presented
allowing in sums for 151 longitudinal harmonics and 1
transverse harmonic.
a b
Fig. 4. Wakefield excited by a sequence of 100 bunches in
the plane dielectric resonator: (a) – at t=3.415 ns, (b) - at
t=99.942ns
In Fig.3 the longitudinal structure of the field excited
by a single bunch is presented. Before bunch exit from the
resonator (t=3.415 ns) structure of the field corresponds to
structure of the field in semi-infinite waveguide, the am
plitude of the field decreases from the position of group
front to the enter of the resonator (line 1 shows the loca
tion of a bunch, 2 – phase front, 3 – group wave front). At
long times, after a multiple reflection of group wave front
from the both end-walls of the resonator, levelling of am
plitude of the field along its length occurs (see the graph
for t=99 ns).
The longitudinal structure of the field created by a se
quence of 100 bunches in the dielectric resonator is presented
on Fig. 4. The upper figure corresponds to the moment of time
when the first bunch of sequence is near to the output of the
resonator (line 1 - the location of the first bunch, 2 – phase
wave front from the first bunch, 3 – group wavefront from the
first bunch). The amplitude of the field grows from a head of
sequence to the position of the group wave front, excited by
the first bunch, and then decreases to the enter of the resonator.
Wakefield in the resonator qualitatively and quantitatively co
incides with the field in semi-infinite waveguide up to exit of
the first bunch from the waveguide (see Fig. 2). At major
times, after exit of all bunches from the resonator, the homo
geneous distribution of amplitude is established in the waveg
uide.
Comparing Fig. 2 and Fig. 4 it follows, that in the res
onator it is possible to excite wakefield with the ampli
tude considerably exceeding amplitude of the field in the
semi-infinite waveguide. At that the regularity of oscilla
tions is conserved.
4. ACKNOWLEDGEMENTS
The study is supported in part by CRDF Grant No.
UP2-2569-KH-04
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МОДЕЛИРОВАНИЕ ВОЗБУЖДЕНИЯ КИЛЬВАТЕРНОГО ПОЛЯ ПОСЛЕДОВАТЕЛЬНОСТЬЮ
ЭЛЕКТРОННЫХ СГУСТКОВ В ПРЯМОУГОЛЬНОМ ДИЭЛЕКТРИЧЕСКОМ ВОЛНОВОДЕ
Н.И. Онищенко, Г.В. Сотников
Исследовано возбуждение кильватерного поля электронными сгустками и их последовательностью в прямо
угольных диэлектрических волноводах конечной длины: полу бесконечном волноводе и резонаторе. Определе
ны характеристики кильватерного поля для параметров планируемого в ННЦ ХФТИ эксперимента.
МОДЕЛЮВАННЯ ЗБУДЖЕННЯ КИЛЬВАТЕРНОГО ПОЛЯ ПОСЛІДОВНІСТЮ ЕЛЕКТРОННИХ
ЗГУСТКІВ В ПРЯМОКУТНОМУ ДІЕЛЕКТРИЧНОМУ ХВИЛЕВОДІ
М.І. Онищенко, Г.В. Сотников
Досліджені процеси збудження кільватерного поля електронними згустками та їх послідовністю в прямокут
них діелектричних хвилеводах скінченої довжини: напів обмеженого хвилеводу та резонаторі. Визначені ха
рактеристики кільватерного поля для параметрів запланованого в ННЦ ХФТІ експерименту.
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