Wakefield excitation in dielectric waveguides by a sequence of relativistic electron bunches
The results of theoretical and experimental studies of the wakefield excitation in a dielectric waveguide of а fi-nite length by a long sequence of relativistic electron bunches was carried out to reveal the possibility of the wakefield amplitude enhancement at summing coherent fields of separate bu...
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Національний науковий центр «Харківський фізико-технічний інститут» НАН України
2015
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irk-123456789-1121912017-01-25T11:09:12Z Wakefield excitation in dielectric waveguides by a sequence of relativistic electron bunches Kiselev, V.A. Onishchenko, I.N. Sotnikov, G.V. Новые методы ускорения заряженных частиц The results of theoretical and experimental studies of the wakefield excitation in a dielectric waveguide of а fi-nite length by a long sequence of relativistic electron bunches was carried out to reveal the possibility of the wakefield amplitude enhancement at summing coherent fields of separate bunches when the bunch repetition frequency coincides with the excited field frequency. In accordance with the theory the stepwise increasing dependence of the wakefield amplitude upon the dielectric waveguide length was experimentally obtained. Проведено теоретичні та експериментальні дослідження збудження кільватерного поля в діелектричному хвилеводі кінцевої довжини довгою послідовністю релятивістських електронних згустків для з'ясування можливості збільшення амплітуди кільватерного поля підсумовуванням полів окремих згустків при збігу частоти повторення згустків з частотою збуджуваного поля. Згідно з теорією отримано експериментально ступеневе збільшення амплітуди кільватерного поля залежно від довжини діелектричного хвилеводу. Проведены теоретические и экспериментальные исследования возбуждения кильватерного поля в диэлектрическом волноводе конечной длины длинной последовательностью релятивистских электронных сгустков для выяснения возможности увеличения амплитуды кильватерного поля суммированием полей отдельных сгустков при совпадении частоты повторения сгустков с частотой возбуждаемого поля. Согласно теории получено экспериментально ступенчатое увеличение амплитуды кильватерного поля в зависимости от длины диэлектрического волновода. 2015 Article Wakefield excitation in dielectric waveguides by a sequence of relativistic electron bunches / V.A. Kiselev, I.N. Onishchenko, G.V. Sotnikov // Вопросы атомной науки и техники. — 2015. — № 4. — С. 111-116. — Бібліогр.: 9 назв. — англ. 1562-6016 PACS: 41.60.-m, 41.75.Lx, 41.75.Ht, 96.50.Pw http://dspace.nbuv.gov.ua/handle/123456789/112191 en Вопросы атомной науки и техники Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
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Новые методы ускорения заряженных частиц Новые методы ускорения заряженных частиц |
| spellingShingle |
Новые методы ускорения заряженных частиц Новые методы ускорения заряженных частиц Kiselev, V.A. Onishchenko, I.N. Sotnikov, G.V. Wakefield excitation in dielectric waveguides by a sequence of relativistic electron bunches Вопросы атомной науки и техники |
| description |
The results of theoretical and experimental studies of the wakefield excitation in a dielectric waveguide of а fi-nite length by a long sequence of relativistic electron bunches was carried out to reveal the possibility of the wakefield amplitude enhancement at summing coherent fields of separate bunches when the bunch repetition frequency coincides with the excited field frequency. In accordance with the theory the stepwise increasing dependence of the wakefield amplitude upon the dielectric waveguide length was experimentally obtained. |
| format |
Article |
| author |
Kiselev, V.A. Onishchenko, I.N. Sotnikov, G.V. |
| author_facet |
Kiselev, V.A. Onishchenko, I.N. Sotnikov, G.V. |
| author_sort |
Kiselev, V.A. |
| title |
Wakefield excitation in dielectric waveguides by a sequence of relativistic electron bunches |
| title_short |
Wakefield excitation in dielectric waveguides by a sequence of relativistic electron bunches |
| title_full |
Wakefield excitation in dielectric waveguides by a sequence of relativistic electron bunches |
| title_fullStr |
Wakefield excitation in dielectric waveguides by a sequence of relativistic electron bunches |
| title_full_unstemmed |
Wakefield excitation in dielectric waveguides by a sequence of relativistic electron bunches |
| title_sort |
wakefield excitation in dielectric waveguides by a sequence of relativistic electron bunches |
| publisher |
Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
| publishDate |
2015 |
| topic_facet |
Новые методы ускорения заряженных частиц |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/112191 |
| citation_txt |
Wakefield excitation in dielectric waveguides by a sequence of relativistic electron bunches / V.A. Kiselev, I.N. Onishchenko, G.V. Sotnikov // Вопросы атомной науки и техники. — 2015. — № 4. — С. 111-116. — Бібліогр.: 9 назв. — англ. |
| series |
Вопросы атомной науки и техники |
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2025-07-08T03:31:13Z |
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2025-07-08T03:31:13Z |
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| fulltext |
ISSN 1562-6016. ВАНТ. 2015. №4(98) 111
WAKEFIELD EXCITATION IN DIELECTRIC WAVEGUIDES
BY A SEQUENCE OF RELATIVISTIC ELECTRON BUNCHES
V.A. Kiselev, I.N. Onishchenko, G.V. Sotnikov
National Science Center “Kharkov Institute of Physics and Technology”, Kharkov, Ukraine
E-mail: onish@kipt.kharkov.ua
The results of theoretical and experimental studies of the wakefield excitation in a dielectric waveguide of а fi-
nite length by a long sequence of relativistic electron bunches was carried out to reveal the possibility of the wake-
field amplitude enhancement at summing coherent fields of separate bunches when the bunch repetition frequency
coincides with the excited field frequency. In accordance with the theory the stepwise increasing dependence of the
wakefield amplitude upon the dielectric waveguide length was experimentally obtained.
PACS: 41.60.-m, 41.75.Lx, 41.75.Ht, 96.50.Pw
INTRODUCTION
Particle accelerators, as unique tools for solving the
frontier high energy physics problems, have excessive
sizes and cost that requires great efforts and large finan-
cial expenses for their building. Discovery of a new
particle like the Higgs boson, crucial in determining the
consistency of the standard model, requires a focus on
the creation of Higgs factory, based on the collider with
the necessary energy and luminosity of the colliding
beams. If basing on traditional methods of acceleration,
such colliders are also large in size and high in cost.
This motivates research and development aimed at find-
ing and implementing new methods of high-gradient
acceleration into accelerator physics and technology to
decrease the collider size. Promising of these is the ac-
celeration in the wakefield excited in plasma or dielec-
tric structure by intensive bunch or a powerful laser
pulse.
This presentation relates to the concept of the elec-
tron accelerator based on the acceleration with the
wakefield excited in a dielectric structure by a regular
sequence of relativistic electron bunches. It is a variant
of two-beam accelerator, in which electron bunches are
accelerated with wakefields excited in the dielectric
structure by a regular sequence of relativistic electrons.
Wakefields as a Cerenkov radiation, excited in the THz
range, are considered as promising ones for the new
methods of acceleration.
By accelerating rate dielectric wakefield methods
are intermediate (more than 1 GeV/m) between tradi-
tional methods with metal structures (less than
0.1 GeV/m) and plasma wakefield method (up to
100 GeV/m). However, in spite of the limitation of the
accelerating rate due to the dielectric breakdown contra-
ry to plasma case, the dielectric section in future collid-
ers has an advantage since it is devoid of the problems
with positron part of wakefield collider and ion collapse
that are inevitable for plasma section.
As it has been reported early [1] in NSC KIPT for
enhancing the amplitude of the excited wakefield the
concept of a dielectric wakefield accelerator has been
proposed, in which three approaches should be used
together: "multi-bunch" scheme [2, 3] to increase the
wakefield by the coherent summation of the wakefields
of the individual bunches of the long sequence; "multi-
mode" scheme [4, 5] to increase the wakefield by the
summation of a lot of equidistant transverse modes of
the wakefield excited in the dielectric structure of rec-
tangular cross-section; "resonator" scheme [6, 7] to in-
crease the wakefield by the use of the resonator, which
provides energy accumulation of excited wakefields for
the whole sequence of bunches, i.e. allows avoiding
travelling of energy away from the structure with the
group velocity [8, 9], which restricts the number of
bunches, which wakefields build-up leads to the total
wakefield increase. In this paper the theoretical and ex-
perimental investigations in details of the "multi-bunch"
scheme are presented.
1. STATEMENT OF THE PROBLEM
Investigations of the "multi-bunch" scheme are con-
cluded to finding the dependence of the wakefield am-
plitude at a dielectric waveguide exit upon the number
of exciting bunches. Early we have found [10] the
waveform of the excited wakefield after a single bunch
or a sequence of them. Wakefield after a single bunch
consists of Cerenkov radiation and posterior transition
radiation of slightly less intensity originated at the
waveguide entrance. The length l of the Cerenkov radia-
tion train behind the bunch is
)
0
(1
vg
v
l L= − , (1)
where L is distance from the waveguide entrance to the
exciting bunch propagating inside of the waveguide, vg
is group velocity of wakefield wave, v0 is velocity of the
bunch. At the exit of waveguide of the length L0 the
duration of wakefield pulse will be observed
0 0 1)
0
(L vl
v v vgg
τ = −= . (2)
At the injection of a resonant sequence of bunches
(bunch repetition frequency coincides with wakefield
frequency frep =f0) into the dielectric waveguide of finite
length L0, not all bunches of the sequence increase the
total wakefield due to the removal of the excited field
from the output end of the waveguide with the group
velocity vg. Maximal number of bunches, wakefields
summation of which leads to the increase in the total
wakefield is given by the expression:
0 0 1)max (L v
vg
N
λ
= − , (3)
where λ=2π/kz=2πfrep/v0 is wavelength of the excited
wakefield mode, kz is its longitudinal wavenumber. In-
jection of subsequent bunches over Nmax does not in-
crease the total wakefield. The spatial longitudinal dis-
tribution of wakefield along the waveguide of finite
mailto:onish@kipt.kharkov.ua
ISSN 1562-6016. ВАНТ. 2015. №4(98) 112
length L0 evolves from stepwise triangular form for
N<Nmax to stepwise linearly growing up to the entrance
for N≥Nmax. At that the temporal behavior of the wake-
field at the waveguide exit is stepwise linearly growing
in time for N<Nmax up to saturation for N≥Nmax.
According to (3) varying the length of the dielectric
waveguide L allows to observe wakefied at the wave-
guide exit from various Nmax including Nmax =1, 2, 3,… .
Thus, instead of the resonant sequence of various small
number of bunches, which is difficult to realize in the
experiments, especially a single bunch or several
bunches, without cutting long sequence (6000 bunches
in our experiment) by unique technique, we can use
dielectric waveguides of various lengths compared with
wavelength. In particular, for the waveguide of the
length less the excited wavelength a “single bunch” sce-
nario can be realized, because wakefield trains of all
bunches do not overlap, so that the field envelope of the
entire sequence has an wakefield amplitude the same as
for a single bunch. Therefore, the dependence of the
total wakefield on number of injected bunches we inves-
tigate by means of the dependence of the total wakefield
on the length of the dielectric waveguide.
There are two variants of the realization of this idea.
For cylindrical geometry of dielectric waveguide elec-
tron bunches propagate along the axis and interact with
dielectric through its whole length. For this case we
change the active dielectric length by varying its whole
length by means of a set of dielectric pieces. In the se-
cond variant used for rectangular dielectric waveguide
there is the possibility to deflect bunches by magnetic
field at needed distant from waveguide entrance due to
the presence of two walls without dielectric plates. For
this case the length of dielectric waveguide is constant
and interaction length is varied by the length of the
bunches way before deflecting.
2. THEORY
For the purpose of the better interpretation of the ex-
perimental results of dependence of an excited longitu-
dinal electric wakefield the PIC simulation close to the
experimental conditions was performed. The matter is
that the experimental measurements of a longitudinal
electric field are fulfilled in vacuum part of the metal
waveguide. The wakefield excited in dielectric is par-
tially reflected at dielectric-vacuum boundary. Thus, in
a dielectric part of the waveguide the field can accumu-
late. Having measurements of an electric field in vacu-
um area it is necessary to draw a conclusion on value of
the same field in the dielectric part.
Below results of researches of dependence of the
longitudinal electric field Ez measured in different
points of dielectric structure, upon length of the dielec-
tric part are presented.
The geometry of researched dielectric structure is
shown in Fig. 1.
For numerical calculations we used the experimental
parameters (see in section V). We supposed that the
input end of a waveguide is short-circuited, and the out-
put end is open into the free space. For reduction of in-
fluence of the reflected wave on a measured field in a
waveguide the output end of a waveguide was comple-
mented by the free space with length, equal to two
wavelengths of the lowest excited mode. For the given
cross sizes of the dielectric part and energy of electrons
of a bunch the wavelength is calculated to be
λ = 10.64 cm.
Fig. 1. General view of the dielectric structure,
excited by sequence of electron bunches. Into a metal
cylindrical waveguide of length Ls the dielectric part
of length Ld is inserted (yellow color). Electron bunches
(blue color) propagated along a cylinder axis
from left to right
To prove the coherency of summation of wakefields
of N bunches in accordance with the statement of the
problem we should change the dielectric part length Ld
and observe stepwise linear growth of longitudinal die-
lectric field amplitude Ez_total=NEz_single with Ld increas-
ing, at that N=Ld/λ, N<Nmax. For N≥Nmax Ez_total saturates
and does not grow with further increasing of N.
In Fig. 2 dependences of the maximum and mini-
mum (module) values of a longitudinal electric field on
the axis of the structure on length of the dielectric part
are shown. The electric probe is located on a structure
axis. The structure was excited by sequence of 21
bunches.
0,00 5,32 10,64 15,96 21,28 26,60 31,92
0
200
400
600
800
1000
1200
1400
E
z_
m
ax
(V
/c
m
)
Ld (cm)
Ez_max
|Ez_min|
z=0.9*650mm
Fig. 2. Maximum and minimum of the longitudinal
electric field at distance . sz 0 9L= from waveguide
entrance depending on of the dielectric part length.
Markers show calculated points, between calculated
points spline interpolation is carried out. Vertical grid
lines are drawn by each half length
of the lowest resonant wave
From Fig. 2 follows that the longitudinal electric
field in vacuum part of structure in average grows line-
arly with increasing of the dielectric part length oscillat-
ing with the period equal to half wavelength of the low-
est excited mode. Oscillations evidence the reflection of
excited wakefield on the dielectric-vacuum boundary
leading to wakefield accumulation at the dielectric part
multiple to half wavelength as it occurs in the resonator
(i.e. waveguide is not perfect). Transition radiation con-
ISSN 1562-6016. ВАНТ. 2015. №4(98) 113
tributes essentially (it is comparable with Cerenkov ra-
diation) only at Ld<λ, i.e. for “single bunch” scenario.
Its contribution at larger Ld is smaller because it is not
coherent contrary to Cerenkov radiation of resonant
sequence of bunches, which wakefielfs are coherently
added by a stepwise way. Looking aside from transition
radiation and oscillations caused with reflections we can
conclude that Cerenkov radiations of resonant bunches
are summated coherenly giving resulting linear growth
with dielectric part length (i.e. with number of bunches)
with the step after each subsequent bunch.
Dependence of wakefield in structure on time is pre-
sented in Fig. 3. Dielectric part length Ld=32.1 cm was
approximately equaled to three wavelengths of the low-
est resonant mode. Structure was excited by a sequence
of 42 bunches; the bunch repetition period is 0.356 ns.
Stepwise rising field is a characteristic feature of the
coherent addition of wakefields in the resonator that
confirms the existence of reflections in the system lead-
ing to oscillatory behavior of the wakefield dependence
on Ld.
Fig. 3. Temporal dependence of longitudinal electric
field zE on axis at dz L=
3. EXPERIMENTAL SETUP
The scheme of the experimental setup on which the
experiments were performed on the wakefield excitation
in the dielectric structure of cylindrical and rectangular
cross-section by a sequence of relativistic electron
bunches is shown in Fig. 4.
Fig. 4. 1 – accelerator "Almaz-2M"; 2 – magnetic ana-
lyzer; 3 – diaphragm; 4 – dielectric structure;
5 – waveguide; 6 – transverse magnetic field; 7 – Teflon
vacuum plug; 8 – microwave probe; 9 – oscilloscope;
10 – glass plate
Relativistic electron beam energy is 4.5 MeV, pulse
beam current – 0.8 A, pulse duration 2 µs. Each pulse
represents a sequence of N = 6000 electron bunches
with a duration of 60 ps each, interval between bunches
300 ps bunch charge 0.26 nC. Frequency of bunch repe-
tition frep=2805 MHz.
To study the multi-bunch regime of wakefield exci-
tation we used copper cylindrical waveguide with an
inner diameter of 85 mm and a wall thickness of 2 mm,
filled with dielectric (Teflon ε=2.04, tgδ=4·10-4). Outer
diameter of the dielectric insert is 85 mm and the diame-
ter of the channel in the dielectric insert equal 2.1 cm
was calculated so that the bunch repetition frequency frep
coincides with the wakefield frequency f0 excited in the
dielectric waveguide (frep=f0).
In experiments the amplitude of the excited wake-
field was measured by microwave probe, at changing
the dielectric part length by using a set of cylindrical
dielectric inserts with channel for bunches, each
2.66 cm in length corresponding to 1/4 of the excited
wave length. Theoretical calculations have shown that
for the parameters of our experimental installation the
principal mode Е01 of excited Cerenkov wakefield has
group velocity vg=0.492 с. According to (3), this means
that for the length of the dielectric waveguide L=λ the
excited Cerenkov wakefields of bunches do not overlap
and therefore are not summated. As a result, the ampli-
tude of the total field of the entire sequence of bunches
is equal to the amplitude of the first bunch wakefield,
i.e. scenario of the excitation by a single bunch is real-
ized. The gradual increase in the length of the dielectric
part to 35 cm allows to investigate the evolution of the
wakefield excitation successively by a sequence of 1, 2,
3 and 4 bunches. Note that at the input boundary of a
dielectric waveguide the transition radiation is generat-
ed, which should be measured by taking L<<λ, and sub-
tracted from the total signal.
4. EXPERIMENTAL RESULTS
Experiments were started at “initial” structure (see
Fig. 4) without careful matching to approach to wave-
guide mode of operation. Measurements of the amplitude
of the excited wakefield depending on the dielectric
length of the dielectric waveguide (manufactured as a set
of filling Teflon inserts of length ΔL=0.25 λ, each) were
carried out at the bunch repetition frequency 2805 MHz,
which coincides with the frequency of the excited wake-
field. Preliminary experiments have shown that at in-
creasing the length of the dielectric part, along with lin-
ear growth of the wakefield amplitude, assumed in ac-
cordance to (3), the periodic oscillations of increasing
amplitude were observed (Fig. 5). Spatial period of the-
se oscillations is multiple to a half wavelength of the
principal mode. Such behavior of the obtained depend-
ence may be arisen due to the partial reflection of the
excited wake wave from the dielectric part exit end, as
well as from the exit of the metallic waveguide and
from a vacuum dielectric plug.
As it can be seen from Fig. 5, even in the absence of
dielectric in the waveguide (Ld=0) at the dielectric
waveguide exit RF-signal is registered. It can be caused
by the transition radiation excitation during bunches
propagation through the input boundary of the dielectric
waveguide (metallic diaphragm). Its value is reduced by
2 times, if after diaphragm the dielectric insert of length
(Ld=1 cm) much smaller than the excited wavelength is
placed so we can neglect excited Cerenkov radiation.
When subtracting this transition radiation field, it be-
comes possible to investigate the assigned task finding
the dependence of the amplitude of total Cerenkov
wakefield on the length of dielectric part, and hence
upon the number of coherently exciting bunches.
ISSN 1562-6016. ВАНТ. 2015. №4(98) 114
Fig. 5. Amplitude of Ez of excited wakefield
on the dielectric part length
To reduce the level of reflections, a series of chang-
es in the installation were performed, allowing reducing
the reflection coefficient, i.e. to improve the standing
wave ratio (SWR) of the dielectric structure so it be-
comes “matched” structure. These include:
– installation of a dielectric cone at the exit of the
dielectric waveguide to reduce reflection from the die-
lectric-vacuum boundary;
– installation of a conical horn at the exit of the ex-
perimental setup to reduce reflection from the output
end of the metallic waveguide;
– optimization of the thickness of the dielectric vac-
uum plug, for which the reflection coefficient at a given
wavelength is minimal.
SWR dependence for the “initial” configuration on
the length of a set of filling inserts made from Teflon
(step ΔL=0.25 λ) exactly such as in beam experiment
(see Fig. 5) for the “initial” structure is shown in
Fig. 6 (1).
Fig. 6. SWR dependence for round cylindrical dielectric
waveguide tract upon length of Teflon filling:
1 – “initial” dielectric structure;
2 – “matched” dielectric structure
Observed periodic changes SWR (from 1.05 to 1.8),
caused by the reflections of the incident wave from the
output end of a set of cylindrical dielectric inserts, from
the end of the waveguide and from the dielectric vacu-
um plug.
SWR dependence for the “matched” configuration
of waveguide-dielectric structure on the dielectric
waveguide length within L=(0…0.25) λ, with optimum
thickness of vacuum dielectric plug d=0.5 λ, with a con-
ical copper horn at output of waveguide-dielectric struc-
ture, and with absorbing ferrite load behind the horn is
shown in Fig. 6 (2).
From the comparison of SWR dependency round di-
electric waveguide tract on length of Teflon filling for
the initial and the matched configuration of the structure
it can be seen that the made modifications allow to low-
er essentially SWR of matched configuration of dielec-
tric structure.
Fig. 7. Scheme of the installation for “matched”
dielectric waveguide: 1 – accelerator "Almaz-2M";
2 – magnetic analyzer; 3 – diaphragm; 4 – insulator;
5 – waveguide; 6 – transverse magnetic field; 7 – vacu-
um dielectric plug; 8 – RF-probe; 9 – oscilloscope;
10 – glass plate; 11 – additional waveguide with horn;
12 – ferrite absorber
If all conditions for reflections reducing in the
“matched” waveguide dielectric structure are satisfied
the measurements of total amplitude of the excited
wakefield depending on the length of the dielectric
waveguide (and hence on number of bunches) were per-
formed at the experimental setup shown in Fig. 7.
Dependence of the excited wakefield amplitude on
the length of the dielectric waveguide is shown in
Fig. 8. From Fig. 9 follows that the amplitude of the
excited wakefield increases proportionally to the length
of the dielectric part, i.e. according to (3) also to the
number of bunches, evidencing coherent wakefield
summation for Nmax bunches.
Fig. 8. Dependence of the amplitude of the excited
wakefield on the length of the dielectric waveguide
Measurement of the energy loss of relativistic
electron bunches. To compare the energy loss of
bunches with the magnitude of the excited wakefield the
measurements of the energy spectra of electrons as they
pass through the dielectric structure were made. On the
energy spectra of electrons we can judge by the imprints
on the glass plate of the beam electrons deflected by
transverse magnetic field. Energy losses were deter-
mined by comparing the imprints of the beam electrons
passing through the empty waveguide and through the
waveguide filled with dielectric inserts. Independently
the energy spectra were found with help of magnetic
analyzer at the accelerator exit and the dielectric struc-
ture exit.
Measurements were carried out at a length of dielec-
tric Ld = 29.14 cm and Ld = 26.48 cm, i.e. at maximum
ISSN 1562-6016. ВАНТ. 2015. №4(98) 115
and minimum amplitudes of the wakefield (see Fig. 8)
and also in the absence of dielectric in the waveguide.
It has been shown that at the length of the dielectric
structure Ld = 26.48 cm, imprints of electron beam pass-
ing through the structure almost coincide with the im-
prints of the beam electrons passed through the empty
waveguide. With a length of dielectric Ld = 29.14 cm
shift of imprint about 3 mm was observed, which, ac-
cording to the calibration of imprints by magnetic ana-
lyzer, corresponds to energy loss of electron bunches
80 keV (see Fig. 9).
Fig. 9. Imprints of electron bunches deflected
by transverse magnetic field: in the absence
of dielectric and for dielectric of length 26.48 cm (a);
for dielectric of length 29.14 cm (b)
These results were confirmed by measuring the en-
ergy spectra of bunches by magnetic analyzer, placed at
dielectric structure exit. The resulting spectra of the
beam electrons passed waveguide without dielectric
structure and with dielectric 29.14 cm length are shown
in Fig. 10, from which it follows that the energy loss of
electron bunches was 100 keV. For dielectric of length
L = 26.48 cm spectrum practically does not shift.
4,0 4,1 4,2 4,3 4,4 4,5 4,6 4,7 4,8 4,9 5,0
0,0
0,1
0,2
0,3
0,4
0,5
0,6
0,7
0,8
0,9
1,0
I/I
m
ax
Eb (MeV)
empty
dielectric
Fig. 10. Electron energy spectra:
waveguide without dielectric (black);
with dielectric of length 29.14 cm (red)
Since by theoretical calculations a single bunch ex-
cites wakefield Ez=150 V/cm, then the coherent addition
of the fields of 4 bunches with dielectric structure of the
length 30 cm of the energy loss for the “matched” struc-
ture with small reflections should constitute 18 keV,
which are within the accuracy of measurement and can-
not be registered neither by magnetic analyzer nor by
imprint of the bunches on the glass plates. Recorded in
the experiment energy losses of bunches constitute
80…100 keV correspond to “initial” waveguide when
an accumulation of wakefield to large amplitudes takes
place. Indeed, at dielectric of length 29.14 cm wakefield
reaches of order 1…2 keV/cm, which leads to energy
loss of bunches comparable by order to value with the
measured one by magnetic analyzer.
Rectangular cross-section. For rectangular wave-
guide filled with two dielectric plates there is the possi-
bility to deflect bunches to the waveguide walls, which
are without dielectric plates. By placing magnetic field
at various distances from the waveguide entrance we
can vary the length of bunches interaction with dielectric
waveguide and measure dependence of wakefield ampli-
tude on active dielectric length at fixed dielectric wave-
guide length. Such linear dependence is presented in
Fig. 11 that validates theoretical prediction (3).
Fig. 11. Dependence of wakefield amplitude on interac-
tion length of bunches with dielectric waveguide
CONCLUSIONS
It is shown that in the dielectric waveguide structure,
while passing through it a regular sequence of relativ-
istic electron bunches coherent summation of wake-
fields excited by bunches is occurred. At that the num-
ber of bunches, whose wakefields are coherently sum-
mated determined by the length of the dielectric struc-
ture and group velocity of the excited wave.
Energy loss of bunches, measured by magnetic ana-
lyzer, corresponds to the value of the excited wakefield
amplitude.
Work supported by Global Initiatives for Prolifera-
tion Prevention (GIPP) program, project ANL-T2-247-
UA (STCU Agreement P522).
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Article received 10.06.2015
ВОЗБУЖДЕНИЕ КИЛЬВАТЕРНОГО ПОЛЯ В ДИЭЛЕКТРИЧЕСКИХ ВОЛНОВОДАХ
ПОСЛЕДОВАТЕЛЬНОСТЬЮ РЕЛЯТИВИСТСКИХ ЭЛЕКТРОННЫХ СГУСТКОВ
В.А. Киселев, И.Н. Онищенко, Г.В. Сотников
Проведены теоретические и экспериментальные исследования возбуждения кильватерного поля в ди-
электрическом волноводе конечной длины длинной последовательностью релятивистских электронных
сгустков для выяснения возможности увеличения амплитуды кильватерного поля суммированием полей
отдельных сгустков при совпадении частоты повторения сгустков с частотой возбуждаемого поля. Согласно
теории получено экспериментально ступенчатое увеличение амплитуды кильватерного поля в зависимости
от длины диэлектрического волновода.
ЗБУДЖЕННЯ КІЛЬВАТЕРНОГО ПОЛЯ В ДІЕЛЕКТРИЧНИХ ХВИЛЕВОДАХ
ПОСЛІДОВНІСТЮ РЕЛЯТИВІСТСЬКИХ ЕЛЕКТРОННИХ ЗГУСТКІВ
В.О. Кисельов, I.М. Oніщенко, Г.В. Сотніков
Проведено теоретичні та експериментальні дослідження збудження кільватерного поля в діелектричному
хвилеводі кінцевої довжини довгою послідовністю релятивістських електронних згустків для з'ясування
можливості збільшення амплітуди кільватерного поля підсумовуванням полів окремих згустків при збігу
частоти повторення згустків з частотою збуджуваного поля. Згідно з теорією отримано експериментально
ступеневе збільшення амплітуди кільватерного поля залежно від довжини діелектричного хвилеводу.
INTRODUCTION
1. STATEMENT OF THE PROBLEM
2. THEORY
3. EXPERIMENTAL SETUP
4. EXPERIMENTAL RESULTS
CONCLUSIONS
Возбуждение кильватерного поля в диэлектрических волноводаХ последовательностью релятивистских электронных сгустков
збудження кільватерного ПОЛЯ В діелектричних хвилеводах ПОСЛІДОВНІСТЮ релятивістських ЕЛЕКТРОННИХ згустків
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