Investigations of the physical processes in multibunch dielectric wakefield accelerator
The main results of theoretical and experimental researches of the physical processes in a dielectric wakefield accelerator based on the excitation of accelerating wakefield in a dielectric structure by a long sequence of electron bunches are represented. Enhancement of the excited wakefield amplitu...
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| Date: | 2015 |
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| Format: | Article |
| Language: | English |
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Національний науковий центр «Харківський фізико-технічний інститут» НАН України
2015
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| Cite this: | Investigations of the physical processes in multibunch dielectric wakefield accelerator / I.N. Onishchenko // Вопросы атомной науки и техники. — 2015. — № 6. — С. 25-36. — Бібліогр.: 18 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1859593209192120320 |
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| author | Onishchenko, I.N. |
| author_facet | Onishchenko, I.N. |
| citation_txt | Investigations of the physical processes in multibunch dielectric wakefield accelerator / I.N. Onishchenko // Вопросы атомной науки и техники. — 2015. — № 6. — С. 25-36. — Бібліогр.: 18 назв. — англ. |
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| description | The main results of theoretical and experimental researches of the physical processes in a dielectric wakefield accelerator based on the excitation of accelerating wakefield in a dielectric structure by a long sequence of electron bunches are represented. Enhancement of the excited wakefield amplitude is achieved through coherent addition wakefields of individual bunches, wakefields summation of the equidistant transverse modes and wakefields storage in the resonator. Acceleration of bunches in the total wakefield is realized at dividing sequence of bunches in the exciting and accelerated parts in any ratio by an appropriate frequency detuning of bunch repetition frequency relative to the excited principal transverse mode. The change in the dielectric constant and loss tangent of used dielectrics under exposure to 100 MeV electron beam is investigated.
Представлено основні результати теоретичних і експериментальних досліджень фізичних процесів у діелектричному кільватерному прискорювачі, заснованому на збудженні прискорюючого кільватерного поля в діелектричній структурі довгою послідовністю електронних згустків. Збільшення амплітуди збуджуваного кільватерного поля досягається за рахунок когерентного складання кільватерних полів окремих згустків, підсумовування полів еквідистантних поперечних мод та накопичення полів у резонаторі. Прискорення згустків у сумарному кільватерному полі реалізовано поділом послідовності згустків на збуджуючу і прискорювану частини в будь-якому співвідношенні за допомогою відповідної розстройки частоти слідування згустків щодо частоти збуджуваної основної поперечної моди. Досліджено зміну діелектричної проникності і тангенс кута втрат застосовуваних діелектриків під впливом радіаційного опромінення їх 100 МеВ-електронним пучком.
Представлены основные результаты теоретических и экспериментальных исследований физических процессов в диэлектрическом кильватерном ускорителе, основанном на возбуждении ускоряющего кильватерного поля в диэлектрической структуре длинной последовательностью электронных сгустков. Увеличение амплитуды возбуждаемого кильватерного поля достигается за счет когерентного сложения кильватерных полей отдельных сгустков, суммирования полей эквидистантных поперечных мод и накопления полей в резонаторе. Ускорение сгустков в суммарном кильватерном поле реализовано разделением последовательности сгустков на возбуждающую и ускоряющую части в любом соотношении с помощью соответствующей расстройки частоты следования сгустков по частоте возбуждаемой основной поперечной моды. Исследовано изменение диэлектрической проницаемости и тангенс угла потерь применяемых диэлектриков под воздействием радиационного облучения их 100 МэВ-электронным пучком.
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| first_indexed | 2025-11-27T16:49:20Z |
| format | Article |
| fulltext |
ISSN 1562-6016. ВАНТ. 2015. №6(100) 25
NOVEL AND ADVANCED ACCELERATION TECHNIQUES
INVESTIGATIONS OF THE PHYSICAL PROCESSES IN MULTIBUNCH
DIELECTRIC WAKEFIELD ACCELERATOR*
I.N. Onishchenko
National Science Center “Kharkov Institute of Physics and Technology”, Kharkov, Ukraine
E-mail: onish@kipt.kharkov.ua
The main results of theoretical and experimental researches of the physical processes in a dielectric wakefield
accelerator based on the excitation of accelerating wakefield in a dielectric structure by a long sequence of electron
bunches are represented. Enhancement of the excited wakefield amplitude is achieved through coherent addition
wakefields of individual bunches, wakefields summation of the equidistant transverse modes and wakefields storage
in the resonator. Acceleration of bunches in the total wakefield is realized at dividing sequence of bunches in the
exciting and accelerated parts in any ratio by an appropriate frequency detuning of bunch repetition frequency rela-
tive to the excited principal transverse mode. The change in the dielectric constant and loss tangent of used dielec-
trics under exposure to 100 MeV electron beam is investigated.
PACS: 41.75.Ht; 41.75.Lx
INTRODUCTION
To investigate nature on the smallest scale, which is
composed of the fundamental particles and forces, parti-
cle accelerators have played a main role of tools as mi-
croscopes. The present high-energy frontier colliders
producing the center-of-mass energy of 100 GeV [1]
give the possibility to study the world of nature, of
which the size can be seen into nearly one-trillionth
micron. Today we are launching forth into a new energy
regime of the order of TeV [2, 3], in which profound
fundamental questions is expected to be answered on
the origin of mass, the predominance of matter over
antimatter and the existence of supersymmetry and so
on. High energy ion accelerators including proton and
heavy-ion colliders [4] can reveal in-situ synthesis of
the nuclear matter by producing quark-gluon plasmas at
the quark-hadron phase transition temperature around
one-trillion Ks, which is thought as the high energy den-
sity state at 10
-5
s after the Big Bang of our universe.
However ILC [2, 3], and LHC [4] – scale accelera-
tors are very close to the limit of what we can practical-
ly afford to build using conventional technologies, even
collaboratively. The first understanding of this situation
was stated in [6], where three ideas were declared by
Veksler (Dubna), Budker (Novosibirsk), and Fainberg
(Kharkov). The only Fainberg proposal to use of plasma
waveguides as accelerating structures has survived and
was later modified by Dawson et al. [7, 8] as a wake-
field accelerating scheme, in which high-gradient accel-
erating field is built up as a wakefield excited in plasma
by a short high power laser pulse or a short bunch of the
large charge. Another potential candidate for future high
gradient particle acceleration, allowing to overcome the
accelerating rate limit 100 MeV/m of conventional ac-
celerators, is dielectric loaded (DL) accelerating struc-
tures [9], in which wakefield is excited by an intense
electron bunch or a sequence of bunches. As it has been
shown in theoretical investigations [10] and in the re-
cent experiments [11],
___________________________________________
*Results of these investigations were reported at the satellite
meeting “Multibunch dielectric wakefield accelerator” to Int. Work-
shop on Future Linear Colliders (LCWS14), Belgrade, Serbia, 2014.
the maximum accelerating gradient in dielectric struc-
tures, being limited by the electric breakdown due to the
tunneling and collisional ionization effects, can be
achieved above 1 GeV/m, i.e. on the order higher com-
paring to the conventional metallic accelerating struc-
tures. Besides, DL structures are more acceptable due to
the developed technology of micro-fabrication, homo-
geneity, UHF-matching etc.
In this work the concept of multi-bunch dielectric
wakefield accelerator is investigated [12, 13]. The theo-
retical and experimental studies of the following prob-
lems are carried out:
- "multi-bunch" issue that is concluded to the wakefield
enhancement due to the summation of coherent wake-
fields driven by a regular sequence of electron bunches;
- "multi-mode" issue that is concluded to the wake-
field enhancement due to the summation of many equi-
distant transversal modes of wakefield, excited in rec-
tangular dielectric structure;
- "resonator" issue that is concluded to the wakefield
enhancement by using a resonator to avoid the effect of
group velocity so that the energy of excited wakefield
does not vacate the dielectric structure during the whole
sequence of bunches;
- “injection” problem that is concluded to displacing
rear tail of the bunch sequence into accelerating phase
of the wakefield by means of detuning bunch repetition
frequency and excited wakefield frequency;
- “plasma-dielectric” modification with plasma filled
transit channel for focusing of bunches and enhance-
ment of wakefield excitation;
- influence of exposure to relativistic electron beam
on radiation resistance and dielectric electrodynamic
properties of dielectric components (including zirconi-
um ones).
1. WAKEFIELD EXCITATION [14]
1.1. EXPERIMENTAL FACILITY
As a result of works on the restoration of the klystron
amplifier, update the electron gun and master oscillator,
which were performed at linear resonant electron acceler-
ator "Almaz-2M", the relativistic electron beam, which
energy can be varied in the range 2.5…4.8 MeV, pulsed
mailto:onish@kipt.kharkov.ua
ISSN 1562-6016. ВАНТ. 2015. №6(100) 26
current 0.5…1.0 А, pulse duration 0.1…2.0 s. Beam
pulse presents a sequence of N = 300…6000 electron
bunches each of charge within 0.16…0.32 nC, radius
0.5 cm, duration 60 ps (i.e. length 1.7 cm) and interval
between bunches 300 ps (at bunch repetition frequency
2805 MHz). Bunch repetition frequency can be changed
within 2803…2807 MHz. Energy distribution width is
within 7…9%. A chamber in which the dielectric struc-
ture can be placed was attached to the accelerator
"Almaz-2М". In such a way the experimental facility
has been created for research of wakefield excitation by
a sequence of the relativistic electron bunches in the
dielectric structures of round and rectangular cross sec-
tion and acceleration of electrons by excited wakefields.
The scheme of the experimental set up is shown in
Fig. 1.
Fig. 1. The scheme of the experimental set up.
1 – accelerator "Almaz-2М"; 2 – magnetic analyzer;
3 – diaphragm; 4 – dielectric structure; 5 – metal
waveguide; 6 – traversal magnetic field; 7 – vacuum
teflon plug; 8 – microwave probe; 9 – oscilloscope;
10 – glass plate; 11 – waveguide with a horn
The dielectric structure was a copper cylindrical
waveguide (5) of the inner diameter of 85 mm, filled
with annual Teflon tube (4) (ε=2.04, tgδ=4 10
-4
) of the
outer diameter equal to the inner diameter of the copper
waveguide and transit channel of the diameter 2.1 cm
for bunches. The length of the dielectric part is 31 cm
equal to 3 wavelengths of the principal mode.
Electron energy spectra were measured by a magnet-
ic analyzer (2) at the accelerator exit and by declining
electrons with transversal magnetic field (6) on glass
plate (10) at the dielectric structure exit.
1.2. "MULTI-BUNCH" EXCITATION
"Multi-bunch" issue concluded to the statement that
the intense wake field excited by a bunch with a large
charge can be achieved by a long periodic sequence of
bunches with a low charge each, but an equivalent total
charge. To clarify the possibility of coherent summation
of individual bunches fields it is needed to change the
number of bunches in the sequence. Because of the dif-
ficulty of producing a set of sequences with various
number of bunches in the performed studies waveguides
of various length were used. The possibility of such a
substitution follows from the fact that due to the output
of the excited wave from the waveguide of finite length
with the group velocity vg the number of bunches of the
sequence of any duration, which contributes to the
growth of the total wakefield at the waveguide exit is
limited. Maximum number of bunches N, which wake-
fields during coherent summation increase the ampli-
tude of the total field is directly proportional to the
length of the waveguide L: N=L/(v0/vg-1), where is
length of the excited wave equal to the distance between
the bunches, v0 is bunch velocity.
The dependence of the excited field at dielectric
waveguide output on time for the two waveguide length
L=/4, L=/2, and vg = v0/2 is shown in Fig. 2,a,b. It
can be seen that the amplitude of the field does not
change for L.
a b
c d
Fig. 2. Dependence of Cherenkov wakefield on time
at output end of the dielectric waveguide of length:
a – / 4L ; b – / 2L ; c – L ; d – 2L .
Number of bunches 10N
With the further increase in the length of the wave-
guide the excited wakefield is growing stepwise by each
length (Figs. 2,c,d and 3).
Fig. 3. Dependence of Cherenkov wakefield
on waveguide length at the waveguide exit
Fig. 4. Model of the dielectric structure, excited by
sequence of electron bunches, taken for simulation
To account the transition radiation, which inevitably
occurs on electrodynamic jumps in real structures, and
reflections of excited fields in imperfectly matched
waveguides, the numerical simulation of model of the
ISSN 1562-6016. ВАНТ. 2015. №6(100) 27
dielectric structure close to the experiment (Fig. 4) was
carried out. Into a metal cylindrical waveguide of length
Ls the dielectric part of length Ld is inserted (yellow
color). Electron bunches (blue color) propagate along a
cylinder axis from left to right.
Fig. 5 shows the dependence of obtained the total
excited field on the dielectric structure length.
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
a
x
(
V
/c
m
)
Ld (cm)
Ez_max
|Ez_min|
Fig. 5. Maximum and minimum of the longitudinal
electric field at exit on of the dielectric part length
Existence of maxima and minima on curves of de-
pendence of a wakefield from length of the dielectric
plug is connected with two factors. Firstly, when dielec-
tric lengths are multiple to a half of wavelength of a
resonant mode the reflection of a wave excited by a
bunch on a dielectric-vacuum boundary is minimum.
Such behavior is similar to passing of plane wave
through a dielectric plate.
Secondly, the partially reflected wave is coherently
added with a direct wave, and the full field grows in a
segment of dielectric tube that will lead to increasing of
the radiated field in case of the subsequent falling of a
wave on boundary of the section of mediums. The situa-
tion with growth of a field is similar to accumulation of
energy in the resonator.
The experimentally obtained linear growth of the to-
tal wakefield excited in the dielectric waveguide by a
long sequence of 6∙10
3
bunches (each of charge 0.26 nC
and duration of 60 ps, bunch repetition frequency
2805 MHz) upon the variable length of the dielectric
waveguide (0…35 cm, step 2.5 cm), evidencing the
coherent addition of wakefields of the bunches, which
fields overlap with increasing of the waveguide length.
By such a method the measurement of the values of
wakefield excited by 1, 2, 3 and 4 bunches was carried
out, agreed with theoretical calculation and numerical
simulation.
Fig. 6. 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 – vacuum dielectric plug; 8 – RF-probe;
9 – oscilloscope; 10 – glass plate; 11 – additional
waveguide with trumpet; 12 – ferrite absorber
Improved matching (adiabatic transitions and ab-
sorbers) (Fig. 6), which decreases reflections, allows to
obtain the dependence of wakefield amplitude on the
dielectric structure length (Fig. 7) similar to the ob-
tained one in simulation (see Fig. 5).
Fig. 7. Dependence of Ez amplitude of excited wakefield
on the matched dielectric waveguide length
In the case of dielectric with rectangular cross-section
there is the possibility to make influence of reflections the
same for various length of bunches interaction with die-
lectric part of the waveguide. For a rectangular wave-
guide with two dielectric plates the opportunity occurs to
deflect e electron bunches on the “bare” walls of the
waveguide, where no dielectric plates (Fig. 8). Arranging
magnetic field region (N-S) at different distances from
the dielectric waveguide exit we can change the interac-
tion length by shifting (N-S) and measure the dependence
of the excited wakefield amplitude upon the length of the
interaction length. At that measurements were carried
out at the same length of the whole dielectric waveguide
avoiding changes in the conditions of reflections when
varying the interaction length.
Fig. 8. 1 – accelerator "Almaz-2M"; 2 – magnetic ana-
lyzer; 3 – diaphragm; 4 – waveguide; 5 – dielectric;
6 – dielectric plug; 7 – wavemeter VMT-10;
8 – oscilloscope
Fig. 9. Dependence of wakefield amplitude on interac-
tion length of bunches with dielectric waveguide
For such experiment wakefield at the dielectric
waveguide output linearly depends on the interaction
length of bunches with dielectric part (Fig. 9), that is
ISSN 1562-6016. ВАНТ. 2015. №6(100) 28
consistent with the theoretical prediction, confirming
coherent summation of wakefields of bunches.
1.3. "MULTI-MODE" EXCITATION
The purpose of research "multi-mode" approach to
prove that the summation of fields of all transverse
modes excited in the dielectric waveguide by a sequence
of bunches gives a peaked signal of alternative sign for
total wakefield with respectively enhanced amplitude.
Most effectively process of addition takes case under
frequency spectrum of transverse modes as much as
possible the close to the equidistant one. In this case the
wakefield looks like sequence of narrow peaks of an
opposite polarity of large amplitude.
Let's consider a semi-infinite waveguide, having
form of two parallel ideally conducting planes with dis-
tance L between them. The waveguide is completely
filled with uniform dielectric of permittivity . The in-
put is short-circuited by perfectly conductive transverse
wall. A sequence of bunches with period T is injected
into the waveguide. The following model of transverse
profile of bunches density is chosen:
0
0
0
0 0
cos , ,
( ) 2
0, / 2 , / 2.
b b
b
b b
x
x x x
R x x
L x x x x L
(1)
In the longitudinal direction bunches are infinitely
thin. Expression for the wakefield in semi-infinite plane
dielectric waveguide has the form:
,ch tr
z z zE E E
3 1
2
0 2 2
cos( )cos( )2
4
N
ch n b n
z
s n odd
n b
k x k xQ
E
L
k x
0 0
( ) ( ) cos ( )n
g
z z z
t sT t sT t sT
v v v
1
2
0 2 2
cos( )cos( )8
4
N
tr n b n
z
s n odd
n b
k x k xQ
E
L
k x
2 2
1` 2` 2
1
( ) ( ) ( 1) ( ) ( )m m m
s s m ns
mpr pr
z z
t sT t sT r r J y
v v
2
0 1 22
1 2
1
( ) ( ) ( 1) ( ) ( ) . (2)m m
ns s m nsm
mg s
z
t sT J y r J y
v r
The spatial structure of wakefield excited by a se-
quence of electron bunches in a multimode regime in
the plane dielectric waveguide was calculated by numer-
ical methods for parameters: 60dL , number of
bunches 20N , number of transverse modes
mod 21N ,
frequency of the transverse fundamental mode is
0 0 / 2 / 2 1/ 2.802repf T GHz, transverse size
of waveguide 5.12xL cm, transverse size of bunches is
/ 0.04b xx L , dielectric permittivity 2.1 . The spatial
structure of excited wakefield is shown in Figs. 10,a,b.
For experimental investigations of multi-mode
scheme for enhancing wakefield amplitude there were
made dielectric waveguide of circular cross section
fillеd with dielectric from Teflon (ε = 2.045) and two
rectangular dielectric waveguides based on a standard
metallic waveguide R26 with two types of dielectric
plates from quartz (ε=3.8), whose dimensions were cal-
culated for obtaining single- or multi-mode of operation
for wakefield excitation. The calculations were per-
formed taking into account the conditions providing the
Cherenkov resonance of bunches with the principal
mode at the frequency ω0, coinciding with the bunch
repetition frequency ωrep = ω0.
Fig. 10,а. Spatial structure of wakefield at the moment
of time / 60t T
Fig. 10,b. Increased scale wakefield dependence on
longitudinal coordinate (fragment of Fig. 10,a)
To measure the frequency spectrum of wakefield ex-
cited by a sequence of bunches in such dielectric wave-
guide, the signal with help of the microwave probe was
applied to the wavemeter VMT-10 or directly to the
oscilloscope TDS6154 with a bandwidth of 15 GHz. In
the first case, the spectrum was determined by the
standard procedure for the wavemeter. In the second
case, the spectrum was obtained by the method of fast
Fourier transform (FFT) or "direct" calculation of the
Fourier integral over one period of the waveform, and
for the whole duration of experimentally obtained wave-
form of wakefield signal.
In theoretical studies for determining the frequency
spectrum of excited eigen radial modes of the dielectric
waveguide a single bunch that moves in an infinite die-
lectric waveguide is used. Because of the complexity of
a single bunch obtaining using accelerator "Almaz-2M",
instead of a single-bunch scenario we proposed and
used another one. The length of the dielectric wave-
guide excited by a long sequence of bunches is taken of
such value that for the available group velocity the
wakefield trains of bunches do not overlap.
For cylindrical dielectric waveguide length L=λ (at
vg=v0/2), i.e. a single-bunch scenario, the experimentally
frequency spectrum measured with wavemeter
WMT-10 in the range of 2.5…7.5 GHz is shown in
Fig. 11. It is seen a prevailing large amplitude of the
microwave signal at bunch repetition frequency
2.805 GHz and a wideband frequency spectrum in the
range of 4.5…6 GHz of much smaller amplitude. A
wideband spectrum is associated with non-multiple fre-
quency of radial modes to the bunch repetition frequen-
cy and transition radiation inevitably arisen at the input
boundary.
ISSN 1562-6016. ВАНТ. 2015. №6(100) 29
Fig. 11. Spectrum of microwave radiation excited
by a long sequence of bunches in cylindrical dielectric
waveguide of length L=λ
To determine the frequency spectrum of transition
radiation a separate experiment was performed, in
which the sequence of bunches prop a through the
waveguide without dielectric, but in the presence of a
metal diaphragm, which is usually located dielectric.
Small peaks of radiation at frequencies of 3.6 GHz and
5.2 GHz were detected, that allows estimating the con-
tribution of transition radiation in the excited spectrum.
Another method for determining the frequency spec-
tra excited in the dielectric waveguide is concluded to
frequency filtering of radiation by Teflon vacuum plug
of various thicknesses. Waveform of microwave radia-
tion signal was taken by microwave probe, located be-
hind the Teflon plug, and applied to the oscilloscope
TDS6154. Taking into account that the maximum pas-
sage of the plug observed at its thickness equal to
halflength of the incident wave, it is possible by chang-
ing the thickness of the plug to pass through the plug the
wakefield of selected frequency excited in the dielectric
waveguide.
Fig. 12,a shows the oscillogram of microwave radia-
tion excited in the dielectric waveguide of length Ld=3λ
at the thickness of the dielectric plug 5 cm, close to a
half-wavelength of the principal mode (λ=10.6 cm). At
this thickness of dielectric plug principal mode passes the
plug with minimal reflection, but radiation of shorter
wavelengths pass worse. Fig. 12,b shows the normalized
spectra obtained using FFT (blue curve) and with the help
of "direct" calculation of the Fourier integral (red curve)
for the waveform presented in Fig. 12,a. Fig. 12,c shows
the spectra for a sample of length equal to the length of
one period of L=λ from the whole waveform. It is evident
that for the whole length of the waveform (see Fig. 12,b)
only the first mode of the excited wakefield stands out,
the other modes do not appear, "spilling" over the nearest
frequencies that are multiple to the bunch repetition fre-
quency. For the length of the waveform sample equal to
the length of one period (see Fig. 12,c) the second mode
at a frequency of 6.7 GHz clearly stands out.
Fig. 12. Oscillogram of microwave signal at the output
of the dielectric waveguide and the normalized
frequency spectrum of the signal at the thickness
of the Teflon vacuum plug of 5 cm
When the thickness of the plug is decreased to
3.6 cm the amplitude of the microwave radiation with a
frequency 2.805 GHz is reduced due to the increase of
the reflection coefficient. At oscillograms the waveform
distortions are observed (Fig. 13,a) due to the passage
through the plug of excited modes of higher frequen-
cies. In this case the spectra obtained from the experi-
mental waveform of whole length by FFT and "direct"
calculation of the Fourier integral (Fig. 13,b) show that
in addition to the principal mode the oscillations at fre-
quencies that are multiple to the bunch repetition fre-
quency with much smaller amplitude are presented.
Spectra obtained by FFT and "direct" calculation of the
Fourier integral for the waveform sample of the length
equal to the length of one period, taken from the whole
waveform is shown in Fig. 13,c. It is seen the frequency
of the second and even the third radial modes.
Fig. 13. Oscillogram of microwave signal at the output
of the dielectric waveguide and the normalized
frequency spectrum of the signal at the thickness
of the Teflon vacuum plug of 3.6 cm
For rectangular dielectric waveguide with multi-
mode excitation by a sequence of bunches the frequency
spectrum, measured by wavemeter VMT-10, is shown
in Fig. 14.
Fig. 14. Spectrum of microwave radiation excited in
rectangular dielectric waveguide of length L=λ
Large amplitude at the frequency of the principal
mode coinciding with bunch repetition frequency is
explained by the fact that for larger values of the dielec-
tric permittivity the reflection from the dielectric-
vacuum boundary increases and such structure of length
multiple to the halfwavelength of the excited mode be-
comes a resonator.
For the parameters of relativistic electron bunches
and dielectric waveguide of circular cross section, used
in the experiments, the frequency spectrum of transverse
modes excited by a single bunch in an infinite wave-
guide were theoretically determined. Although these
modes are not equidistant, the summation of their fields
allows increasing the amplitude of the excited field by
about 30%. Experiments showed that the amplitude of
the total wakefield signal exceeds the amplitude of the
principal mode signal only 10%. This slight excess of
the total signal amplitude compared to the amplitude of
the principal mode signal caused firstly by the non-
equidistance of excited modes and secondly by detuning
between their frequencies and bunch repetition frequen-
ISSN 1562-6016. ВАНТ. 2015. №6(100) 30
cy ωrep under conditions of reflections in the imperfect
waveguide.
In multi-mode rectangular dielectric waveguide the
total signal amplitude higher by more than 60% than the
amplitude of the principal mode signal, that is deter-
mined by better equidistance of excited modes in the
rectangular waveguide.
1.4. "RESONATOR" SCHEME OF EXCITATION
The aim the "resonator" concept is, firstly, to in-
crease the number of bunches of the sequence, adding
wakefields of which increases the total wakefield in
comparison with the case of a waveguide case, and,
secondly, to increase the amplitude of the total wakefield
by adding fields of excited equidistant (hence resonant)
modes. Remind (see section 1.2) that in the case of a
semi-infinite waveguide the maximum number of bunch-
es, which increases the total wakefield, measured at the
waveguide exit, is given by the expression
Nmax=1+L/(v0/vg-1). In the “resonator” concept this limi-
tation, caused by the removal of the wakefield from the
waveguide exit with the group velocity vg, is absent, i.e.
all bunches of the sequence contribute to the increase in
the wakefield amplitude, which grows proportionally to
the total number of bunches Nb. In this case, coherent
energy losses of the bunch grow with its number, and the
total energy loss of the whole sequence is proportional to
Nb
2
. In the resonator with quality factor Q= all bunches
of the long sequence increase the total wakefield in the
resonator. The amplitude of the total wakefield (accord-
ingly, the number of bunches, contributing to the field
increase) is limited by the finite quality factor Q.
For excitation of the wakefields in dielectric resona-
tor by a sequence of bunches the resonant conditions of
the coincidence of bunch repetition frequency ωm with
Cherenkov radiation frequency ω0 (ωrep=ω0) and, simul-
taneously, with the principal eigen frequency of the res-
onator ωr1, i.e. ωrep=ω0=ωr1 should be fulfilled. In the
case of a planar dielectric resonator for providing sum-
mation of wakefields (Cherenkov radiation) of bunches,
fields of radial modes and fields of resonator harmonics,
i.e. the operation of all three concepts-multibunch, mul-
timode, and resonator ones, the fulfillment of these res-
onant conditions is imposed the requirements on the
length L and the transverse size of the transit channel a
of the dielectric resonator. Namely, the resonator length
L should be multiple of the number of half-wavelengths
of the principal mode. At the resonator length
2
0 0 01, /L Na v c , where is dielectric per-
mittivity, N is number of the first longitudinal harmon-
ics of the resonator, being in Cerenkov resonance with
the beam at bunch repetition frequency, the longitudinal
harmonics with number l=Nm, where m is transverse
modes number, are automatically equidistant and coin-
cide with the corresponding transverse modes by fre-
quencies. All of them are occurred in Cerenkov reso-
nance with the beam. It provides peaking and increasing
the amplitude of the total wakefield at the summation of
the sinusoidal fields of the equidistant modes and har-
monics. To fulfill the conditions for "multibunch" con-
cept the transverse size of the transit channel a should
be chosen accordingly to the expression
2
0 0/ 2 1repa v f , where frep is the bunch repetition
frequency.
It was shown that the eigen transverse modes for a
rectangular cross-section are closer to the equidistance
ones than the radial modes of round cross-section. By
this reason along with the cylindrical resonator the reso-
nator of rectangular cross-section was experimentally
investigated with an attempt to find out the summation
of the transverse modes and the corresponding increase
in the amplitude of the total wakefield.
The wakefield excitation is realized by a long se-
quence of 6∙10
3
electron bunches in dielectric resonators
of 4 configurations:
- cylindrical compound-resonator consisting of two
parts: filled with dielectric and empty (without dielec-
tric) ones, each of length multiple their half-wavelength,
that allows to carry out diagnostics of bunches and
wakefield without disturbing the processes of excitation
in the dielectric part (i.e. making equivalent processes in
a single dielectric resonator);
- quartz single-mode dielectric resonator of rectan-
gular cross-section;
- quartz multimode dielectric resonator of rectangu-
lar cross-section;
- zirconia multimode dielectric resonator of rectan-
gular cross-section at fulfillment of resonant conditions-
coincidence of the bunch repetition frequency ωm with
Cherenkov radiation frequency ω0 (ωm=ω0) and, simul-
taneously, with the eigen fundamental frequency of the
resonator ωr, i.e. at fulfillment of ωm=ω0=ωr.
In the absence of losses in the resonator (Q=) and
the multiplicity of frequencies of transverse modes (i.e.
their equidistance), declared conditions should provide
coherent summation of wakefield of all bunches and all
excited transverse modes, and thereby increase the total
wakefield to the level of field, excited by a single bunch
with a charge equivalent to the total charge of all
bunches of the sequence. For finite Q-factor the de-
pendence of the total wakefield upon the resonator Q-
factor experimentally investigated and found the level
of excitation of transverse modes and their contribution
to the total wakefied (Fig. 15).
Fig. 15. Dependence of the wakefield amplitude on the
duration of bunch sequence for different Q-factors
of the compound-resonator: 1 Q1=65; 2 Q2=268;
3 Q3=539; 4 Q4=676
ISSN 1562-6016. ВАНТ. 2015. №6(100) 31
It is shown that in the case of a cylindrical com-
pound-resonator with increasing duration of the se-
quence the total field increases and saturates, remaining
constant for larger durations. With the growth of the Q-
factor the number of bunches of the sequence contrib-
uting to the increase in the total wakefield increases.
The long sequence of 6∙10
3
bunches in our experiment is
practically equivalent by saturation amplitude to the
sequence of infinite number of bunches.
At the achieved maximum Q-factor Q = 676 of the
cylindrical compound-resonator, consisting of part of
length L1 = 3d, filled with Teflon (ε = 2.045; tgδ =
2·10
4
), with the transit channel of diameter 21mm and
of empty part of length L2 = v/2, the sequence of 6∙10
3
electron bunches of charge 0.26 nC and energy
4.5 MeV, with a diameter of 1 cm and a duration of
60 ps, each excites wakefield in an empty part of Ezv
=24 kV/cm and in the transit channel of the dielectric
part Ezd =11.8 kV /cm.
Experiments were performed on the excitation of a
cylindrical compound-resonator at various lengths of the
dielectric part L1=d, 2d, 3d; wherein the length of the
empty part is the same L2 = v/2. It is shown that with
increasing length of the dielectric part the excited wake-
field increases. A theoretical model of wakefield excita-
tion taking into account change in Q-factor and feed-
back time delay was elaborated. A quantitative explana-
tion of the observed increase of the wakefield with die-
lectric part L1 elongation.
Measurements of the amplitude of the total field and
the amplitude of the principal mode field showed that
they practically do not differ from each other. The oscil-
logram of Ezv component of the total field at the end of
the empty part of the compound-resonator at lengths
L1=3d и L2 = v(ωr1), ωr1 is fundamental mode fre-
quency, obtained with oscilloscope TDS6154, is shown
in Fig. 16. Note that the signals in Figs.16,a,b are atten-
uated in 36dB and 25dB, correspodingly, to be proper
for the oscilloscope. It is seen that in the compound-
resonator mainly one mode, the frequency of which
coincides with the frequency of bunch repetition fre-
quency of the resonator and ω0 =ωrep =ωr1 =2∙2.803 is
excited. Wakefield excitation in the compound-
resonator by a long sequence of bunches with a repeti-
tion frequency of ωm and frequency filtering in the
compound-resonator with eigen frequency ωr1 leads to
the excitation in the compound resonator of only the
principal radial mode with frequency ω0 = ωrep = ωr1.
а b
Fig. 16. Oscillograms of wakefield excited by
a sequence of 6∙10
3
bunches in the compound-resonator
(а L1=3d, L2 = v(ωr1); b L1=3d,
L2 = 10v(ωr2)), obtained using TDS 6154
The wakefield excitation by a sequence of bunches
in multimode (thick plates) dielectric (quartz ε = 2.045;
tgδ = 2·10
-4
) rectangular resonator showed that wake-
field increase to Ezd =7 kV/cm in comparison with the
case of the waveguide due to the wakefield summation
of larger number of bunches. Expected amplitude
"peaking" and increasing principal mode amplitude
caused by the addition of transverse modes in the wave-
guide case at the excitation by a single bunch, in the
experiment with a resonator of rectangular (the same for
circular) cross-section and a long sequence of bunches
were not observed. The reason for this result is nonreso-
nant transverse modes, besides principal one. As a re-
sult, the total wakefield is monochromatic.
The wakefield excitation by the sequence bunches in
the single-mode (thin plates) quartz resonator of rectan-
gular cross section at the double frequency
ω0=2ωrep.was performed. There was realized the excita-
tion of monochromatic wakefield with amplitude
Ezd=2.8 kV/cm. Monochromaticity in this case follows
from the fact that in the appropriate waveguide case one
bunch excites mainly one mode at the frequency
ω0=2ωrep, with which coupling coefficient is maximal.
Other modes are almost not excited.
The experiment with such resonator showed the ex-
citation monochromatic wakefield increased compared
to the waveguide case due to more number of bunches
which wakefields, contribute to the total field.
The wakefield excitation by a sequence of bunches
in multimode zirconia dielectric (ε = 23; tgδ = 10
-3
) rec-
tangular resonator was carried out. At resonant condi-
tions prevailing excitation of principal mode to the level
200 V/cm was observed. Such low level is caused by
large loss tangent.
It is demonstrated the presence of excited second ra-
dial mode at a frequency 6.7 GHz in the resonator of the
cylindrical geometry and the frequencies of several
transverse modes for a rectangular geometry, whose
contribution to the total wake field is not essential un-
like to the case of the waveguide. The reason of this
inessentiality, which does not to allow enhancing the
total wakefield, is nonmultiplicity of the mode frequen-
cies to the principal mode frequency and therefore not
getting into the resonance with bunch repetition fre-
quency and eigen frequency of the resonator.
2. “INJECTION” PROBLEM FOR BUNCHES
ACCELERATION [15]
To solve the "injection" problem using introducing
detuning between bunch repetition frequency and fre-
quency of excited wakefield, that allows obtaining driv-
ing and accelerated bunches from the same sequence.
For the case of introduced detuning the theoretical and
experimental studies of the wakefield excitation in the
dielectric waveguide/resonator by a part of electron
bunches-drivers of a periodic sequence and the accelera-
tion by this wakefield of the other part of the bunches-
witnesses of the same sequence. Such situation becomes
possible due to successive shift of bunches by phase of
excited wakefield. In the performed experiments the
frequency of dielectric wakefield is fixed and deter-
mined by the Cherenkov resonance (coincidence the
velocity of bunches and the phase velocity of the excit-
ISSN 1562-6016. ВАНТ. 2015. №6(100) 32
ed wave of the dielectric waveguide). The bunch repeti-
tion frequency is varied by change of the frequency of
master oscillator "Rubin" of klystron amplifier. In this
concept of "excitation- acceleration" process using the
same sequence of bunches there is no need for addition-
al linac injector for bunches-witnesses producing, which
simplifies the experimental demonstration of bunches
acceleration in the excited wakefield.
In the case of resonance, i.e. coincidence of bunch
repetition frequency frep and frequency of the principal
mode of excited wakefield f0 all bunches are occurred in
the decelerating phase and lose energy to excite wake-
field. In the presence of frequency detuning Δf=frep-f0≠0
bunches of the first part of the sequence occurred in the
decelerating phases of excited field lose energy to the
increase in total wakefield and bunches of the next part
of the sequence, shifted to the region of the accelerating
phases of wakefield excited by the previous part of the
sequence, gain an additional energy.
For point and monoenergetic bunches the number of
bunches N
*
of the first part of the sequence, exciting
wakefield, evaluated from the phase shift of N
*-
th bunch
on π is equal N
*
=frep/2Δf. The next part of the sequence
of bunches of the same duration is accelerated.
Calculated electron energy spectra for monoenergetic
bunches in the single-mode approximation for the cases
of infinitely thin ring bunches (red) and bunches with
rectangular longitudinal and transverse profiles (blue) are
shown in Fig. 17. Following parameters of the dielectric
waveguide and the sequence of electron bunches are
taken: radius of the metal tube is b = 4.325 cm, radius of
the transit channel is a = 1.44 cm, dielectric constant is
2.1 , radius of the bunches is / 0.5br a , number of
bunches in the sequence is N = 500, charge of bunch is
90.32 10Q C , detuning value was chosen to be Δf/frep=
0.002, 1 / 3b bt is the duration of a single bunch.
Fig. 17. Electron energy spectra for a sequence
of 500 infinitely thin ring bunches (red)
and rectangular ones(blue) at detuning Δf/frep=0.002
It is seen that in the case of an infinitely thin ring
bunches energy spectrum of interacted bunches has two
narrow maxima (red) corresponding to the accelerated
and decelerated bunches. Maximal increase of the rela-
tivistic factor is 0.9 or 410 keV for the initial en-
ergy 4.5 MeV. For bunches with finite longitudinal and
transverse dimensions broadening of the energy spec-
trum is essential (blue). Instead of narrow peaks two
poorly defined maxima are occurred. More broadening
of the energy spectrum is caused by existence of accel-
erating (decelerating) wakefield gradient inside the elec-
tron bunches.
Let us take into account also existing in the experi-
ment the initial electron energy spread of the bunch,
which is described by a model distribution function
2
0
2
( )
0
1
f e
, where is characteristic spread
of relativistic factor,
0 is its averaged value. We con-
sider injection of a sequence of relativistic electron
bunches into dielectric resonator without losses in the
presence of detuning between the bunch repetition fre-
quency and wakefield frequency. In Fig. 18 the electron
energy distribution function before and after interaction
for initial energy spread 0.5 and number of
bunches is 1000N is presented.
а b
Fig. 18. Initial distribution function f0 (red line),
final distribution function f (black line):
а – Δf/ frep =0; b – Δf/ frep = 0.001
It can be seen that for the resonant case Δf/frep=0
the distribution function is shifted to the left as a whole,
i.e. all electrons lose their energy for wakefield excita-
tion. For the case of detuning Δf/frep=0.001 distribution
function broadening caused by deceleration and acceler-
ation of electron bunches takes place. Maximize energy
in this case is about 175 keV.
Fig. 19,a,b shows obtained energy spectra of the
electrons of the beam passing through the resonator
without dielectric when there is no Cerenkov interaction
of bunches with the resonator (black spectra, which are
close to the initial ones at the resonator input) and
through the resonator with a dielectric tube (red spectra
obtained after excitation of wakefield and interaction
with it) for two cases: resonant one (zero detuning Δf=0,
see Fig. 19,a) and nonresonant one (nonzero detuning
Δf=2.5 MHz, see Fig. 19,b).
Fig. 19. Energy spectra of electron bunches passing
through the resonator without dielectric (black curves)
and a resonator with dielectric tube (red curves):
а – Δf=0; b – Δf = frep - f0 = 2.5 МHz
From Fig. 19 follows that at the presence of dielec-
tric in the case of resonance Δf = 0 the energy spectrum
is shifted by 400 keV as a whole to lower energies that
is caused by the energy loss of all the bunches on the
wakefield excitation. In the case of detuning between
the bunch repetition frequency and the frequency of
wakefield Δf = frep - f0= 2.5 MHz a part of bunches of
the sequence, shifting over phase, falls into the acceler-
ating phase of the wakefied excited by previous bunches
ISSN 1562-6016. ВАНТ. 2015. №6(100) 33
of the same sequence and gain energy. In this case, in
the electron energy spectrum there are observed both the
electrons losing energy (-150 keV) and electrons gain-
ing additional energy (+150 keV).
By detuning it can be regulated the number of
bunches from the sequence which excite the wakefield,
and the number of subsequent bunches from the same
sequence that fall into the accelerating phase of the
wakefield and gain additional energy. With increase of
frequency detuning the conditions arise when wakefield
beating is observed with several parts of the sequence
consisting of decelerated and accelerated bunches.
3. PLASMA-DIELECTRIC VERSION [16]
The presence of plasma in the channel for bunches
transit allows compensating space charge of bunches
and preventing bunch electrons hit the dielectric wall,
and thus improve the bunches propagation through the
channel and increase the excited wakefield amplitude at
exit. In addition, plasma changes the dispersion charac-
teristics of waveguide/resonator and wakefield topogra-
phy in the channel excited by a sequence of bunches at
Cherenkov resonance.
Note that in considered case the wakefield consists
of the dielectric field modified with plasma and pure
plasma field excited at different frequencies, except
coincidence of plasma frequency ωp and frequency of
the modified dielectric field ω0 (ωp=ω0). Different fre-
quencies allow in case of the scheme with a single driv-
er-bunch and a single bunch-witness to place bunch-
witness in the phase where it will be accelerated by a
large longitudinal dielectric field (its radial field for
relativistic bunches is insignificant) and focused by a
large radial plasma field (Fig. 20).
а b
Fig. 20. a – axial profile of longitudinal (solid) and
transverse forces (dashed), acting on a test bunch at a
distance of 0.95 cm from the waveguide axis;
b – radial profile of longitudinal (solid) and transverse
(dashed) forces acting on a test bunch located in the
first maximum of accelerating field at a distance
of 7.56 cm from the head of driver bunch
The performed theoretical studies of electrodynam-
ics of dielectric waveguide with an axial transit channel,
filled with plasma show that the presence of plasma in
transit channel leads to changes in the topography of the
principal mode of the dielectric wakefield, so that in the
channel r=0…1.0 cm wakefield becomes volumetric.
Caused by this the growth of the coupling coefficient of
bunches with a wave provides an increase of the longi-
tudinal field amplitude in the channel more for higher
plasma density (Fig. 21).
For a sequence of bunches the situation is compli-
cated by the fact that the presence of plasma in the
channel violates the resonance condition of the coinci-
dence bunch repetition frequency ωrep and frequency of
the dielectric field ω0 modified with plasma. As a result
at the presence of plasma the total wakefield beat is
arisen with significantly reduced amplitude. Neverthe-
less a single bunch scenario can be realized for the long
sequence of bunches if we take the waveguide length
L = λ (see section 1.2).
Fig. 21. Topography of wakefield excited by a single
bunch in transit channel of cylindrical dielectric wave-
guide filled with plasma of various plasma densities
The situation becomes more complicated in the res-
onator case because of the need to comply with addi-
tional resonance with the eigen frequencies of the resona-
tor ωn, i.e. ωrep = ω0= ωn
3.1. EXPERIMENTAL SETUP
The scheme of experimental setup is shown in
Fig. 22. Relativistic electron bunches penetrate through
a titanium foil with a thickness of 30 and enter into
the dielectric waveguide of round cross section, filled
with dielectric with transit channel of diameter 21 mm for
the passage of bunches.
Fig. 22. Scheme of experimental setup: 1 – accelerator;
“Almaz-2M”; 2 – titanium foil; 3 – vacuum meter;
4 – dielectric waveguide; 5 – dielectric microwave
matcher; 6 – ferrite absorber; 7 – microwave probe;
8 – oscilloscope; 9 – double Faraday cup;
10 – vacuum pump
For realization of the waveguide case it is needed to
avoid reflections of the excited wakefield. For this pur-
pose, the dielectric insert is ended with dielectric mi-
crowave matcher, and on Teflon vacuum cap ferrite
absorber is placed. For obtaining single bunch regime
the length of the dielectric insert was chosen equal to
length of the excited dielectric wave L = λ.
Plasma in the transit channel of the dielectric wave-
guide is produced by the beam itself when it passes
through the neutral gas of regulated pressure filling the
transit channel due to the beam-plasma discharge (BPD)
with the excited wakefield developing at pressure 1 Torr
and due to the collisional ionization by beam electrons at
higher pressures.
ISSN 1562-6016. ВАНТ. 2015. №6(100) 34
To study focusing relativistic electron bunches dou-
ble Faraday cup (9) is used in which the focusing effect
is determined by the presence of the beam current in-
crease in the second cup and a simultaneous decrease in
the beam current in the first cylinder.
3.2. EFFICIENCY OF WAKEFIELD EXITATION
As shown by the oscillograms of the microwave sig-
nals envelope obtained by means of a microwave probe
placed at the exit of the dielectric waveguide having a
dielectric insert of length L = λ under neutral gas pres-
sure in the transit channel in range 0.02...1 Torr, the
amplitude of excited wakefield (see Fig. 22,b) exceeds
the amplitude of wakefield excited in the dielectric
waveguide without plasma (see Fig. 23,a,c).
a b c
Fig. 23. Oscillograms of the envelope of the microwave
signals of wakefields (blue) for various gas pressure:
a – Р = 10
-3
Torr; b – 0.5 Torr; c – Р = 140 Torr.
Red oscillograms – beam current
In the case of a waveguide and a single bunch re-
gime the dependence of the amplitude of the excited
longitudinal wakefield on the axis for the wide range of
the gas pressure is shown in Fig. 23 (red curve). It is
seen that in the pressure under which BPD develops and
plasma is formed the wakefield wave topography in the
channel becomes volumetric (in agreement with the
theory (see Fig. 21)), that increases the coupling coeffi-
cient of the bunch with the wakefield wave and leads to
the increase in the excited wakefield amplitude com-
pared with the case without gas injection (Fig. 24, hori-
zontal red line).
Fig. 24. Dependence of excited wakefield Ez upon
neutral gas pressure in the transit channel
In the case of dielectric resonator (matching ele-
ments were removed and metal exit plug was installed)
under conditions of the double-resonance ω0 = ωrep = ωn
(coincidence of Cherenkov frequency ω0 with bunch repeti-
tion frequency ωrep and simultaneously with eigen fre-
quency of the resonator ωn the wakefield amplitude
grows significantly. This is due to the fact that the num-
ber of bunches which contribute to the total wakefield is
limited only by Q-factor (for conventional Q it is hun-
dreds of bunches), whereas in the case of the waveguide
the number of bunches, determined by the waveguide
length and the group velocity, does not exceed tens of
bunches. However, unlike the waveguide case with a
single bunch regime in the resonator case all bunches
involved in wakefield build-up excitation, i.e. bunch
repetition frequency ωrep comes into play, and resonator
eigen frequencies ωn are present.
3.3. FOCUSING DRIVER-BUNCHES
In the case of the waveguide (matched exit) in a sin-
gle bunch regime (L = λ) both mentioned resonances are
absent and all bunches are in the same conditions of
exciting bunches-drivers. Fig. 25 shows theoretically
obtained [17] the dielectric and plasma wakefields ex-
cited by a single bunch for two plasma densities.
a b
Fig. 25. The total longitudinal component of dielectric
and plasma wakefields (solid, black) and transverse
component of plasma wakefield (dashed, red) for plas-
ma densities: a – np=10
10
cm
-3
; b – np=10
11
cm
-3.
It is seen that the bunch of finite length and finite ra-
dius is occurred in its own wakefield – longitudinal die-
lectric (decelerating) and radial plasma (focusing) ones.
Radial defocusing dielectric field with its almost uniform
longitudinal field over radius is insignificant. As a result
bunch-driver will be focused by its excited plasma
wakefield along with the focusing due to compensation
in the plasma of its radial electric field [18].
Fig. 26 shows the waveform of the beam current,
experimentally obtained with a double Faraday cup at
vacuum Р = 10
-3
Torr (see Fig. 26,a) and at neutral gas
pressure in the transit channel of dielectric waveguide P
= 0.5 Torr (see Fig. 26,b), when plasma is intensively
produced. The increase in current in the second cup
while its reducing in the second one for the second case
evidences focusing electron bunches, more at a higher
plasma density for gas pressure P = 0.5 Torr.
а b
Fig. 26. Oscillograms of beam current taken from
double Faraday cup: top – first cylinder; bottom –
second cylinder; а – Р = 10
-3
Torr; b – Р = 0.5 Torr
4. CHANGE OF ELECTRODYNAMIC AND
MECHANICAL PROPERTIES OF
DIELECTRIC MATERIALS UNDER
ELECTRON BEAM IRRADIATION
Irradiation of samples made from zirconium nanoc-
eramics (ZrO2-4 wt% MgO) was carried out by using
ISSN 1562-6016. ВАНТ. 2015. №6(100) 35
electron linac LUE-40 with electron beam energy up to
100 MeV. There were 20 samples irradiated with differ-
ent fluencies of the electron beam (from 210
16
to
210
18
cm
-2
) and the energy of the particles up to
90 MeV. The change in temperature of samples during
irradiation did not exceed 100С. Studies of the irradiat-
ed samples allowed obtaining the information about
induced activity and changes in the electrodynamics’
and mechanical properties of zirconium nanoceramics.
A measurement of change of the dielectric properties of
nanoceramic samples with a diameter of 10 mm and
thickness 2.5 mm was carried out by using the resonator
method with a partial/full filling RF cavity. Comparison
of the resonant frequency and Q-factor of resonators
before and after irradiation showed the followings:
- permittivity is reduced by (0.230.02)%;
- loss tangent was not changed within range 3%.
To investigate the influence of electron irradiation
on the mechanical properties of zirconium nanoceramics
two samples ZrO2-4 wt% MgO with diameter of 10 mm
were selected. The first of them was irradiated by elec-
tron beam with energy of 45 MeV, the second one was
irradiated by electron beam with energy of 89 MeV. The
fluence was 210
16
cm
-2
. Studies of the samples showed
that irradiation leads to phase transitions in the structure
of the dielectric, and to phase transformation of cubic
zirconia. In the grains under irradiation by the electron
beam with energy of 45 MeV the formation of lens-
shaped grains of tetragonal phase took place. With in-
creasing electron beam energy to 89 MeV these grains
grow and turn into crystals of lamellar shape. These
changes in the structure of the zirconium nanoceramics
lead to the formation of a composite structure. At that
the fragility of the material is decreased and hardness is
decreased from 12.2 to 10.8 and 10.5 GPa after irradia-
tion of the ceramic material by the electron beam with
energy 45 and 89 MeV, respectively.
CONCLUSIONS
The possibility of wakefield amplitude enhancing in
"multibunch", "multimode" and "resonator" regimes of
the excitation is theoretically and experimentally inves-
tigated. It is shown that the coherence at coincidence of
bunch repetition frequency and excited wakefield fre-
quency in "multibunch" regime and the accumulation of
wakefields at multiplicity of eigen frequencies of the
resonator to the bunch repetition frequency and excited
wakefield frequencies in "resonator" regime provides
enhancement of the total wakefield. Impossibility to
realize coincidence/multiplicity of mentioned frequen-
cies with Cherenkov resonance frequencies of trans-
verse modes because of their nonequidistance causes
insufficiently effective enhancing of the total wakefield
amplitude.
The acceleration of bunches in wakefield excited by
bunches of the same sequence at introduction of detun-
ing between bunch repetition frequency and excited
wakefield frequency is demonstrated.
It is found that the presence of plasma in the transit
channel leads to the excitation of the plasma wakefield
which focuses both driving and accelerated bunches.
Determined that the irradiation of samples made
from zirconium nanoceramics (ZrO2-4 wt% MgO) by
100 MeV electron beam with fluency of order 10
18
сm
-2
changes the dielectric permittivity by 0.2%, that is suffi-
ciently to destroy the conditions of Cherenkov reso-
nance in the acceleration process.
Mechanical properties of zirconium nanoceramics
are changed too. Fragility is decreased and hardness is
reduced.
ACKNOWLEDGEMENT
Work supported by Global Initiatives for Prolifera-
tion Prevention (GIPP) program, project ANL-T2-247-
UA (STCU Agreement P522).
REFERENCES
1. John R. Rees. The Stanford Linear Collider // Scien-
tific American. 1989, v. 261, № 4, p. 36-43.
2. H. Braun, R. Corsini, T. D'Amico, et al. The CLIC
RF power source: a novel scheme of two-beam ac-
celeration for electron-positron linear colliders /
CLIC-Note-364. 1998.
3. J. Brau, Y. Okada, N. Walker, et al. International
Linear Collider / Reference Design Report. 2007.
4. CERN / LHC Design Report. 2008.. Available from
http://ab-div.web.cern.ch/ab-div/ Publications/LHC-
DesignReport.html
5. Maury Tigner. “Does Accelerator-Based Particle
Physics Have a Future?” // Physics Today. 2001,
January, p. 36.
6. V.N. Veksler // Proc. Symp. CERN, Geneva, 1956,
v. 1, p. 80-83. G.I. Budker. Ibid, p. 68-75.
Ya.B. Fainberg. The use of plasma waveguides as
accelerating structures. Ibid, p. 84-92.
7. T. Tajima, J.M. Dawson. Laser electron acceleration
// Phys. Rev. Letters. 1979, v. 43, № 4, p. 267.
8. P. Chen, J.M. Dawson, R. Huff, T. Katsouleas. Ac-
celeration of electrons by the interaction of a bunched
electron beam with a plasma // Phys. Rev. Letters,
1985, v. 54, № 7, p. 692.
9. W. Gai, P. Schoessow, B. Cole, et al. Experimental
Demonstration of Wake-Field Effects in Dielectric
Structures // Phys. Rev. Lett. 1988, v. 61, 2756.
10. P. Sprangle, B. Hafizi, R.F. Hubbard. Ionization and
pulse lethargy effects in inverse Cherenkov accelera-
tors // Phys. Rev. E, 1997, v. 55, № 5, p. 5964-5974.
11. M.C. Thompson, H. Badakov, A.M. Cook, et al.
Breakdown Limits on Gigavolt-per-Meter Electron-
Beam-Driven Wakefields in Dielectric Structures //
PRL 100. 2008, 214801.
12. T-B. Zhang, J.L. Hirshfield, T.C. Marshall, B. Hafizi1.
Stimulated dielectric wake-field accelerator // Phys.
L Rev. E. 1997, v. 56, № 4, p. 4647.
13. I.N. Onishchenko, V.A. Kiselev, A.F. Linnik,
G.V. Sotnikov. Concept of dielectric wakefield ac-
celerator driven by a long sequence of electron
bunches // IPAC'13. Shanghai, China. 2013.
14. G.P. Berezina, G.A. Krivonosov, A.F. Linnik,
I.N. Onishchenko, V.S. Us. Matched dielectric
waveguide elaboration for research of multibunch
scheme of wakefield excitation therein // Problems
of Atomic Science and Technology. Series “Nuclear
Physics Investigation”, this issue, p. 60-64.
http://ab-div.web.cern.ch/ab-div/
ISSN 1562-6016. ВАНТ. 2015. №6(100) 36
15. G.P. Berezina, G.A. Krivonosov, A.F. Linnik,
O.L. Omelaenko, I.N. Onishchenko, V.I. Pristupa,
V.S. Us. Electron bunches acceleration at detuning
bunch repetition frequency and frequency of wake-
field excited in a dielectric structure // Problems of
Atomic Science and Technology. Series “Nuclear
Physics Investigation” , this issue, p. 56-59.
16. V.A. Kiselev, A.F. Linnik, IN. Onishchenko, et al.
Wakefield excitation in plasma-dielectric structures
by a sequence relativistic electron bunches // Prob-
lems of Atomic Science and Technology. Series
“Plasma Physics”, 2015, № 1, p. 137-140.
17. R. Knyazev, G.V. Sotnikov. Focusing wakefield for
accelerated bunch in a plasma-dielectric waveguide
// J. of Kharkiv University. 2012, № 1001, p. 64-68.
18. G. Hairapetian, P. Devis, C. Joshi, et al. Transverse
dynamic of a short relativistic electron bunch in a
plasma lens // Phys. Plasma. 1995, v. 2 (6), p. 2555-
2561.
Article received 02.11.2015
ИССЛЕДОВАНИЯ ФИЗИЧЕСКИХ ПРОЦЕССОВ В МУЛЬТИБАНЧЕВОМ ДИЭЛЕКТРИЧЕСКОМ
КИЛЬВАТЕРНОМ УСКОРИТЕЛЕ
И.Н. Онищенко
Представлены основные результаты теоретических и экспериментальных исследований физических про-
цессов в диэлектрическом кильватерном ускорителе, основанном на возбуждении ускоряющего кильватер-
ного поля в диэлектрической структуре длинной последовательностью электронных сгустков. Увеличение
амплитуды возбуждаемого кильватерного поля достигается за счет когерентного сложения кильватерных
полей отдельных сгустков, суммирования полей эквидистантных поперечных мод и накопления полей в
резонаторе. Ускорение сгустков в суммарном кильватерном поле реализовано разделением последователь-
ности сгустков на возбуждающую и ускоряющую части в любом соотношении с помощью соответствующей
расстройки частоты следования сгустков по частоте возбуждаемой основной поперечной моды. Исследова-
но изменение диэлектрической проницаемости и тангенс угла потерь применяемых диэлектриков под воз-
действием радиационного облучения их 100 МэВ-электронным пучком.
ДОСЛІДЖЕННЯ ФІЗИЧНИХ ПРОЦЕСІВ У МУЛЬТІБАНЧЕВОМУ ДІЕЛЕКТРИЧНОМУ
КІЛЬВАТЕРНОМУ ПРИСКОРЮВАЧІ
I.M. Oніщенко
Представлено основні результати теоретичних і експериментальних досліджень фізичних процесів у діе-
лектричному кільватерному прискорювачі, заснованому на збудженні прискорюючого кільватерного поля в
діелектричній структурі довгою послідовністю електронних згустків. Збільшення амплітуди збуджуваного
кільватерного поля досягається за рахунок когерентного складання кільватерних полів окремих згустків,
підсумовування полів еквідистантних поперечних мод та накопичення полів у резонаторі. Прискорення згу-
стків у сумарному кільватерному полі реалізовано поділом послідовності згустків на збуджуючу і приско-
рювану частини в будь-якому співвідношенні за допомогою відповідної розстройки частоти слідування згу-
стків щодо частоти збуджуваної основної поперечної моди. Досліджено зміну діелектричної проникності і
тангенс кута втрат застосовуваних діелектриків під впливом радіаційного опромінення їх 100 МеВ-
електронним пучком.
|
| id | nasplib_isofts_kiev_ua-123456789-112362 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1562-6016 |
| language | English |
| last_indexed | 2025-11-27T16:49:20Z |
| publishDate | 2015 |
| publisher | Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
| record_format | dspace |
| spelling | Onishchenko, I.N. 2017-01-20T17:39:10Z 2017-01-20T17:39:10Z 2015 Investigations of the physical processes in multibunch dielectric wakefield accelerator / I.N. Onishchenko // Вопросы атомной науки и техники. — 2015. — № 6. — С. 25-36. — Бібліогр.: 18 назв. — англ. 1562-6016 PACS: 41.75.Ht; 41.75.Lx https://nasplib.isofts.kiev.ua/handle/123456789/112362 The main results of theoretical and experimental researches of the physical processes in a dielectric wakefield accelerator based on the excitation of accelerating wakefield in a dielectric structure by a long sequence of electron bunches are represented. Enhancement of the excited wakefield amplitude is achieved through coherent addition wakefields of individual bunches, wakefields summation of the equidistant transverse modes and wakefields storage in the resonator. Acceleration of bunches in the total wakefield is realized at dividing sequence of bunches in the exciting and accelerated parts in any ratio by an appropriate frequency detuning of bunch repetition frequency relative to the excited principal transverse mode. The change in the dielectric constant and loss tangent of used dielectrics under exposure to 100 MeV electron beam is investigated. Представлено основні результати теоретичних і експериментальних досліджень фізичних процесів у діелектричному кільватерному прискорювачі, заснованому на збудженні прискорюючого кільватерного поля в діелектричній структурі довгою послідовністю електронних згустків. Збільшення амплітуди збуджуваного кільватерного поля досягається за рахунок когерентного складання кільватерних полів окремих згустків, підсумовування полів еквідистантних поперечних мод та накопичення полів у резонаторі. Прискорення згустків у сумарному кільватерному полі реалізовано поділом послідовності згустків на збуджуючу і прискорювану частини в будь-якому співвідношенні за допомогою відповідної розстройки частоти слідування згустків щодо частоти збуджуваної основної поперечної моди. Досліджено зміну діелектричної проникності і тангенс кута втрат застосовуваних діелектриків під впливом радіаційного опромінення їх 100 МеВ-електронним пучком. Представлены основные результаты теоретических и экспериментальных исследований физических процессов в диэлектрическом кильватерном ускорителе, основанном на возбуждении ускоряющего кильватерного поля в диэлектрической структуре длинной последовательностью электронных сгустков. Увеличение амплитуды возбуждаемого кильватерного поля достигается за счет когерентного сложения кильватерных полей отдельных сгустков, суммирования полей эквидистантных поперечных мод и накопления полей в резонаторе. Ускорение сгустков в суммарном кильватерном поле реализовано разделением последовательности сгустков на возбуждающую и ускоряющую части в любом соотношении с помощью соответствующей расстройки частоты следования сгустков по частоте возбуждаемой основной поперечной моды. Исследовано изменение диэлектрической проницаемости и тангенс угла потерь применяемых диэлектриков под воздействием радиационного облучения их 100 МэВ-электронным пучком. Work supported by Global Initiatives for Proliferation Prevention (GIPP) program, project ANL-T2-247-UA (STCU Agreement P522) en Національний науковий центр «Харківський фізико-технічний інститут» НАН України Вопросы атомной науки и техники Новые и нестандартные ускорительные технологии Investigations of the physical processes in multibunch dielectric wakefield accelerator Дослідження фізичних процесів у мультібанчевому діелектричному кільватерному прискорювачі Исследования физических процессов в мультибанчевом диэлектрическом кильватерном ускорителе Article published earlier |
| spellingShingle | Investigations of the physical processes in multibunch dielectric wakefield accelerator Onishchenko, I.N. Новые и нестандартные ускорительные технологии |
| title | Investigations of the physical processes in multibunch dielectric wakefield accelerator |
| title_alt | Дослідження фізичних процесів у мультібанчевому діелектричному кільватерному прискорювачі Исследования физических процессов в мультибанчевом диэлектрическом кильватерном ускорителе |
| title_full | Investigations of the physical processes in multibunch dielectric wakefield accelerator |
| title_fullStr | Investigations of the physical processes in multibunch dielectric wakefield accelerator |
| title_full_unstemmed | Investigations of the physical processes in multibunch dielectric wakefield accelerator |
| title_short | Investigations of the physical processes in multibunch dielectric wakefield accelerator |
| title_sort | investigations of the physical processes in multibunch dielectric wakefield accelerator |
| topic | Новые и нестандартные ускорительные технологии |
| topic_facet | Новые и нестандартные ускорительные технологии |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/112362 |
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