Elaboration of the plasma-dielectric wakefield accelerator with a profiled sequence of driver electron bunches
A theoretical and experimental study of wakefield excitation by a profiled sequence of relativistic electron bunches in the plasma-dielectric structure, the parameters of which provide the conditions for the excitation of a small decelerating field for all driver bunches with simultaneous growth wit...
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| Date: | 2023 |
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Національний науковий центр «Харківський фізико-технічний інститут» НАН України
2023
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| Cite this: | Elaboration of the plasma-dielectric wakefield accelerator with a profiled sequence of driver electron bunches / I.N. Onishchenko, K.V. Galaydych, R.R. Kniaziev, G.O. Krivonosov, A.F. Linnik, P.I. Markov, O.L. Omelayenko, V.I. Pristupa, G.V. Sotnikov, V.S. Us, D.Yu. Zaleskiy // Problems of Atomic Science and Technology. — 2023. — № 4. — С. 53-60. — Бібліогр.: 14 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1859901771634180096 |
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| author | Onishchenko, I.N. Galaydych, K.V. Kniaziev, R.R. Krivonosov, G.O. Linnik, A.F. Markov, P.I. Omelayenko, O.L. Pristupa, V.I. Sotnikov, G.V. Us, V.S. Zaleskiy, D.Yu. |
| author_facet | Onishchenko, I.N. Galaydych, K.V. Kniaziev, R.R. Krivonosov, G.O. Linnik, A.F. Markov, P.I. Omelayenko, O.L. Pristupa, V.I. Sotnikov, G.V. Us, V.S. Zaleskiy, D.Yu. |
| citation_txt | Elaboration of the plasma-dielectric wakefield accelerator with a profiled sequence of driver electron bunches / I.N. Onishchenko, K.V. Galaydych, R.R. Kniaziev, G.O. Krivonosov, A.F. Linnik, P.I. Markov, O.L. Omelayenko, V.I. Pristupa, G.V. Sotnikov, V.S. Us, D.Yu. Zaleskiy // Problems of Atomic Science and Technology. — 2023. — № 4. — С. 53-60. — Бібліогр.: 14 назв. — англ. |
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| container_title | Problems of Atomic Science and Technology |
| description | A theoretical and experimental study of wakefield excitation by a profiled sequence of relativistic electron bunches in the plasma-dielectric structure, the parameters of which provide the conditions for the excitation of a small decelerating field for all driver bunches with simultaneous growth with the number of bunches of the accelerating total wakefield was carried out. Theoretically, the transformation ratio was found for the parameters of the experiment as the ratio of the total wakefield of the sequence to the field that decelerates driver bunches. In the performed experiments, the total wakefield was measured by the microwave probe. The magnitude of the decelerating field is determined by the shift of the maximum of the spectrum measured by the magnetic analyzer before and after wakefield excitation in the structure. The obtained transformation ratio increases with the number of bunches in the sequence and significantly exceeds this one for a nonprofiled sequence.
Виконано теоретичне та експериментальне дослідження збудження кільватерного поля профільованою послідовністю релятивістських електронних згустків у плазмово-діелектричній структурі, параметри якої забезпечують умови для збудження малого сповільнюючого поля для всіх драйверних згустків з одночасним зростанням з кількістю згустків прискорювального сумарного кільватерного поля. У теорії для параметрів експерименту знайдено коефіцієнт трансформації як відношення повного кільватерного поля послідовності до поля, що сповільнює драйверні згустки. В експерименті сумарне кільватерне поле вимірювалося мікрохвильовим зондом. Величина сповільнюючого поля знаходилась по зсуву максимуму енергетичного спектра, вимірюваного магнітним аналізатором до та після збудження кільватерного поля у структурі. Отриманий коефіцієнт трансформації зростає зі збільшенням кількості згустків у послідовності та значно перевищує такий для непрофільованої послідовності.
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| first_indexed | 2025-12-07T15:58:06Z |
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ISSN 1562-6016. Problems of Atomic Science and Technology. 2023. № 4(146) 53
NEW METHODS OF CHARGED PARTICLES ACCELERATION
https://doi.org/10.46813/2023-146-053
ELABORATION OF THE PLASMA-DIELECTRIC WAKEFIELD
ACCELERATOR WITH A PROFILED SEQUENCE OF DRIVER
ELECTRON BUNCHES
I.N. Onishchenko, K.V. Galaydych, R.R. Kniaziev, G.O. Krivonosov, A.F. Linnik, P.I. Markov,
O.L. Omelayenko, V.I. Pristupa, G.V. Sotnikov, V.S. Us, D.Yu. Zaleskiy
National Science Center “Kharkov Institute of Physics and Technology”, Kharkiv, Ukraine
E-mail: onish@kipt.kharkov.ua
A theoretical and experimental study of wakefield excitation by a profiled sequence of relativistic electron
bunches in the plasma-dielectric structure, the parameters of which provide the conditions for the excitation of a
small decelerating field for all driver bunches with simultaneous growth with the number of bunches of the acceler-
ating total wakefield was carried out. Theoretically, the transformation ratio was found for the parameters of the
experiment as the ratio of the total wakefield of the sequence to the field that decelerates driver bunches. In the per-
formed experiments, the total wakefield was measured by the microwave probe. The magnitude of the decelerating
field is determined by the shift of the maximum of the spectrum measured by the magnetic analyzer before and after
wakefield excitation in the structure. The obtained transformation ratio increases with the number of bunches in the
sequence and significantly exceeds this one for a nonprofiled sequence.
PACS: 41.75.Ht; 41.75.Lx
INTRODUCTION
Currently, high-energy physics requires beams of
charged particles in the TeV energy range to solve fun-
damental problems. The relevant existing colliders
hadron LHC [1] and lepton CLIC [2] and ILC [3])
using traditional acceleration methods have become
extremely huge and expensive. The development of
advanced methods of charged particles acceleration with
an accelerating rate of several orders higher than tradi-
tional ones is necessary to radically reduce the dimen-
sions and cost of future colliders.
CERN has presented an updated strategy for high-
energy physics 2020 UPDATE OF THE EUROPEAN
STRATEGY FOR PARTICLE PHYSICS [4]. In order
to develop the physics program of the future cyclic lep-
ton collider, it is proposed to increase its energy to
175 GeV, and its perimeter to 100 km. By analogy with
the successful long-term operation of the LEP-LHC,
after the lepton collider operation program it is planned
to build in the same tunnel the hadron collider for ener-
gy up to 100 TeV using the LHC as an injector.
Taking into account the wide-ranging theoretical and
experimental studies of new acceleration methods and
the achieved significant results in the wakefield method
of acceleration in plasma with an acceleration rate of
about 50 GeV/m, three orders of magnitude higher than
the traditional one with a beam driver at a length of
0.9 m doubling the energy of a 42 GeV electron bunch
[5]; and with a laser driver at a length of 9 cm reaching
an energy of 4.2 GeV [6] within the framework of the
updated European strategy for high-energy physics, at
the initiative of the International Committee of Future
Accelerators ICFA (International Committee of Future
Accelerators), the collaboration “АLEGRO” (Advanced
LinEar collider study GROup) was created, which of-
fered to build with the joint efforts of many countries
the e+/e -/gamma collider “ALIC” (Advanced Linear
International Collider) of 30 TeV with radically smaller
dimensions, which is based on new methods of accel-
eration [7].
The paper presents the development of the wakefield
method of charged particles acceleration at a high accel-
erating rate, which was started in cooperation with ANL
[8 - 10] and was motivated by the creation of a collabo-
ration ALEGRO for the construction of the collider
ALIC within the framework of the updated European
high-energy physics strategy.
The purpose of the presented researches is to in-
crease the transformation ratio in the multi-bunch plas-
ma-dielectric wakefield accelerator, that is defined as a
ratio of the energy gain by the accelerating electron
bunch to the energy losses of the driver bunches. It is
achieved by appropriate charge profiling of the bunch
sequence.
1. STATEMENT OF THE PROBLEM
One of the important problems in the wakefield
method of acceleration is overcoming the limitation of
the transformation ratio, defined as the ratio of the ener-
gy gain by the accelerating bunch to the energy lost by
the driver bunch for the wakefield excitation.
2w
d
W E L E
R
W E L E
, (A)
which, according to Wilson's theorem, in the linear ap-
proximation for a collinear scheme with two bunches
does not exceed R = 2. This result is due to the fact that
with an increase in the charge Q of the driver bunch, not
only the magnitude of the accelerating field (i.e. the
acceleration rate) is increased, but the distance at which
the driver bunch is slowed down also decreases to the
same extent. One way to overcome this limitation is to
use a profiled driver bunch or a profiled sequence of
bunches.
mailto:onish@kipt.kharkov.ua
54 ISSN 1562-6016. Problems of Atomic Science and Technology. 2023. № 4(146)
If the parameters of the sequence of electron bunches
(the length of the bunches Lb, the spatial period of bunch
following Lm, the profile of the sequence by the charge
of the bunches) and the plasma-dielectric structure (the
wavelength of the excited eigen mode) are chosen as
follows
m
1 2 3
,
,
: : 1:3:5 : ...
b
b
L
L L
Q Q Q
(B)
then each bunch is occurred in the wakefields of previ-
ous bunches and in its own wakefield, namely in the
E0/2 field, where E0 is the excited wakefield behind the
first bunch (Fig. 1).
Fig. 1. Interference of the wakefields of the first three
bunches of the profiled sequence Q1:Q2: Q3=1:3:5,
which move to the left. The wakefield of the 1st bunch
solid curve; 2nd bunch – dotted curve; 3rd bunch –
dotted curve; the total wakefield is the bold curve
It can be seen from Fig. 1 that for the uniformity of
the slowing down fields of each bunch, it is necessary to
profile the bunches by charge as 1:3:5:... Only with this
profiling, also for each bunch, the total wakefield of the
previous bunches together with the field of the bunch
itself give the resulting field E0/2. At the same time,
behind each bunch, the total wakefield grows as NE0,
where N is the number of bunches As a result, the
transformation ratio R=NE0/E0/2=2N instead of
R=N/(N-1/2) for the case of nonprofiled sequence of N
bunches with charge Q1.each. A similar approach was
also considered in [11 - 13].
In the experiments, the parameters of the plasma-
dielectric structure and the profiled sequence of bunches
do not fully correspond to the optimal ones (B) in the
given scheme, in which the transformation ratio increas-
es proportionally to the number of bunches in the se-
quence. It is because parameters of the sequence pro-
duced with accelerator “Almaz-2M” (length of the
bunches Lb, and period of their following Lm) are fixed.
In the set of equations (B), it is possible to vary only the
length of the eigenwave of the structure excited by the
sequence of bunches. The frequency of bunches follow-
ing fm=2.805 GHz, i.e. Lm=10.64 cm, is fixed due to the
accelerator, the geometry of the dielectric structure is
chosen so (a=2.93 cm, b=4.19 cm, =2.045) that the
length of the eigenwave excited by the bunches in the
sum with the length of the bunch lb=1.7 cm (unfortu-
nately also fixed due to the accelerator, it should be
lb=/2) was equal to the period of bunches following
Lm=+lb.
Therefore, the structure becomes non-resonant in
contrast to the resonant one (Lm=) for obtaining the
maximum wake field. The charge of bunches increases
linearly with the number in the sequence, but not as
1:3:5:... In the experiment the transformation ratio was
found as the ratio of the total wakefield excited by the
profiled sequence of bunches, which is measured by a
microwave probe, to the field decelerating driver
bunches, which is determined by the energy losses of
the driver bunches finding from the shift of their energy
spectrum measured by a magnetic analyzer.
2. THEORY AND NUMERICAL RESULTS
2.1. LINEAR THEORY OF WAKEFIELD
EXCITATION
The investigated electrodynamic structure is a metal
waveguide of cylindrical configuration, partially filled
with a dielectric with a channel for charged particles
(drive and test bunches). The channel is filled with ho-
mogeneous cold plasma. A charge-profiled regular se-
quence of drive relativistic electron bunches is injected
into the plasma channel parallel to the waveguide axis
without transverse displacement, and propagates along
the structure, exciting a wakefield. The main goal of this
section is to study the longitudinal structure of the
wakefield components in the case of its excitation by a
profiled sequence of drive bunches, and to determine
the transformation ratio.
In order to construct the analytical expressions for
the components of the wakefield, excited by driver elec-
tron bunches, it is necessary to start with the case of a
point particle, that is, to construct the corresponding
expressions for the Green's function. We assume that a
particle of charge q moves with a constant velocity v
along the structure axis ( z direction). W can write
down its current density as follows:
0
0 0
( )
( ) ( ),z
r r
j q t
r
(1)
where
0r and
0 are its transverse coordinates,
/t z v , and
0t is the particle injection time into the
structure at 0z . The electromagnetic field compo-
nents, and the charge and current densities we expressed
in terms of Fourier transformation as follows:
( , , ) ( , ) ,
( , , ) ( , ) ,
( , , ) ( , ) .
im i
m
m
im i
m
m
im i
z zm
m
r e d r e
r e d r e
j r e d j r e
E E
H H (2)
The wave equations for the Fourier transforms of the
axial electric and magnetic fields
zmE та
zmH obtained
from Maxwell's equations have the following form:
22
2
2
2
2
2
41
,
( )
1
0,
zm zm
zm zm
zm
zm zm
E i jm
r E E
r r r r
H m
r H H
r r r r
(3)
where 2 2 2( ) ( / ) (1 ( ))v , /v c . The
Fourier transforms of the electric field
rmE , mE
and
magnetic field rmH , mH
can be expressed in terms of
the axial components
zmE and
zmH . We consider the
ISSN 1562-6016. Problems of Atomic Science and Technology. 2023. № 4(146) 55
case of the bunches injection along the axis of the
waveguide without an offset, so only azimuthally uni-
form field components ( 0m ) will be excited.
The radial force
rF is expressed through the Fourier
transform of the axial component
zmE as follows
izmr
EF
iv d e
q r
. (4)
Taking the inverse Fourier transform for the Green
functions
GzF and
GrF of the wakefield components
(Green’s functions) in the plasma channel we obtain the
following expressions for the axial force:
02
0 0 0
0
0 0
0 0 0 0
0
0 0 0
0 02
1 0
( )
2 ( , ) ( )
( )
( )
( , ) ( ) cos ( ) ( )
( )
4 ( ) ( )
cos ( ) ( ),
( ) ( )
pGz
p p p
p
p
p p p
p
ps ps
s
s s s ps
I k rF
qk k a k r r r
q I k a
I k r
k a k r r r t t
I k a
qI r I r
t t
a D I a
(5)
and for the radial force:
12
0 0 0
0
0 0
1 0 0 0
0
1 0 0
0 02 2
1 0
( )
2 ( , ) ( )
( )
( )
( , ) ( ) sin ( ) ( )
( )
4 ( ) ( )
sin ( ) ( ),
( ) ( )
pGr
p p p
p
p
p p p
p
ps ps ps
s
s s s ps
I k rF
qk k a k r r r
q I k a
I k r
k r k a r r t t
I k a
qv I r I r
t t
a D I a
(6)
where
p is a plasma frequency, /p pk v is a plas-
ma wavenumber, a is an inner radius of the dielectric
tube,
0 0( , ) ( ) ( ) ( 1) ( ) ( )n
n n nx y I x K y K x I y ,
nI and
nK are the modified Bessel and Macdonald functions of
the n
th
order, ( )ps p s ,
2 2( ) 1 /p p is the
plasma permittivity, ( ) ( ) /s sD dD d , is the
Heaviside function. The frequencies the eigen modes for
the plasma-dielectric waveguide s resonant with the
bunch ( /zk v ) are found using the numerical solu-
tion of the dispersion equation, which has the form:
1 1
0 0
( ) ( , )
( ) 0,
( ) ( , )
p p d d d
p p d d d
I a F a b
D
I a F a b
(7)
where
2 2 2( / ) (1 ( ))p v ,
d is dielectric per-
mittivity, 2 2 2( / ) ( 1)d dv , b is outer radius of
the dielectric tube,
0 0 0 0 0( , ) ( ) ( ) ( ) ( )F x y J x Y y Y x J y ,
1 1 0 1 0( , ) ( ) ( ) ( ) ( )F x y J x Y y Y x J y ,
nJ and
nY are the
n
th
order Bessel and Webber functions respectively. The
field components expressions for the finite-size driver
bunch can be obtained basing on the point particle solu-
tion by the integration over the injection time 0t and
transverse position 0r . We suppose that each driver
bunch in the profiled sequence of bunches has a square
profile of the charge density in both longitudinal and
transverse directions (uniform distribution). The charge
of each bunch in the train grows as an odd number. As a
result the final expressions for the axial and radial forc-
es acting on the bunch particles have the following
form:
0
1 0
( )
1
1 1
0 0 ( )
2 2
0
( )( , ) 4 2 1 1
2 1 ( )
8 (2 1)
( , ) ( )
(2 1)
( ) ( )
( ),
( ) ( )
b
b
N
pz b b
ib b b p b p
N
p b
p b p
i sb b b
ps ps b s
ps s s ps
I k rF r R Q i
q R L N k R I k a
Q i
k R k a
R L N
I r I Rv
a D I a
(8)
1
1 0
( )
1
1 1
2
1 1 ( )
3 2
0
( )( , ) 4 2 1
2 1 ( )
8 (2 1)
( , ) ( )
(2 1)
( ) ( )
( ),
( ) ( )
b
b
N
pr b b
ib b b p
N
p b
p b p
i sb b b
ps ps b s
s s ps
I k rF r R Q i
q R L N I k a
Q i
k R k a
R L N
I r I Rv
a D I a
(9)
where
bR is the bunch radius,
bL is the bunch length,
bN is a number of the drive bunches in the sequence
and
bQ is the charge of the last bunch. An axial struc-
ture of the bunch-excited wakefield components, is de-
scribe by the functions
( , )
( )
p s and
( , )
( )
p s , which
has the form:
( , )
,
,
( , )
,
,
( ( 1) )sin ( ( 1) )
( ( 1) )sin ( ( 1) ),
( ( 1) ) 1 cos ( ( 1) )
( ( 1) ) 1 cos ( ( 1) ) ,
p s
r p s r
r b p s r b
p s
r p s r
r b p s r b
i T i T
i T T i T T
i T i T
i T T i T T
(10)
where
rT is a bunch repetition time, /b bT L v .
2.2. NUMERICAL ANALYSIS
The constructed linear theory of wakefield excitation
by a charge-profiled regular sequence of driver bunches
allows to carry out a numerical analysis of the spatio-
temporal structure of the electromagnetic field in the
plasma-dielectric accelerating structure. For the numeri-
cal analysis in the gigahertz frequency range we used
the parameters of the waveguide and the train of elec-
tron bunches accessible at Kharkov Institute of Physics
and Technology (linac “Almaz-2M”) {1st option}: en-
ergy of electron bunch is W= 2.5 MeV, the inner radius
2.9a cm and the outer radius 4.25b cm of the die-
lectric tube, the dielectric permittivity 2.045d (Tef-
lon), so that the mode with a wavelength
= 7.12 cm resonant with the bunches is excited; the
length of the bunches Lb=1.7 cm, the radius of the
bunches Rb=0.5 cm, distance between the bunches
mod 10.58L cm, the plasma density np= 10
10
cm
-3
. The
dielectric material was assumed to be dispersionless
( ( )d d ). The main goal of the numerical investi-
gations in this section is to analyze the possibility of
obtaining a high value of the transformation ratio and
simultaneous radial focusing both drive and witness
electron bunches. Fig. 2 demonstrates the longitudinal
distributions of an axial force /z zF q E and a radial
56 ISSN 1562-6016. Problems of Atomic Science and Technology. 2023. № 4(146)
force /r rF q E H , acting both on the driver
bunches and accelerated bunch for the case 7bN .
Fig. 2. The axial profiles of the longitudinal (solid line)
and radial (dashed line) forces excited by the bunches,
at the distance
br R from the waveguide axis for the
case 7bN . The upper figure shows the distribution
within the sequence, the lower figure shows
the distribution behind the last bunch. The profiled
sequence of bunches (rectangles) move from right
to left, the first bunch position in the sequence
corresponds to vt z 0
It can be seen that the profile of the axial force is ir-
regular, both in the region inside the sequence of driver
bunches and behind the last driver bunch. The main
reason of the irregularity is following. The axial force is
provided both by the field of eigenmodes of the plasma-
dielectric waveguide and by the field of the plasma
wave, while the radial force is provided mainly by the
field of the plasma wave. The presented force distribu-
tions demonstrate that for the given parameters of the
waveguide and bunches: (i) the axial force changes sign
inside the drive bunches, which leads to transform ratio
decrease, their filamentation and energy spread, (ii) the
force decelerating the drive bunches oscillates along the
sequence of drive bunches, which leads to uneven ener-
gy losses of these bunches, (iii) all drive bunches are in
an increasing (by amplitude) focusing field, with ampli-
tude oscillating along the sequence, which is a positive
property of the plasma-dielectric structure, which, in
turn, leads to an improvement in the transverse stability
of the drive bunches, and can provide a longer length of
the accelerating structure, (iv) due to the difference in
the wavelengths of the working eigenmode of the struc-
ture (7.1215 cm) and the length of the plasma wave
(33.22 cm), it is possible to choose the injection time of
test accelerated electron or positron bunches, that can be
accelerated and focused at the same time. The amplitude
of the transverse field increases due to the coherent
summation of the fields from the sequence of bunches,
while the driver bunches remain in the focusing phases
of the field. The transformation ratio, calculated as the
ratio of the maximum amplitude of the accelerating
electric field, after the last driver bunch, to the average
amplitude of the decelerating electric field is equal to
11R . To increase the transformation ratio, in ongoing
research, it is proposed to use a long sequence of drive
bunches with odd charges. This gives a combination of
increase as due to increase
bN , as well as due to the
reduction of the field that decelerates the driver bunch-
es. Fig. 3 illustrates longitudinal distributions /zF q and
/rF q , that correspond to the case 15bN . Fig. 3
shows that in this case compared to the previous one the
accelerating field (which is determined by the charge of
the last bunch of the sequence) has the same amplitude
value, while the average decelerating electric field de-
creases. In this way, the transformation ratio increases.
In this case is equal to 18R .
Fig. 3. Longitudinal profiles of axial (solid line) and
radial (dashed line) forces excited in the waveguide
at a distance
br R from the axis for the case 15bN
It should be noted, that the parameters for which the
numerical analysis was carried out are not optimal, and
in order to ensure the uniform deceleration of all drive
bunches in the profiled sequence and their uniform en-
ergy loss, it is necessary: (i) the repetition period of the
bunches of the sequence must be equal to the sum of the
wavelength of the first radial mode
1 and the length of
the driver bunch, i.e.
mod 1 bL L , (ii) choose the
length of each bunch equal to half of the working mode
wavelength
1 / 2bL . It should be separately noted,
that the excitation of the focusing fields leads, in turn, to
a decrease in the requirements for external focusing
systems in order to suppress transverse instabilities that
may occur during the passage of bunches along the ac-
celerating structure.
The results of the theoretical consideration for the
second set of experimental parameters {option 2}, in
which the change in the eigen wave length of the struc-
ture by the appropriate choice of the diameter of the
channel for the charged particles allows the condition
mod 1 bL L to be fulfilled, necessary for the stay of
ISSN 1562-6016. Problems of Atomic Science and Technology. 2023. № 4(146) 57
the whole driver bunch in the decelerating field, ob-
tained earlier [14] and shown in Fig. 4.
Fig. 4. Longitudinal profiles of axial (solid line) and
radial (dashed line) forces excited at a distance
br R
from the axis with 7bN , for 2
nd
option with another
а=2.19 сm and W=4.5 МеV, for which 1 =8.84 сm
It can be seen that all driver coils are completely in
the braking field, the amplitude of which oscillates
along the sequence. Oscillations are eliminated when
the condition
1 / 2bL is fulfilled, which cannot be
satisfied in our experiment.
Therefore the theoretical studies of the wakefield ex-
citation in the cylindrical plasma-dielectric waveguide
by a regular charge-profiled sequence of drive electron
bunches have been carried out. A possibility of increas-
ing the transform ratio due to a simultaneous increase of
the drive bunches number and a decrease of an average
field decelerating them has been demonstrated. A spec-
tral analysis of the excited electromagnetic field was
carried out. It is shown that the excitation of the axial
electric field is provided both by the field of the
eigenmodes of the plasma-dielectric waveguide and by
the field of the plasma wave, while the excitation of the
radial force is provided mainly by the field of the plas-
ma wave.
3. EXPERIMENTS ON THE
TRANSFORMATION RATE INCREASE
3.1. FORMATION OF A PROFILED SEQUENCE
WITH THE NECESSARY NUMBER
OF BUNCHES
The electron gun modulator generates a voltage
pulse applied to the cathode with duration of 4 s and
an amplitude of 80 keV. The pulse has a flat top of
2.5 s and gentle fronts. The forming lines of the mas-
ter-generator “Rubin” and the klystron amplifier KIU-
2M provide rectangular pulses with duration of 2 s. All
three modulators are triggered by pulses with adjustable
delay for each channel Fig. 5.
During normal operation of the accelerator, there is
no delay between the pulses that trigger the modulators
of the master magnetron generator and the klystron am-
plifier, so that the microwave power pulse of the klys-
tron amplifier reaches the flat part of the voltage pulse
on the gun. In this case, a rectangular pulse of an accel-
erated beam (that is, an nonprofiled sequence of bunch-
es) with a duration of 2 μs is formed at the output of the
accelerator.
Fig. 5. Arrival time of pulses from the main nodes
of the accelerator “Almaz-2M”
By shifting the pulses of the master generator and
klystron amplifier KIU-2M relative to each other, it is
possible to control the duration of the microwave pulse
entering the input of the accelerator section and, accord-
ingly, the duration of the beam pulse at the output of the
accelerator. When the delay is shifted by 1, 1.5, and
1.9 μs, the duration of the current pulse is 1, 0.5, and
0.1 μs, respectively. Pulses of the beam with a duration
of 0.1 obtained in this way; 0.5; 1.0, and 2.0 μs (the
number of clots, respectively, 300, 1500, 3000, and
6000) are shown on the oscillograms in Fig. 6.
a b c d
Fig. 6. Duration of the beam current pulse:
a τ = 2 μs; b τ = 1 μs; c τ = 0.5 μs; d τ = 0.1 μs
If such pulses are applied with an appropriate time
delay to the linearly increasing leading edge of the gun
voltage pulse, a linearly profiled beam pulse of the
needed duration (i.e. a profiled sequence with an adjust-
able number of bunches) is formed at the accelerator
output. Experimentally obtained oscillograms of pro-
filed sequences of two durations are shown in Fig. 7.
Fig. 7. Oscillograms of profiled sequences of electron
bunches with a duration of 0.4 μs (1200 bunches)
and 0.75 μs (2250 bunches)
3.2. EXCITATION OF WAKEFIELDS
BY A PROFILED SEQUENCE OF BUNCHES
The scheme of the experimental setup, on which the
wakefield excitation in the plasma-dielectric structure
(4) by the profiled sequence of bunches, produced by
58 ISSN 1562-6016. Problems of Atomic Science and Technology. 2023. № 4(146)
the accelerator “Almaz-2M” (1) was studied, is shown
in Fig. 8.
The amplitude of the excited wakefield Ea, needed for
the witness-bunch acceleration, was measured by mi-
crowave probes (8). The amplitude of the retarding field
Er was determined by the shift of the energy spectrum
of the bunch electrons caused by the energy loss for
exciting wakefield and the acceleration length. Energy
spectra were measured using a magnetic analyzer (2, 6,
11, 12).
Fig. 8. Scheme of the experimental setup:
1 accelerator “Almaz-2M”; 2 magnetic analyzer;
3 input diaphragm; 4 Teflon tube; 5 metal resona-
tor; 6 transverse magnetic field; 7 vacuum plug;
8 microwave probe; 9 plunger; 10 additional
waveguide; 11 glass plate; 12 collector
The signal from the microwave probe was fed to the
TDS 6154 oscilloscope. The oscillogram obtained dur-
ing the injection of a sequence of bunches into the struc-
ture lasting 400 ns (1200 bunches) with a linearly in-
creasing charge of the bunches is shown in Fig. 9. It can
be seen that the amplitude of the total wakefield in-
creases during the pulse, that is, with the number of
bunches. At the same time, according to the simulation
(see above), the retarding field remains at the level of
the retarding field of first bunch. Therefore, the trans-
formation coefficient increases with the number of
bunches.
Fig. 9. Oscillogram of the microwave signal
of the wakefield excited in the plasma-dielectric
structure by a profiled sequence of electron bunches
with a duration of 400 ns
In the experiment, the amplitude of the wakefield is
measured by a microwave probe, the voltage from
which is recorded by an oscilloscope. To obtain the field
amplitude in V/m, the microwave probe was calibrated
using the SPECTRAN device, which measures electro-
magnetic radiation in a stationary mode in open space,
namely, microwave power density in W/m
2
, and electric
field strength in V/m.
The design of the microwave probe is selected so
that its sensitivity allows sensing in open space the elec-
tromagnetic radiation generated at a frequency of
2.8 GHz by the G4-80 generator, which can be meas-
ured by the SPECTRAN device. Such a microwave
probe is an LCD coaxial cable with a bare central core
length ¼ λ with a ground detector. The detector is need-
ed due to the lack of an oscilloscope with an ultra-fast
sweep.
It is shown that at the maximum generated micro-
wave power, the voltage obtained from the microwave
probe of 1.5 mV corresponds to the SPECTRAN read-
ings of the microwave power density of 40.08 mW/m
2
,
or the electric field strength of 3.886 V/m. Therefore,
1 mV of voltage from the output of the microwave
probe corresponds to the intensity of the measured elec-
tric field of 2.6 V/m. At the same time, in the pulse gen-
eration mode, the front of the voltage pulse from the
probe is less than 100 ns.
3.3. ENERGY LOSSES OF DRIVER BUNCHES
FOR THE WAKEFIELD EXCITATION
The amplitude of the wakefield, in which the driver
bunches are decelerated, is estimated by their energy
losses along the excitation length, which are determined
by the shift of their energy spectrum. Energy spectra
were obtained using magnetic analyzers at the entrance
and the exit of the plasma-dielectric structure.
Test measurements of energy spectra of the non-
profiled sequence of bunches at the entrance to the
structure (black curve) and at its exit (red curve) are
presented in Fig. 10. The shift of the energy spectrum
towards lower energies indicates the loss of energy by
driver bunches for wakefield excitation. The value of
the spectrum displacement W = 0.15 MeV (see
Fig. 10) corresponds to relative losses W/W = 3%.
Fig. 10. Energy spectra of electrons measured
by a magnetic analyzer for a structure with a length
of 65 cm: 1 initial spectrum;
2 spectrum after wakefield excitation
For control in the middle part of the chamber, the
bunches were turned by magnetic field, passed through
the wall of the vacuum chamber with the same insignif-
icant energy losses for all electrons, and gave impres-
sions on a glass plate. The blackening on the plate by
the bunch electrons turned various angles depending on
their energy also reflected its energy spectrum, which
coincided with the spectrum obtained by magnetic ana-
lyzer.
ISSN 1562-6016. Problems of Atomic Science and Technology. 2023. № 4(146) 59
For a profiled sequence of bunches, the measured
energy losses W by bunches for wakefield excitation at
a known length of excitation L allow finding the decel-
erating field Ed = W/L.
The transformation coefficient R is defined as the ra-
tio of the accelerating field Ea, measured by the micro-
wave probe, to the decelerating field Ed, measured by
the magnetic analyzer:
R = EaL/EdL = Ea/Еd.
Experimentally obtained transformation rate for the
1st variant of the set of experimental parameters (sec-
tion 2.2) R=Ea/Ed = 8, is close to the theoretical one,
although smaller due to the incomplete fulfillment in
theory of the initial conditions of the available experi-
ence (profile of charge increase from the number of
clots, number of involved bunches). In addition, in this
1st option of obtaining the value R = Ea/Ed is not a
transformation rate in its pure form due to the fact that,
as shown in 2.2, for such a set of parameters the energy
of the part of the driver is transformed not only in accel-
erated witness drivers, but also in another part of this
driver.
Experimental measurements of the transformation
ratio for the 2nd option Lm =Lb + (section 2.2) require
the creation of another structure according to its eigen
wavelength , because parameters of the sequence of
bunches Lm and Lb are provided by the accelerator and
are therefore fixed. The results of the further experi-
ments will be presented in the following publications.
3.4. FOCUSING A SEQUENCE OF BUNCHES
BY WAKEFIELD EXCITED
IN PLASMA-DIELECTRIC STRUCTURE
Driving bunches, exciting the wakefield in a plasma-
dielectric structure, are in the decelerating longitudinal
dielectric field and in the focusing radial plasma field.
The radial defocusing field of the dielectric wave, with
its longitudinal field almost uniform in radius, is weak.
Therefore, the driver bunches are focused by the wake-
field excited in plasma.
Fig. 11 shows beam current oscillograms obtained
experimentally using a double Faraday cylinder consist-
ing of two cylinders the first cylinder with a central
hole for recording the peripheral part of the bunches and
the second cylinder for recording the central part of the
bunches that passed through the hole in the first cylin-
der.
a b
Fig. 11. Beam current oscillograms recorded
by GDS-840C oscilloscope from a double Faraday
cylinder (upper curve corresponds to the first cylinder,
lower curve corresponds to the second cylinder)
for two gas pressures: 10
-3
Torr (a); 0.5 Torr (b)
The oscillograms are given for the vacuum case at a
neutral gas pressure in the transient channel of the die-
lectric waveguide of 10
-3
Torr (see Fig. 11,a), when no
plasma is formed, and the plasma case at a pressure of
0.5 Torr (see Fig. 11,b), when the plasma is intensively
formed due to the development of beam-plasma dis-
charge. An increase in the current in the second cylinder
and at the same time its decrease in the first cylinder in
the presence of plasma (see Fig. 11,b) indicates the fo-
cusing effect on the driver bunches. For accelerated
bunches, simultaneous acceleration and focusing is pro-
vided by the choice of right injection phase using ap-
propriate plasma density.
CONCLUSIONS
Theoretical and experimental studies of the wake-
field excitation by a profiled sequence of electron
bunches in a non-resonant plasma-dielectric structure
were carried out for the available parameters of the
structure and the sequence of bunches on the KIPT ex-
perimental installation.
The possibility of a radical increase in the transfor-
mation ratio due to the profiling sequence of the bunch-
es was shown. Such sequence makes it possible to ob-
tain a total accelerating wakefield increasing with the
number of bunches and a non-increasing and much
smaller field decelerating driver bunches. It was found
that both driver and accelerated bunches are focused in
this case by excited plasma wakefield.
ACKNOWLEDGEMENTS
This work was supported by NAS of Ukraine Pro-
gram “Plasma physics and plasma electronics: basic
researches and applications”, Project П4/60-2022.
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Article received 02.07.2023
РОЗРОБКА ПЛАЗМОВО-ДІЕЛЕКТРИЧНОГО КІЛЬВАТЕРНОГО ПРИСКОРЮВАЧА
З ПРОФІЛЬОВАНОЮ ПОСЛІДОВНІСТЮ ДРАЙВЕРНИХ ЕЛЕКТРОННИХ ЗГУСТКІВ
І.М. Оніщенко, К.В. Галайдич, Р.Р. Князєв, Г.О. Кривоносов, А.Ф. Лінник, П.І. Марков, О.Л. Омелаєнко,
В.І. Приступа, Г.В. Сотніков, В.С. Ус, Д.Ю. Залеський
Виконано теоретичне та експериментальне дослідження збудження кільватерного поля профільованою
послідовністю релятивістських електронних згустків у плазмово-діелектричній структурі, параметри якої
забезпечують умови для збудження малого сповільнюючого поля для всіх драйверних згустків з одночасним
зростанням з кількістю згустків прискорювального сумарного кільватерного поля. У теорії для параметрів
експерименту знайдено коефіцієнт трансформації як відношення повного кільватерного поля послідовності
до поля, що сповільнює драйверні згустки. В експерименті сумарне кільватерне поле вимірювалося мікрох-
вильовим зондом. Величина сповільнюючого поля знаходилась по зсуву максимуму енергетичного спектра,
вимірюваного магнітним аналізатором до та після збудження кільватерного поля у структурі. Отриманий
коефіцієнт трансформації зростає зі збільшенням кількості згустків у послідовності та значно перевищує
такий для непрофільованої послідовності.
http://www.sciencedirect.com/science/article/pii/S0168900216002369
http://www.sciencedirect.com/science/article/pii/S0168900216002369
http://www.sciencedirect.com/science/article/pii/S0168900216002369
http://www.sciencedirect.com/science/article/pii/S0168900216002369
http://www.sciencedirect.com/science/article/pii/S0168900216002369
|
| id | nasplib_isofts_kiev_ua-123456789-196174 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1562-6016 |
| language | English |
| last_indexed | 2025-12-07T15:58:06Z |
| publishDate | 2023 |
| publisher | Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
| record_format | dspace |
| spelling | Onishchenko, I.N. Galaydych, K.V. Kniaziev, R.R. Krivonosov, G.O. Linnik, A.F. Markov, P.I. Omelayenko, O.L. Pristupa, V.I. Sotnikov, G.V. Us, V.S. Zaleskiy, D.Yu. 2023-12-11T11:51:09Z 2023-12-11T11:51:09Z 2023 Elaboration of the plasma-dielectric wakefield accelerator with a profiled sequence of driver electron bunches / I.N. Onishchenko, K.V. Galaydych, R.R. Kniaziev, G.O. Krivonosov, A.F. Linnik, P.I. Markov, O.L. Omelayenko, V.I. Pristupa, G.V. Sotnikov, V.S. Us, D.Yu. Zaleskiy // Problems of Atomic Science and Technology. — 2023. — № 4. — С. 53-60. — Бібліогр.: 14 назв. — англ. 1562-6016 PACS: 41.75.Ht; 41.75.Lx DOI: https://doi.org/10.46813/2023-146-053 https://nasplib.isofts.kiev.ua/handle/123456789/196174 A theoretical and experimental study of wakefield excitation by a profiled sequence of relativistic electron bunches in the plasma-dielectric structure, the parameters of which provide the conditions for the excitation of a small decelerating field for all driver bunches with simultaneous growth with the number of bunches of the accelerating total wakefield was carried out. Theoretically, the transformation ratio was found for the parameters of the experiment as the ratio of the total wakefield of the sequence to the field that decelerates driver bunches. In the performed experiments, the total wakefield was measured by the microwave probe. The magnitude of the decelerating field is determined by the shift of the maximum of the spectrum measured by the magnetic analyzer before and after wakefield excitation in the structure. The obtained transformation ratio increases with the number of bunches in the sequence and significantly exceeds this one for a nonprofiled sequence. Виконано теоретичне та експериментальне дослідження збудження кільватерного поля профільованою послідовністю релятивістських електронних згустків у плазмово-діелектричній структурі, параметри якої забезпечують умови для збудження малого сповільнюючого поля для всіх драйверних згустків з одночасним зростанням з кількістю згустків прискорювального сумарного кільватерного поля. У теорії для параметрів експерименту знайдено коефіцієнт трансформації як відношення повного кільватерного поля послідовності до поля, що сповільнює драйверні згустки. В експерименті сумарне кільватерне поле вимірювалося мікрохвильовим зондом. Величина сповільнюючого поля знаходилась по зсуву максимуму енергетичного спектра, вимірюваного магнітним аналізатором до та після збудження кільватерного поля у структурі. Отриманий коефіцієнт трансформації зростає зі збільшенням кількості згустків у послідовності та значно перевищує такий для непрофільованої послідовності. This work was supported by NAS of Ukraine Program “Plasma physics and plasma electronics: basic researches and applications”, Project П4/60-2022. en Національний науковий центр «Харківський фізико-технічний інститут» НАН України Problems of Atomic Science and Technology New methods of charged particles acceleration Elaboration of the plasma-dielectric wakefield accelerator with a profiled sequence of driver electron bunches Розробка плазмово-діелектричного кільватерного прискорювача з профільованою послідовністю драйверних електронних згустків Article published earlier |
| spellingShingle | Elaboration of the plasma-dielectric wakefield accelerator with a profiled sequence of driver electron bunches Onishchenko, I.N. Galaydych, K.V. Kniaziev, R.R. Krivonosov, G.O. Linnik, A.F. Markov, P.I. Omelayenko, O.L. Pristupa, V.I. Sotnikov, G.V. Us, V.S. Zaleskiy, D.Yu. New methods of charged particles acceleration |
| title | Elaboration of the plasma-dielectric wakefield accelerator with a profiled sequence of driver electron bunches |
| title_alt | Розробка плазмово-діелектричного кільватерного прискорювача з профільованою послідовністю драйверних електронних згустків |
| title_full | Elaboration of the plasma-dielectric wakefield accelerator with a profiled sequence of driver electron bunches |
| title_fullStr | Elaboration of the plasma-dielectric wakefield accelerator with a profiled sequence of driver electron bunches |
| title_full_unstemmed | Elaboration of the plasma-dielectric wakefield accelerator with a profiled sequence of driver electron bunches |
| title_short | Elaboration of the plasma-dielectric wakefield accelerator with a profiled sequence of driver electron bunches |
| title_sort | elaboration of the plasma-dielectric wakefield accelerator with a profiled sequence of driver electron bunches |
| topic | New methods of charged particles acceleration |
| topic_facet | New methods of charged particles acceleration |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/196174 |
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