Concept of plasma-dielectric wakefield accelerator. Theory and experiment
The wakefield excitation by a long sequence of relativistic electron bunches in a dielectric waveguide/resonator of round cross-section with transit channel filled with plasma of various densities was theoretically and experimen-tally investigated. Теоретично і експериментально досліджено збудження...
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Національний науковий центр «Харківський фізико-технічний інститут» НАН України
2015
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| Cite this: | Concept of plasma-dielectric wakefield accelerator. theory and experiment / G.P. Berezina, K.V. Galaydych, R.R. Kniaziev, A.F. Linnik, P.I. Markov, O.L. Omelayenko, I.N. Onishchenko, V.I. Pristupa, G.V. Sotnikov, V.S. Us // Вопросы атомной науки и техники. — 2015. — № 4. — С. 97-104. — Бібліогр.: 7 назв. — англ. |
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| author | Berezina, G.P. Galaydych, K.V. Kniaziev, R.R. Linnik, A.F. Markov, P.I. Omelayenko, O.L. Onishchenko, I.N. Pristupa, V.I. Sotnikov, G.V. Us, V.S. |
| author_facet | Berezina, G.P. Galaydych, K.V. Kniaziev, R.R. Linnik, A.F. Markov, P.I. Omelayenko, O.L. Onishchenko, I.N. Pristupa, V.I. Sotnikov, G.V. Us, V.S. |
| citation_txt | Concept of plasma-dielectric wakefield accelerator. theory and experiment / G.P. Berezina, K.V. Galaydych, R.R. Kniaziev, A.F. Linnik, P.I. Markov, O.L. Omelayenko, I.N. Onishchenko, V.I. Pristupa, G.V. Sotnikov, V.S. Us // Вопросы атомной науки и техники. — 2015. — № 4. — С. 97-104. — Бібліогр.: 7 назв. — англ. |
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| container_title | Вопросы атомной науки и техники |
| description | The wakefield excitation by a long sequence of relativistic electron bunches in a dielectric waveguide/resonator of round cross-section with transit channel filled with plasma of various densities was theoretically and experimen-tally investigated.
Теоретично і експериментально досліджено збудження кільватерних полів довгою послідовністю релятивістських електронних згустків у діелектричному хвилеводі/резонаторі круглого перетину з пролітним каналом, який заповнено плазмою різної густини.
Теоретически и экспериментально исследовано возбуждение кильватерных полей длинной последовательностью релятивистских электронных сгустков в диэлектрическом волноводе/резонаторе круглого сечения с пролетным каналом, заполненным плазмой различных плотностей.
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ISSN 1562-6016. ВАНТ. 2015. №4(98) 97
CONCEPT OF PLASMA-DIELECTRIC WAKEFIELD ACCELERATOR.
THEORY AND EXPERIMENT
G.P. Berezina, K.V. Galaydych, R.R. Kniaziev, A.F. Linnik, P.I. Markov, O.L. Omelayenko,
I.N. Onishchenko, V.I. Pristupa, G.V. Sotnikov, V.S. Us
National Science Center “Kharkov Institute of Physics and Technology”, Kharkov, Ukraine
E-mail: onish@kipt.kharkov.ua
The wakefield excitation by a long sequence of relativistic electron bunches in a dielectric waveguide/resonator
of round cross-section with transit channel filled with plasma of various densities was theoretically and experimen-
tally investigated.
PACS: 41.60.-m, 41.75.Lx, 41.75.Ht, 96.50.Pw
INTRODUCTION
The acceleration of charged particles by wakefields
excited by a laser pulse or bunches of charged particles
at their propagation in the slowing down structures, is a
perspective direction in high energy physics, which de-
velops rapidly. With extra high accelerating gradients
wakefield methods of acceleration allows to achieve
energy of accelerated particles in TeV range at much
shorter length than in conventional accelerators. One of
the advanced method of acceleration is the acceleration
by wakefields excited by relativistic electron bunches in
dielectric structure [1]. The presence of plasma in the
transit channel for bunches allows to compensate space
charge of bunches and prevent the falling electrons of
bunches on dielectric walls, and consequently to im-
prove the passage of bunch through the channel and
increase amplitude of the excited wakefield at the exit.
In addition, plasma changes dispersion characteristics of
waveguide/resonator and topography of the wakefield in
the channel, excited by a sequence of bunches on Che-
renkov resonance. Notice that the excited wakefield
consists of dielectric field, modified with plasma and
directly plasma fields excited on different frequencies,
except for the case of coincidence of plasma frequency
and frequencies of modified dielectric field. Different
frequencies allow, in case of the scheme with a single
bunch-driver and a single bunch-witness, to place the
latter one into the region of phases, where it will be ac-
celerated by the high longitudinal field of dielectric
wave (radial field for relativistic bunches is negligible)
and focused by the high radial plasma field [2].
In this paper, wakefield excitation by a sequence of
relativistic electron bunches in a cylindrical dielectric
waveguide/resonator which trasit channel is filled with
isotropic plasma are investigated. Based on the theoreti-
cally obtained expressions for the components of the
electromagnetic field the spatial structure of transverse
and longitudinal forces are studied and to consider en-
hancing excited wakefields and focusing accelerated
bunches by them due to the plasma filled channel. Mod-
ernization resonant electron accelerator "Almaz-2M" is
carried out, that allowed to obtain a sequence of 6·103
electron bunches, each of 1.7 cm length, 1 cm in diame-
ter, charge 0.26 nC, and energy 4.5 MeV. The period
bunch repetition 300 ps. Dielectric structure of circular
cross-section is designed and manufactured. The system
of dosed inlet of neutral gas into the axial channel of the
structure and pumping is constructed, which enables to
obtain in the channel plasma of different density due to
ionization of the neutral gas directly by the front part of
the bunch sequence. Preliminary experiments on wake-
fields excitation in hybrid plasma-dielectric structure are
presented.
1. THEORY
1.1. ANALYTICAL EXPRESSIONS
FOR EXCITED FIELDS
To investigate the influence of the dielectric medium
on the excitation of plasma wakefield we find wakefield
excited by an electron bunch moving in a plasma wave-
guide with an annular dielectric insert. Plasma wave-
guide is homogeneous plasma cylinder of radius a, sur-
rounded by perfectly conducting metal tube of radius b.
The dielectric insert fills the space between the venal
tube and plasma. The excitation of the waveguide will
be considered in the approximation of linear isotropic
plasma of density np. Driving axis electron bunch has
radius rb and length Lb. At some distance from the driv-
er-bunch an accelerated witness-bunch is placed. Ge-
ometry of the wakefield structure is shown in Fig. 1
Fig. 1. Geometry of plasma-dielectric
wakefield accelerating structure
Excited azimuthally symmetric wakefield is de-
scribed by the following set of Maxwell equations:
1 ,r z HE E
z r c t
ϕ∂∂ ∂
− = −
∂ ∂ ∂
1 ,rH D
z c t
ϕ∂ ∂
− =
∂ ∂
(1)
( )1 1 4z
z
DrH j
r r c t cϕ
π∂∂
= +
∂ ∂
,
where rE , zE are radial and longitudinal components of
the electric field; rD , zD are radial and longitudinal
mailto:onish@kipt.kharkov.ua
ISSN 1562-6016. ВАНТ. 2015. №4(98) 98
components of the electric induction; Hϕ
is azimuthal
component of magnetic field.
First, determine the wakefield of a bunch shaped as
an infinitely thin axially symmetric ring of radius 0r for
which the current density is given by
0 0( ) ( )
2z
Qj r r t
r
δ δ τ
π
= − − , (2)
where 0/t z vτ = − ; 0t is time, when bunch crosses the
plane 0z = ; 0v is its speed, Q is bunch charge; δ is
Dirac delta function.
Using (2) the dependence of the forced solution of
the system (1) on time and longitudinal coordinates is
determined only by variable. τ Performing Fourier
transform in the variableτ
1( , ) ( , ) exp( )
2
E H d E H iω ω τ ωτ
π
∞
−∞
= ∫
(3)
from the system (1)-(2) we obtain the equation for the
Fourier transform of the longitudinal component of the
electric field:
2
2
02
0
1 1 ( )z
z
Er E
r r r v
ω
ω
ω β ε ω∂∂ − − = ∂ ∂
2 0
0 02
0
( )1 ( ) exp( )
( )
r rQi i t
v r
δω β ε ω ω
π ε ω
− = −
. (4)
The radial component of the electric field and the
component of the azimuthal magnetic field are ex-
pressed by zE ω
:
0
02
0
, ( ) ,
( ) 1
z
r r
EcE i H E
r
ω
ω ϕω ω
β β ε ω
ω β ε ω
∂
= =
− ∂
(5)
0 0 /v cβ = ; 2 2( ) ( ) 1 /p pε ω ε ω ω ω= = − ; if r a< and
( ) dε ω ε= if a r b≤ < ; 24 /p pe n mω π= is plasma
frequency; e− and m are charge and mass of electron;
dε is relative permittivity of dielectric insert which we
assume independent on frequency.
Equation (4) is equivalent to the system consisting
from three equations written in each of partial areas
0r r< , 0r r a< < and a r b< ≤ . Solving it with taking
into account boundary conditions:
0 0
0 0 0
0
( 0) , ( ) 0, ( 0) ( 0),
( 0) ( 0), ( 0) ( 0),
( 0) ( 0) exp( )
z z z z
z z
E r E r b E r r E r r
E r a E r a H r a H r a
QH r r H r r i t
сr
ω ω ω ω
ω ω ϕω ϕω
ϕω ϕω ω
π
= < ∞ = = = − = = +
= − = = + = − = = +
= + − = − =
(6)
we obtain:
( ) ( ) ( )
( )
( )
( ) ( )
2
0 00
0 02 2
0 0
1 1
02
000
0 0 0
0 0 0
1 ( ) 1( ) ( )
( ) ( )
( ) ( , ) exp( ) ,
,1 ( )
( ) ( , )1( )
( ) ( )
p pp
z p p
p p
pp d d
d
d dpp
p d d
z
p d
I r K aQE r a i I r K r
c DI a
K a F a b i t
F a bK a
I r F r bQE a r b i
ac D I a F a
ω
ω
κ κβ ε ωω κ κ
π β ε ω ωκ
κε ω κ κγ ω
κ κκβ ε ω
κ κ κ
π β ω κ κ
>
< >
−
< = − +
× −
−
≤ ≤ = −
( ) 0exp( ).
, d
i t
b
ω
κ
(7)
In (7) 0 1,I I and 0 1,K K are modified Bessel and
Macdonald functions of zero and first order, according-
ly;
0 0 0 0 0( , ) ( ) ( ) ( ) ( )F x y J x N y N x J y= − ,
1 1 0 1 0( , ) ( ) ( ) ( ) ( )F x y J x N y N x J y= − + ,
0 1( ), ( )J x J y та 0 1( ), ( )N x N y – Bessel and Neumann
functions of zero and first order, accordingly;
( ) ( )
2 2
2 2 2 2
0 02 2
0 0
1 ( ) ; 1 ;p p d dv v
ω ωκ β ε ω κ β ε= − = −
2
0/ 1d d dγ ε β ε= − . Sign < (> ) means the least (most)
values of r та 0r . The dispersion function that is in-
cluded in the denominator of expressions (7) has the
form:
( )
( ) ( )
1 1
2
000
( ) ( , )( ) .
,1 ( )
pp d d
d
d dpp
I a F a bD
F a bI a
κε ω κ κω γ
κ κκβ ε ω
= +
−
(8)
Other components of the electromagnetic field are
expressed by zE ω using (5).
Performing inverse Fourier transform, after calculat-
ing integrals using the theory of residues we obtain final
expressions for wakefield of the bunch in the shape of
an infinitely thin ring:
02 2
0 0
0
0 0 0
0 0 02
0 0 0
0 0 0 0
0 0 0
( )
( , ) cos ( )
( )
( ) ( ) cos ( )2 2( , , , ) ( ) , ,
( ) ( ) '( )
( ) ( , ) cos ( )2 ,
( ) ( , ) '( )
p
p p p p
p
s s
p p s
z s s
s p p s
s s s
p d d s
s s s
p d d s
I k r
k a k a k r t
I k a
I r I r tQ aE r t r t r a
a v I a I a D
I r F r b ta a r
v I a F a b D
ω τ
κ κ ω ττ τ
κ κ ω
κ κ κ ω τ
κ κ κ ω
<
>
< >
∆ −
−
= − Θ − + <
−
≤
∑
,
s
b
≤
∑
(9)
ISSN 1562-6016. ВАНТ. 2015. №4(98) 99
( )
( )
0 02
0
0
1 0 0
0 0 02 2
0 0 0 0
0 0 1
2
0 00 0
( ) ( ,
) sin ( )
( )
( ) ( ) sin ( )2 2( , , , ) ( ) , ,
( ) ( ) '( ) 1 ( )
( , )2
,1
p p p
p p
p
s s
p p s
r s s
s p p s p s
s s s
p d d
s s s
p d dd
I k r k a k rdk a t
dr I k a
I r I r tQ aE r t r t r a
a v I a I a D
I r F r ba
I a F av
ω τ
κ κ ω ττ τ
κ κ ω β ε ω
κ κ κ
κ κ κβ ε
< >
< >
∆
−
−
= Θ − + <
−
−
−
∑
( )
( )0sin
, ,
'( )
s
s s
t
a r b
Db
ω τ
ω
−
≤ ≤
∑
(10)
( )
( ) ( )
( )
0 0 1 0
2
0 00
0 0 0
0 0 01
2
0 00
( ) ( ) ( ) sin ( ) , ,
( ) ( ) '( )1 ( )4( , , , ) ( )
sin4 ( , ) , ,
'( ),1
s s
p s p p s
s s
s p p sp s
s s s
p sd d d
s s s
s sp d dd
I r I r t r a
I a I a DQH r t r t
ac I r tF r b a r b
DI a F a b
ϕ
ε ω κ κ ω τ
κ κ ωβ ε ω
τ τ
κ ω τε κ κ
ωκ κ κβ ε
−
<
−= Θ −
− −
≤ ≤
−
∑
∑
(11)
where ( )xΘ is Heaviside function; 0/p pk vω= ;
( )s
p p sκ κ ω ω= = ; ( )s
d d sκ κ ω ω= = ; ( )'( )
s
s
dDD
d ω ω
ωω
ω =
= ,
and eigen frequencies sω are determined from the solu-
tion of the dispersion equation:
( ) 0sD ω = . (12)
The first terms in the expressions for the electric
field (9)-(10) describe plasma wakefield
( 0,p pε ω ω= = ). It is localized in the transit channel.
This field does not depend on the parameters of the die-
lectric structure and becomes zero on the boundaries of
the channel. These terms in (9)-(10) coincide with the
expressions for electric fields plasma oscillations in an
isotropic plasma waveguide [3]. If in these expressions
the radius the plasma cylinder a →∞ , we obtain ex-
pressions for wakefield in infinite plasma [4]. Other
terms in (9)-(11) describe the electric field of eigen os-
cillations of dielectric structure (for brevity, we will call
them dielectric ones). Note that according to (11) in
plasma wakefield there is no magnetic field Hϕ.
Expressions (9)-(11) do not contain terms that de-
scribe the quasi-static field of the bunch space charge.
Quasi-static additives can be obtained by generalizing
solutions for dielectric wakefield on the case of purely
imaginary eigen frequencies
s siω ω→ . But as shown by
numerical calculations [5] for relativistic bunches the
quasi-static field is too small compared with the propa-
gating wakefield. Further we neglect it.
To find wakefield of pencil bunch of finite length
with arbitrary charge distribution inside it necessary to
integrate expression (7) over all r0, t0 with correspond-
ing distribution function 0 0( , )n r t .
1.2. NUMERICAL CALCULATIONS
For numerical calculations of excited wakefield we
take dielectric waveguide (see Fig. 1) with a=1.1 cm,
b=4.3 cm, permittivity εd=2.1 (Teflon), and accordingly
to the accelerator "Almaz-2M" [6] electron bunch of
energy 4.5 MeV, charge Q=-0.32 nC, radius rb=1.0 cm,
and length lb=1.7 cm. We assume that the charge distri-
bution inside the bunch is uniform and described by:
[ ]0
0 0 0 0 02
2( , ) ( ) ( / ) ( ) ,b b
b b
vn r t t t L v r r
L r
= Θ −Θ − Θ − , (13)
Fig. 2 shows the dependence of eigen frequencies of
plasma-dielectric waveguide on plasma density.
Fig. 2. Eigen frequencies of plasma-dielectric structure
depending on plasma density: curve 0 – plasma wake-
field; 1-6 – the first 6 solutions of dispersion equation
(8) and (12) for ωs
For the considered range of plasma densities eigen
frequencies of dielectric wakefields are weakly depend-
ent on plasma density. This allows to independently
governing the frequencies and amplitudes of dielectric
and plasma wakefields.
As follows from Fig. 2 Cherenkov resonant frequen-
cy of the first dielectric radial mode in the absence of
plasma is ω = 17.025⋅109, or spatial period is ~10.6 cm.
It is known [3, 4] that the amplitude of the plasma
wakefield is maximal at a certain plasma density. For
the above given parameters of the waveguide and bunch
amplitudes of longitudinal and transversal electric fields
are maximal at approximately the same density plasma
12~ 10m
p pn n= cm-3, which corresponds to the dimen-
sionless parameter kpa=2. Calculations show that for
such plasma density plasma wakefield greatly exceeds
the total dielectric wakefield (i.e. of all excited radial
modes). So the resulting wakefield is formed mainly by
plasma wakefield, which longitudinal and transverse
components are shifted in phase by π/2. It means that
accelerated bunch will not be focused. With decrease in
plasma density the amplitude of both longitudinal and
transverse components of plasma wakefield are reduced.
At a certain density plasma longitudinal field of plasma
wakefield becomes less than the total longitudinal field
ISSN 1562-6016. ВАНТ. 2015. №4(98) 100
of dielectric modes. But radial component of plasma
wakefield is large enough yet.
These two types of waves − plasma and dielectric
fields – have different spatial periods. Therefore, there
is a phase, where the maximum of the total longitudinal
field can correspond to the minimum of the total trans-
verse field full cross field. Thus, placing accelerated
bunch at phase of maximum accelerating field (mainly
dielectric one) it can be simultaneously focused by
transverse field (mainly plasma one).
Figs. 3-6 show the results of calculations for plas-
ma density np=1010cm-3 (plasma frequency
ωp = 5.64⋅109, wavelength λp = 2πv0 / ωp = 33.2 сm).
Fig. 3 shows the distribution of axial longitudinal
and transverse forces acting on a accelerated bunch lo-
cated at a distance 0.95 cm from the structure axis.
Comparing above dependencies it follows that placing
accelerated bunch at a distance 7 or 39.1 cm from the
head of driver-bunch provides simultaneous the acceler-
ation and radial focusing accelerated bunch.
Fig. 3. Axial profile of longitudinal (solid line) and trans-
verse (dashed line) forces, acting on accelerated bunch
located at a distance 0.95 cm from the structure axis
As seen from the figure, the radial force has nearly
harmonic dependence on the longitudinal coordinate
with a period equal to ~ 33 cm, i.e. plasma field makes
predominant contribution to the radial force. At the
same time, its contribution to the accelerating longitudi-
nal force is contrary small. Longitudinal force mainly
determines by dielectric eigen modes.
Fig. 4. Transverse profile of longitudinal (solid line) and
transverse (dashed line) forces, acting on the accelerated
bunch, located in the first maximum of accelerating field
at a distance 7.562 cm from the head of driver-bunch
Fig. 4 shows the radial dependence of the longitudi-
nal and transverse forces acting on the accelerated bunch,
located in the first maximum of accelerating field at a
distance 7.562 cm from the head of driver-bunch.
Figs. 5 and 6 present separately components in the
full force shown in Fig. 3. It is seen that plasma wake-
field makes predominant contribution to the focusing
force, while the total field of the dielectric eigen modes
makes predominant contribution to the accelerating gra-
dient.
Fig. 5. Axial profile of longitudinal (black line) and
transverse (red line) forces of dielectric wakefield,
acting on accelerated bunch located at a distance
0.95 cm from the structure axis
Fig. 6. Axial profile of longitudinal (black line) and
transverse (red line) forces of plasma wakefield, acting
on accelerated bunch located at a distance 0.95 cm
from the structure axis
2. ЕXPERIMENTAL INVESTIGATIONS
2.1. UPDATING ELECTRON ACCELERATOR
«АLMAZ-2М»
Updated electron gun. The efforts to update the
electron gun of the accelerator included the change of
lanthanum-hexaboride (LaB6) cathode, the increase of
the cathode emission by more intensive heating with
electron beam bombardment and optimization of elec-
tron-optics parameters. The general view of an electron
gun and the gun chamber is shown in Fig. 7.
a b
Fig. 7. Electron gun: 1 − unit of electron beam heat-
er of the cathode; 2 − cathode unit; 3 − anode (a);
b − electron gun chamber (b)
ISSN 1562-6016. ВАНТ. 2015. №4(98) 101
As a result the 2-times increase of electron gun cur-
rent from 0.7 A to 1.4 A is obtained at the electron gun
cathode voltage 80 kV.
Restoration of the master oscillator. In our experi-
ments for the wakefield excitation in dielectric struc-
tures it is necessary to vary the bunch repetition fre-
quency in order to achieve its coincidence with the eig-
en frequency of the exited wakefield if it is need to ex-
cite maximal wakefield by the whole sequence of
bunches, or to make detuning between these frequencies
that allows for one part of bunch sequence to be oc-
curred in the accelerating phases of wakefield excited
by another part of bunch sequence, and thus to realize
accelerated witness-bunches without additional injector.
This problem of bunch repetition frequency variation
can be solved by using a klystron amplifier, wherein the
frequency of the master-oscillator can be changed in a
required range.
For these purposes we restored master-oscillator,
based on magnetron MI-30, 10 kW HF-signal (in the
frequency range 2750…2850 MHz) of which was am-
plified by klystron KIU-12M up to the power
15…20 MW. Measurements of the microwave signal
amplitude of the master-oscillator on the frequency
were performed (Fig. 8).
Fig. 8. Dependence of amplitude of the microwave
signal upon master-oscillator frequency
It is shown that the maximum amplitude of the mi-
crowave signal was found in the frequency range
2803…2807 MHz.
The output power of the master-oscillator was meas-
ured by means of the calibrated detector and the 40dB
attenuator. Oscillogram of the envelope of the micro-
wave signal of the master-oscillator is shown in Fig. 9.
Fig. 9. Oscillogram of the envelope of the microwave
signal of the master-oscillator
Restoration of the klystron KIU-12M. As a source
of high-frequency power for linear electron accelerator
«Almaz-2M» pulsed klystron amplifier KIU-12M is
used. The problem of klystron KIU-12M restoration is
caused by complete elimination of their production. In
this connection the technology of restoration of the klys-
tron has been developed and implemented. It allowed to
achieve the parameters of the restored klystron which are
close to those of produced industrial klystrons. In particu-
lar, Fig. 10 shows the level of the pulsed output power of
the restored klystron upon anode voltage, measured at
pulse duration 2 µs and repetition frequency 50 Hz.
Fig. 10. The the output pulse power of the klystron
dependence of upon anode voltage
Fig. 11 shows a photograph of the restored klystron
KIU-12M. Updated electron accelerator «Almaz-2M»
with modernized electronic gun, restored master-
oscillator and klystron KIU-12M is shown in Fig. 12.
Fig. 11.
Photo of
restored
klystron
KIU-12M
Fig. 12. Electronic accelerator
«Almaz-2M».
Electron beam parameters:
energy 4.5 MeV, pulsed current
of 0.8 A, pulse duration 2 µs.
The number of bunches 6·103, each
of length 1.7 cm, diameter 1 cm,
and charge 0.26 nC.
Period of bunch repetition 300 ns
2.2. MEASUREMENTS OF BEAM PARAMETERS
Experimental setup.
The scheme of the facility is shown in Fig. 13.
The sequence of relativistic electron bunches obtained
using a linear resonant electron accelerator (1), is trans-
ported through the waveguide partially filled with dielec-
tric. By means of the magnetic analyzer (2) located at the
accelerator exit it is possible to measure electron energy
distribution for bunches injected in the dielectric structure
(4). The output end of the waveguide is closed by the
teflon plug (7) to provide vacuum inside the dielectric
structure and allow excited wakefields to propagate
through it into atmosphere to be for measured by means
of the microwave probe (8). For measurements of elec-
ISSN 1562-6016. ВАНТ. 2015. №4(98) 102
tron energy distribution of the bunches after interaction
with dielectric structure the teflon plug can be ex-
changed by a metal flange with a window made from a
titanic foil of thickness 50 μm through which the bunch-
es can cross and propagate into atmosphere.
Fig. 13. 1 − accelerator "Almaz-2М"; 2 − magnetic
analyzer; 3 − diaphragm; 4 – dielectric structure;
5 − waveguide; 6 − traversal magnetic field; 7 – vacu-
um teflon plug; 8 − microwave probe; 9 − oscilloscope;
10 − metal collector; 11 − waveguide with a horn
Measurements of the beam parameters.
Beam current. For measuring beam current of up-
dated accelerator electron beam was injected into at-
mosphere through the titan foil. By means of a Faraday
cup located behind the titan foil, the beam current was
measured with and without switching on the output fo-
cusing magnetic lens of the accelerator. Oscillograms of
the beam current for these cases are shown in
Figs. 14,а,b.
As sensitivity of oscilloscope was 5 V/div for the
first case the amplitude of signal from the Faraday cup
is equal 25 V (see Fig. 14,а). Taking into account that
load resistance was 25 Ω we can conclude that the value
of beam current was 1 A. Without switching on the fo-
cusing lens the beam current was 0.8 A (see Fig. 14,b).
a b
Fig. 14. Oscillograms of electron beam current on ac-
celerator exit: focusing lens switched on (a);
focusing lens switched off (b)
Fig. 15. Beam imprints on the glass plates located at the
accelerator exit in vertical (left) and horizontal (below)
planes: focusing lens switched on (a);
focusing lens switched off (b)
Transverse sizes of the beam. By the treatment of
the distribution of the intensity of the darkening of the
glass plates placed behind the output foil, the traversal
distribution of the beam density and the traversal sizes
of the beam at the accelerator exit were measured
(Fig. 15). From the Figs. 15,a,b one can conclude that
the beam diameters estimated as a half-width of the
glass darkening distribution are: 11 and 11 mm in verti-
cal and horizontal planes, correspondingly, for switched
on focusing lens; and 11.6 and 12.4 mm in vertical and
horizontal planes, correspondingly, for switched off
focusing lens.
Electron energy spectrum of the beam. Electron en-
ergy spectra of the beam ejected from the accelerator
and measured by the magnetic analyzer (2), at various
frequencies of the master oscillator (i.e. various bunch
repetition frequencies), are shown in Fig. 16.
Fig. 16. The energy spectra of electrons in the beam at
different frequencies of the master oscillator:
f=2804 MHz (a); f=2805МHz (b); f=2806 MHz (c);
f=2807 MHz (d)
The optimal operation mode of the accelerator pre-
sented in Fig. 16, at which the current is large (up to
1 A), and the half-width of an electron energy spectrum
is small (within 7…9%), occurs for frequencies in the
range of 2804…2807 MHz. Changing frequency of the
master oscillator, it is possible to change of the electron
beam energy within 2.5…4.8 MeV.
Variation of the beam pulse duration. Changing the
duration of the beam pulse, i.e. the number of bunches
in the consequence can be achieved by shift in time the
microwave pulse of the master oscillator relatively to
the high-voltage pulse of the klystron amplifier. Beam
pulse duration is determined by the time overlap of
these two pulses. The beam pulse durations 2.0, 1.0, 0.5,
and 0.1 μs (sequence of 6000, 3000, 1500, and 300
bunches, correspondingly) obtained in such a way for
three time shifts 0, 1.0, 1.5, and 1.9 μs are shown in
oscillograms of Fig. 17.
a b c d
Fig. 17. Pulse duration of beam current for time shift τ:
τ =0 μs (a); τ =1.0 μs (b); τ =1.5 μs (c); τ =1.9 μs (d)
ISSN 1562-6016. ВАНТ. 2015. №4(98) 103
3. PRELIMINARY EXPERIMENTS
ON WAKEFIELD EXCITATION
Dielectric structure of circular cross-section. The
measured permittivity value ε of Teflon was equal ε =
2.04 ± 0.01, and tgδ = 2⋅10-4. Accordingly to these data
the dielectric cylindrical structure consisting of a copper
tube with inner diameter d2 = 85 mm and the dielectric
insert with inner and outer diameter d1=21.1 mm;
d2=85 mm, was calculated and made (Fig. 18).
Fig. 18. Dielectric waveguide of circular cross-section;
d1=21.1 mm; d2=85 mm; d3=89 mm
The measurements of the value of change in the Q
factor of the metal resonator of length 65 cm when fill-
ing it with the dielectric insert of length 44 cm. In
Fig. 19 the resonance curves of the metal resonator
without insert (Fig.19,a) and with an insert (Fig.19,b)
are presented. From these curves it follows that the Q
factor of the empty metal resonator Q0=ω0/2δ
=f0/Δf=2806 (2δ=Δω=2π Δf) decreases to Qd =1122,
when the dielectric insert was input in the resonator.
a b
Fig. 19. Resonance curves for: resonator without (a),
and with insert (b)
Experimental observation of the excited wakefield.
Using oscilloscope TDS 6154C, 15 GHz we firstly in
our experiments obtained the realization of 3 GHz oscil-
lations (Fig. 20) of the wakefield excited by electron
bunches passing through the dielectric structure of cir-
cular cross-section (copper tube, 65 cm long and 8.5 cm
by inner diameter) filled with Teflon insert of length
35 cm, transit channel diameter 2.11 cm.
.
Fig. 20. Oscillogram of wakefield excited
in a dielectric waveguide
4. PRODUCTION OF PLASMA
IN AXIAL CHANNEL
The scheme and photo of experimental setup is
shown in Fig. 21. Relativistic electron bunches pro-
duced by resonant electron accelerator “Almaz-2M”
penetrates through a titanium foil with a thickness of
30 µm and enter into the dielectric waveguide of circu-
lar cross-section, filled with Teflon insert which has the
transit channel of diameter 2.1 cm for the passage of
bunches. To avoid reflections of the excited wakefield
the dielectric insert is ended with dielectric cone, and on
Teflon vacuum plug a ferrite absorber is placed.
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.
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 due to the
beam-plasma discharge development at pressure around
1Torr by the excited wakefield and due to the collisional
ionization by beam electrons at higher pressures.
Fig. 21. Scheme of experimental setup:
1 − accelerator "Almaz-2M"; 2 − titanium foil; 3 – leak
valve; 4 − dielectric waveguide; 5 − matching dielectric
cone; 6 − ferrite absorber; 7 − microwave probe;
8 − oscilloscope GD-840S; 9 − double Faraday cup;
10 − vacuum pump
Plasma density was measured by HF probe or using
an open barrel shaped cavity [7] with and without die-
lectric insert at neutral gas pressure P=10-3…760 Тоrr.
Measurements showed that at the injection of relativ-
istic electron bunches into waveguide without dielectric
plasma of average density 1010…5·1010см-3is formed
and in the presence of a dielectric plasma density is in-
creased by more than twice and the rate of plasma den-
sity increase is significantly high (Fig. 22).
ISSN 1562-6016. ВАНТ. 2015. №4(98) 104
a b
Fig. 22. Temporal dependence of the plasma density
formed by injecting bunches through the neutral gas
at pressure of P = 600 Torr: without (a),
and with dielectric (b)
CONCLUSIONS
Dispersion equation is obtained and topography of
wakefields generated by relativistic electron bunches in
hybrid plasma-dielectric structure is studied. The rate of
acceleration and focusing force for accelerated bunch is
determined.
Experimental installation "Plasma-dielectric wake-
field accelerator" is designed and built which includes
upgraded linear electron accelerator "Almaz-2M",
plasma-dielectric structures and diagnostic equipment to
investigate electron bunches and excited wakefields are
designed and manufactured.
This work was supported by NAS of Ukraine pro-
gram "Perspective investigations on plasma physics,
controlled thermonuclear fusion and plasma technolo-
gies", Project P-1/63-2015.
REFERENCES
1. 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 // Proc. IPAC. 2013, p. 1259.
2. R.R. Knyazev, G.V. Sotnikov. Focusing wakefield
for accelerated bunch in a plasma-dielectric wave-
guide // J. of Kharkiv University. 2012, № 1001,
p. 64-68.
3. V.А. Balakirev, N.I. Кarbushev, O.О. Ostrovsky,
Yu.V. Тkach. Theory of Cherenkov amplifiers and
generators on relativistic beams. Kiev: “Naukova
dumka”, 1993, p. 161.
4. R. Keinigs and M. Е. Jones. Two-dimensional dy-
namics of the plasma wakefield accelerator // Phys.
Fluids. 1987, v. 30, № 1, p.252-263.
5. R.R. Kniaziev, G.V. Sotnikov. Quasistatic field in-
fluence on bunches focusing by wakefields in the
plasma-dielectric waveguide // Proc. IPAC. 2013,
p. 1256.
6. I.N. Onishchenko, A.K. Berezin, V.A. Kiselev,
G.V. Sotnikov, et al. The wake-field excitation in
plasma-dielectric structure by sequence of short
bunches of relativistic electrons // Proc. Particle Ac-
celerator Conf. PAC'95 (IEEE, 1995). p. 782.
7. I.N. Moskalev, A.M. Stefanovsky. Diagnostics of
plasma by using open cylinder resonators. Moscow:
«Atomizdat», 1985, p. 145.
Article received 10.06.2015
КОНЦЕПЦИЯ ПЛАЗМЕННО-ДИЭЛЕКТРИЧЕСКОГО КИЛЬВАТЕРНОГО УСКОРИТЕЛЯ.
ТЕОРИЯ И ЭКСПЕРИМЕНТ
Г.П. Березина, К.В. Галайдыч, Р.Р. Князев, А.Ф. Линник, П.И. Марков, О.Л. Омелаенко, И.Н. Онищенко,
В.И. Приступа, Г.В. Сотников, В.С. Ус
Теоретически и экспериментально исследовано возбуждение кильватерных полей длинной последова-
тельностью релятивистских электронных сгустков в диэлектрическом волноводе/резонаторе круглого сече-
ния с пролетным каналом, заполненным плазмой различных плотностей.
КОНЦЕПЦІЯ ПЛАЗМОВО-ДІЕЛЕКТРИЧНОГО КІЛЬВАТЕРНОГО ПРИСКОРЮВАЧА.
ТЕОРІЯ І ЕКСПЕРИМЕНТ
Г.П. Березіна, К.В. Галайдич, Р.Р. Князєв, A.Ф. Лінник, П.І. Марков, О.Л. Омелаєнко, I.М. Oніщенко,
В.I. Приступа, Г.В. Сотніков, В.С. Уc
Теоретично і експериментально досліджено збудження кільватерних полів довгою послідовністю реля-
тивістських електронних згустків у діелектричному хвилеводі/резонаторі круглого перетину з пролітним
каналом, який заповнено плазмою різної густини.
INTRODUCTION
1. THEORY
1.1. ANALYTICAL EXPRESSIONS FOR EXCITED FIELDS
1.2. numerical calculations
2. еXPERIMENTAL INVESTIGATIONS
2.1. UPDATING ELECTRON ACCELERATOR «АLMAZ-2М»
3. Preliminary experiments on wakefield excitation
4. PRODUCTION OF PLASMA IN AXIAL CHANNEL
концепция плазменно-диэлектрического кильватерного ускорителя. теория и эксперимент
|
| id | nasplib_isofts_kiev_ua-123456789-112146 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1562-6016 |
| language | English |
| last_indexed | 2025-12-07T18:32:00Z |
| publishDate | 2015 |
| publisher | Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
| record_format | dspace |
| spelling | Berezina, G.P. Galaydych, K.V. Kniaziev, R.R. Linnik, A.F. Markov, P.I. Omelayenko, O.L. Onishchenko, I.N. Pristupa, V.I. Sotnikov, G.V. Us, V.S. 2017-01-17T18:29:27Z 2017-01-17T18:29:27Z 2015 Concept of plasma-dielectric wakefield accelerator. theory and experiment / G.P. Berezina, K.V. Galaydych, R.R. Kniaziev, A.F. Linnik, P.I. Markov, O.L. Omelayenko, I.N. Onishchenko, V.I. Pristupa, G.V. Sotnikov, V.S. Us // Вопросы атомной науки и техники. — 2015. — № 4. — С. 97-104. — Бібліогр.: 7 назв. — англ. 1562-6016 PACS: 41.60.-m, 41.75.Lx, 41.75.Ht, 96.50.Pw https://nasplib.isofts.kiev.ua/handle/123456789/112146 The wakefield excitation by a long sequence of relativistic electron bunches in a dielectric waveguide/resonator of round cross-section with transit channel filled with plasma of various densities was theoretically and experimen-tally investigated. Теоретично і експериментально досліджено збудження кільватерних полів довгою послідовністю релятивістських електронних згустків у діелектричному хвилеводі/резонаторі круглого перетину з пролітним каналом, який заповнено плазмою різної густини. Теоретически и экспериментально исследовано возбуждение кильватерных полей длинной последовательностью релятивистских электронных сгустков в диэлектрическом волноводе/резонаторе круглого сечения с пролетным каналом, заполненным плазмой различных плотностей. en Національний науковий центр «Харківський фізико-технічний інститут» НАН України Вопросы атомной науки и техники Новые методы ускорения заряженных частиц Concept of plasma-dielectric wakefield accelerator. Theory and experiment Концепція плазмово-діелектричного кільватерного прискорювача. Теорія і експеримент Концепция плазменно-диэлектрического кильватерного ускорителя. Теория и эксперимент Article published earlier |
| spellingShingle | Concept of plasma-dielectric wakefield accelerator. Theory and experiment Berezina, G.P. Galaydych, K.V. Kniaziev, R.R. Linnik, A.F. Markov, P.I. Omelayenko, O.L. Onishchenko, I.N. Pristupa, V.I. Sotnikov, G.V. Us, V.S. Новые методы ускорения заряженных частиц |
| title | Concept of plasma-dielectric wakefield accelerator. Theory and experiment |
| title_alt | Концепція плазмово-діелектричного кільватерного прискорювача. Теорія і експеримент Концепция плазменно-диэлектрического кильватерного ускорителя. Теория и эксперимент |
| title_full | Concept of plasma-dielectric wakefield accelerator. Theory and experiment |
| title_fullStr | Concept of plasma-dielectric wakefield accelerator. Theory and experiment |
| title_full_unstemmed | Concept of plasma-dielectric wakefield accelerator. Theory and experiment |
| title_short | Concept of plasma-dielectric wakefield accelerator. Theory and experiment |
| title_sort | concept of plasma-dielectric wakefield accelerator. theory and experiment |
| topic | Новые методы ускорения заряженных частиц |
| topic_facet | Новые методы ускорения заряженных частиц |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/112146 |
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