Focusing of electron bunches in the plasma-dielectric rectangular slowing-down structure
Results of analytical and numerical researches of excitation of wakefield and dynamics of the charged particles in the plasma-dielectric rectangular slowing-down structure are provided. Based on that the analytics in linear approach for overdense plasma shows that at the certain density of plasma...
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irk-123456789-1153592017-04-04T03:02:24Z Focusing of electron bunches in the plasma-dielectric rectangular slowing-down structure Markov, P.I. Kniaziev, R.R. Onishchenko, I.N. Sotnikov, G.V. Новые и нестандартные ускорительные технологии Results of analytical and numerical researches of excitation of wakefield and dynamics of the charged particles in the plasma-dielectric rectangular slowing-down structure are provided. Based on that the analytics in linear approach for overdense plasma shows that at the certain density of plasma the superposition of plasma and dielectric waves allows to accelerate test bunch with its simultaneous focusing, we have made simulation by the "particle in cell" method of excitation of wakefield for several cases with different plasma density. The carried-out numerical modeling has confirmed predictions of the analytical theory, having shown an acceleration of test bunch with its simultaneous focusing. Представлены результаты численных исследований возбуждения кильватерных полей и динамики заряженных частиц в плазменно-диэлектрической прямоугольной замедляющей структуре. Основываясь на том, что аналитика в линейном приближении для сверхплотной плазмы показывает, что при определенной плот- ности плазмы суперпозиция плазменной и диэлектрической волн позволяет ускорять тестовый сгусток с его одновременной фокусировкой, мы выполнили моделирование методом “частица в ячейке” возбуждения кильватерных полей для нескольких случаев с разной плотностью плазмы. Проведенное численное моделирование подтвердило предсказания аналитической теории, продемонстрировав ускорение тестового сгустка с одновременной его фокусировкой. Представлено результати чисельних досліджень збудження кільватерних полів і динаміки заряджених часток у плазмово-діелектричній прямокутній сповільнюваній структурі. Ґрунтуючись на тому, що аналітика в лінійному наближенні для надщільної плазми показує, що при певній щільності плазми суперпозиція плазмової й діелектричної хвиль дозволяє прискорювати тестовий згусток з його одночасним фокусуванням, ми виконали моделювання методом “частинка у гнізді” збудження кільватерних полів для декількох випадків з різною щільністю плазми. Проведене чисельне моделювання підтвердило пророкування аналітичної теорії, продемонструвавши прискорення тестового згустка з одночасним його фокусуванням. 2016 Article Focusing of electron bunches in the plasma-dielectric rectangular slowing-down structure / P.I. Markov, R.R. Kniaziev, I.N. Onishchenko, G.V. Sotnikov // Вопросы атомной науки и техники. — 2016. — № 3. — С. 57-61. — Бібліогр.: 16 назв. — англ. 1562-6016 PACS: 41.75.Ht, 41.75.Lx, 41.75.Jv, 96.50.Pw http://dspace.nbuv.gov.ua/handle/123456789/115359 en Вопросы атомной науки и техники Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine |
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Новые и нестандартные ускорительные технологии Новые и нестандартные ускорительные технологии |
| spellingShingle |
Новые и нестандартные ускорительные технологии Новые и нестандартные ускорительные технологии Markov, P.I. Kniaziev, R.R. Onishchenko, I.N. Sotnikov, G.V. Focusing of electron bunches in the plasma-dielectric rectangular slowing-down structure Вопросы атомной науки и техники |
| description |
Results of analytical and numerical researches of excitation of wakefield and dynamics of the charged particles
in the plasma-dielectric rectangular slowing-down structure are provided. Based on that the analytics in linear approach
for overdense plasma shows that at the certain density of plasma the superposition of plasma and dielectric
waves allows to accelerate test bunch with its simultaneous focusing, we have made simulation by the "particle in
cell" method of excitation of wakefield for several cases with different plasma density. The carried-out numerical
modeling has confirmed predictions of the analytical theory, having shown an acceleration of test bunch with its
simultaneous focusing. |
| format |
Article |
| author |
Markov, P.I. Kniaziev, R.R. Onishchenko, I.N. Sotnikov, G.V. |
| author_facet |
Markov, P.I. Kniaziev, R.R. Onishchenko, I.N. Sotnikov, G.V. |
| author_sort |
Markov, P.I. |
| title |
Focusing of electron bunches in the plasma-dielectric rectangular slowing-down structure |
| title_short |
Focusing of electron bunches in the plasma-dielectric rectangular slowing-down structure |
| title_full |
Focusing of electron bunches in the plasma-dielectric rectangular slowing-down structure |
| title_fullStr |
Focusing of electron bunches in the plasma-dielectric rectangular slowing-down structure |
| title_full_unstemmed |
Focusing of electron bunches in the plasma-dielectric rectangular slowing-down structure |
| title_sort |
focusing of electron bunches in the plasma-dielectric rectangular slowing-down structure |
| publisher |
Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
| publishDate |
2016 |
| topic_facet |
Новые и нестандартные ускорительные технологии |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/115359 |
| citation_txt |
Focusing of electron bunches in the plasma-dielectric rectangular slowing-down structure / P.I. Markov, R.R. Kniaziev, I.N. Onishchenko, G.V. Sotnikov // Вопросы атомной науки и техники. — 2016. — № 3. — С. 57-61. — Бібліогр.: 16 назв. — англ. |
| series |
Вопросы атомной науки и техники |
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2025-07-08T08:39:27Z |
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| fulltext |
NOVEL AND ADVANCED ACCELERATION TECHNIQUES
FOCUSING OF ELECTRON BUNCHES IN THE PLASMA-DIELECTRIC
RECTANGULAR SLOWING-DOWN STRUCTURE
P.I. Markov1, R.R. Kniaziev1,2, I.N. Onishchenko1, G.V. Sotnikov1
1National Science Center “Kharkov Institute of Physics and Technology”, Kharkov, Ukraine;
2V.N. Karazin Kharkiv National University, Kharkov, Ukraine
E-mail: pmarkov@kipt.kharkov.ua
Results of analytical and numerical researches of excitation of wakefield and dynamics of the charged particles
in the plasma-dielectric rectangular slowing-down structure are provided. Based on that the analytics in linear ap-
proach for overdense plasma shows that at the certain density of plasma the superposition of plasma and dielectric
waves allows to accelerate test bunch with its simultaneous focusing, we have made simulation by the "particle in
cell" method of excitation of wakefield for several cases with different plasma density. The carried-out numerical
modeling has confirmed predictions of the analytical theory, having shown an acceleration of test bunch with its
simultaneous focusing.
PACS: 41.75.Ht, 41.75.Lx, 41.75.Jv, 96.50.Pw
INTRODUCTION
Acceleration of charged particles by wakefields ex-
cited by relativistic electron bunches in dielectric struc-
tures is an actively developing direction for new me-
thods of acceleration [1, 2]. The experimental research
carried out, at ANL and SLAC, confirmed [3, 4] the
suitability of this method of acceleration of charged
particles. The dielectric wakefield accelerator is now
considered to be a promising candidate for future elec-
tron-positron colliders in the TeV energy range [5].
Despite, as shown theoretically and experimentally,
possibilities of obtaining a high acceleration rates, one
problem that is not solved completely remains − diffi-
culties with stabilization of the transverse motion of the
drive and accelerated bunches and thereby obtaining
accelerated bunches of particles with a small emittance.
In this article the possibility of using plasma filling the
drift channel of a dielectric structure is considered for
this purpose. Such plasma can be created as a result of a
capillary discharge in a dielectric tube [6]. The use of
plasma for focusing an accelerated bunch is not a new
proposition. The focusing properties of plasma were
investigated in PWFA both in the linear condition [7, 8]
and in a non-linear regime [9, 10]. But in the linear con-
dition the peak of an accelerating field corresponds to
zero focusing field, and in the non-linear regime the
region of acceleration is localized only near a drive
bunch because of plasma destruction caused by a nonli-
near plasma wave.
In order to avoid these restrictions using a plasma-
dielectric structure was proposed [11, 12]. As we will
demonstrate below, this idea has shown acceleration of
test bunch with its simultaneous focusing.
Historically the majority of researches on wakefields
in dielectric structures are carried out for cylindrical
configurations. Recently considerable interest is shown
to planar and rectangular configurations of dielectric
structures. It is caused by the following advantages of
such structures [13]:
• simplicity of production;
• easy tuning of operating frequency by means of
adjustment of metal walls of wave guide, free from di-
electric;
• for given frequency and acceleration voltage they
can accumulate more energy, than cylindrical configura-
tions that leads to decreasing of beam loading;
• additional internal focusing − structure of the
transverse forces operating on electron beam is similar
available at quadrupole focusing;
• the possibility of implementation of multimode
operation of excitation leading to significant increase in
wakefield amplitude.
STATEMENT OF THE PROBLEM
Rectangular dielectric waveguide under investigation
represents the metal waveguide having the cross sizes
a×b with two dielectric slabs (dielectric permittivity is
equal to ε), covering opposite wide walls of a wave-
guide (Fig. 1).
Fig. 1. Schematic view of a rectangular dielectric wave-
guide. Yellow bricks show dielectric slabs, pink cylinder
shows driver electron bunch and blue cylinder shows
witness bunch
The drift channel of dielectric structure is filled with
plasma.
The driver electron bunch, passes through the axis of
slowing-down structure and excites wakefield.
In certain delay time delt after the driver bunch the
witness bunch is injected in system and gets under in-
fluence of wakefield of the driver.
ISSN 1562-6016. ВАНТ. 2016. №3(103) 57
Parameters of driver bunch at numerical simulation
have been chosen such, as in the experimental installa-
tion “Almaz-2”.
Dielectric slab dimensions for given bunches and
waveguide were calculated using theory of excitation of
multizone dielectric waveguides [14, 15], this consid-
eration was expounded in ref. [16]. In Table parameters
used in calculation are given.
Parameters used in calculation
Waveguide R32
Dimensions (a×b), mm 34.04×72.14
Operating frequency, GHz 5.594
Slab dimensions (are located
along wide wall of a wave-
guide), mm
5.7×72.14
Waveguide length L, cm 99.26
Relative dielectric
constant ε (quartz)
3.8
Bunch energy E0, MeV 4.5
Driver bunch charge, nC 0.26
Witness bunch charge, nC 0.026
Driver and witness bunch
diameter, mm
10.0
Driver and witness bunch
axial RMS dimension 2σ
(Gaussian charge distribu-
tion), mm
17.0
Drive and witness full
bunch length used in PIC
simulation, mm
34.0
Plasma density np, ×109cm-3 2.5 5 10 15 20
Delay time delt of witness
bunch, ns 0.
62
3
0.
46
2
0.
26
6
0.
26
6
0.
26
6
GENERALITIES
The Lorentz force ( ), ,x y zF F F=F affecting on the
electron moving with initial relativistic speed
0 0zv k= = ⋅v v
in external electric ( ), ,x y zE E E=E
and magnetic fields for case of non-magnetic dielectric
has form:
( )
( )
0
0
;
;
,
x x y
y y x
z z
F e E H
F e E H
F e E
β
β
= − ⋅ − ⋅
= − ⋅ + ⋅
= − ⋅
(1)
where 0 0zv cβ = , e is electron charge, c is light speed
in vacuum, ,x yH H are components of magnetic field
strength.
For the electrons injected with energy 0 4.5 MeVE =
0 0.9948β = and force (1) is completely defined by de-
pendence of fields on coordinates and time as change of
electrons speed is negligible.
Focusing of bunch is provided by cross force compo-
nents xF and yF , while, acceleration carries out longi-
tudinal force component zF .
It is expected that when filling the drift channel of
rectangular dielectric waveguide with plasma, similar to
the cylindrical configuration [11, 12], transverse com-
ponents of fields obtain certain axial profiles that allows
choosing such arrangement of the witness bunch in rela-
tion to the driver when transverse forces will squeeze
the witness, while longitudinal force will accelerate it.
RESULTS OF 3D-PIC CODE SIMULATION
During numerical simulation using our 3D-PIC code
we analyzed wakefield configuration and dynamics of
electron bunches at their motion in the drift chamber.
Several numerical experiments for the different plasma
density pn have been made.
Fig. 2. Snapshots of Lorentz force components for time
point 3.2 ns: a, b – cross xF in the midplane
of waveguide 2 1.702 cmy a= = ; c, d – cross yF
in the midplane of waveguide 2 3.607cmx b= = ;
e, f – longitudinal zF in the midplane of waveguide
2 3.607cmx b= = . Plasma density in pictures: a, c, e –
9 35 10 cmpn −= ⋅ ; b, d, f – 0pn =
In Fig. 2 comparative snapshots of Lorentz force
components for time point 3.2 ns for dielectric wave-
guide with plasma filling of the drift channel,
9 35 10 cmpn −= ⋅ (see Fig. 2,a,c,e) and without plasma
(Fig. 2,b,d,f) are shown.
Comparing transverse components of force xF in
Fig. 2,a and Fig. 2,b, and also yF in Fig. 2,c and
Fig. 2,d, we see that in the system filled with plasma in
the area of location of electron bunches there are strong
forces affecting on the witness bunch and focusing it. In
waveguide without plasma filling transverse forces are
ISSN 1562-6016. ВАНТ. 2016. №3(103) 58
concentrated mainly on the structure periphery where
bunches are not present. Therefore in dielectric wave-
guide without plasma focusing of bunches is practically
absent.
For the explanation of the mechanism of focusing in
Fig. 3 are shown the configuration space combined with
dependences of longitudinal Fz and transverse forces Fy,
Fx, and also cross profile of bunches for
9 35 10 cmpn −= ⋅ ( 0.21b pn n = ). Plasma (Langmuir)
frequency is 0.635 GHzpf = .
Fig. 3. The configuration space combined with depen-
dences of longitudinal Fz(z) and transverse forces Fy(z),
Fx(z), and also cross profile of bunches for 9 35 10pn cm−= ⋅
The field ( )zF z was measured on bunch axis
( 3.607cmx = , 1.702cmy = ), field ( )yF z − along the
upper edge of bunch ( 3.607cmx = , 2.202cmy = ), and
field ( )xF z − along the right edge of bunch
( 4.107cmx = , 1.702cmy = ).
The witness is injected in system through delay time
0.4623 nsdelt = after injection of the driver. One can see
in Fig. 3, that this provides synchronization of witness
with the accelerating and focusing wakefield phases: the
witness bunch is in positive phase of longitudinal force
zF and in negative phase of transverse forces yF and
xF . The cross profile of bunches shows that at the exit
end of waveguide focusing of the witness occurs on
azimuth. Its diameter decreases to 8.75 mm, i.e. by
1.143 times from initial diameter 10 mm.
In Fig. 4,a the phase plane energy vs. longitudinal
coordinate combined with dependence of longitudinal
force ( )zF z is depicted. In Fig. 4,b distribution function
of electrons of the driver and witness bunches on energy
is shown at that initial bunch energy is 0 4.5E = MeV.
As appears from the schedules provided in Fig. 4,
electrons of the driver bunch, exciting wakefield, are
slowed down while electrons of the witness bunch are
accelerated in this field.
Thus, as it is possible to see in Figs. 3 and 4, we
succeed to focus the witness bunch and to accelerate it
at the same time.
At changing of plasma density the behavior of sys-
tem will not change essentially. However, as the plasma
frequency defining the period of the transverse focusing
forces changes it is necessary to correct delay time delt
so that not to leave acceleration phase, remaining at the
same time in focusing phase of the witness bunch.
Fig. 4. The phase plane energy vs. longitudinal
coordinate combined with dependence of longitudinal
force ( )zF z (a); distribution function of electrons
of the driver and witness bunches on energy,
0 4.5E MeV= (b)
At further increase in plasma density up to
10 32 10 cmpn −= ⋅ in behavior of system it is not observed
any basic changes. Only increases the transverse focus-
ing forces and, respectively, focusing of the witness
bunch improves. In Fig. 5 influence of change of plasma
density on focusing of the witness bunch is shown.
Fig. 5. Diameter of the witness bunch depending on
plasma density. Measurements of diameter were taken
in time 3.2 ns when the driver bunch appears
at the waveguide exit
Nonmonotonic variation of diameter of the witness
bunch at changing of plasma density which is visible in
Fig. 5 explains Fig. 6. Here configuration spaces com-
bined with dependences of longitudinal zF and trans-
verse yF forces for different plasma density are shown.
At the high plasma density 10 32 10 cmpn −= ⋅ the phase
of maximum of the accelerating longitudinal force zF
does not match minimum of the focusing transverse
force yF . Therefore, placing the witness bunch in phase
of the best acceleration, we receive different extent of
focusing for the “head” and “tail” of bunch. Approx-
imately trapezoid profile of longitudinal section of the
witness bunch as it is possible to see it in Fig. 6,e is
ISSN 1562-6016. ВАНТ. 2016. №3(103) 59
consequence of it. At the plasma density
10 31.5 10 cmpn −= ⋅ phasing between maximum of the
accelerating force zF and minimum of the focusing
force yF improves that leads to reduction of distortion
of axial profile of the witness bunch (see Fig. 6,d). At
10 310 cmpn −= variation of diameter at the beginning
and the end of the witness bunch there is even less (see
Fig. 6,c). The best phasing between maximum of the
accelerating force zF and minimum of the focusing
force yF in the studied system is achieved at the plasma
density 9 35 10 cmpn −= ⋅ . Thus the distortion of axial
profile of the witness bunch is minimal (see Fig. 6,b). In
Fig. 6,a the case of the smallest plasma density investi-
gated by us is shown 9 32.5 10 cmpn −= ⋅ . At such density
of plasma the witness bunch starts bringing distortions
in configuration of transverse components of electro-
magnetic fields and, therefore, in distribution of the
transverse focusing forces xF and yF . It leads to that,
despite good phasing between the accelerating and fo-
cusing, a distortion of axial profile of witness bunch
increases.
Fig. 6. The configuration space combined
with dependences of longitudinal ( )zF z and transverse
( )yF z forces for different plasma densities:
a – 9 32.5 10 cm ;pn −= ⋅ b – 9 35 10 cm ;pn −= ⋅
c – 10 310 cm ;pn −= d – 10 31.5 10 cm ;pn −= ⋅
e – 10 32 10 cmpn −= ⋅
For increasing of amplitude of the accelerating field
it is possible to increase charge of driver bunch, or to
use periodic sequence of driver bunches with repetition
rate multiple to the operating frequency of dielectric
waveguide. In the experimental installation “Almaz-2”
the second way is used. In this connection it’s interest-
ing to trace configuration of bunches at their passing
through the drift chamber in presence and absence of
plasma filling the drift channel.
In Fig. 7 the configuration space, combined with de-
pendences of longitudinal ( )zF z and transverse forces
( )yF z and ( )xF z at injection of bunch sequence with
repetition rate of 2.8047 GHz is shown. This frequency
is equal the half of eigen frequency of vacuum dielectric
waveguide. Plots at the left in Fig. 7 correspond to case
of plasma density 10 31 10 cmpn −= ⋅ . Right plots are ob-
tained for the vacuum case 0pn = . The observation
time in Fig. 7 is 5.4 ns. At this moment the 16th bunch
starts entering the resonator.
Fig. 7. Configuration space, combined with depen-
dences of longitudinal ( )zF z and transverse forces
( )yF z and ( )xF z at injection of sequence of bunches.
10 31 10 cmpn −= ⋅ (at the left) and 0pn = (at the right)
One can see from the Fig. 7 that in the second half of
the resonator, at 60 cmz > bunches on plots at the left
have the smaller cross size, than on plots at the right that
testifies to focusing of sequence of driver bunches in
plasma filled system.
CONCLUSIONS
The carried-out numerical simulation has confirmed
predictions of the analytical theory, having shown acce-
leration of test bunch with its simultaneous focusing in
rectangular dielectric waveguide with plasma filling of
the drift channel. This behavior of witness bunch is sim-
ilar the same focusing in cylindrical plasma dielectric
wakefield structure.
Focusing of the witness bunch happens uniformly on
azimuthal angles.
With increasing of plasma density the focusing in-
creases.
Filling of the drift channel with plasma promotes fo-
cusing of periodic sequence of driver bunches.
ACKNOWLEDGEMENTS
Work supported by NAS of Ukraine program "Pers-
pective investigations on plasma physics, controlled
thermonuclear fusion and plasma technologies", Project
P-1/63-2015 "Development of physical principles of
plasma-dielectric wakefield accelerator".
ISSN 1562-6016. ВАНТ. 2016. №3(103) 60
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Article received 20.01.2016
ФОКУСИРОВКА ЭЛЕКТРОННЫХ СГУСТКОВ В ПЛАЗМЕННО-ДИЭЛЕКТРИЧЕСКОЙ
ПРЯМОУГОЛЬНОЙ ЗАМЕДЛЯЮЩЕЙ СТРУКТУРЕ
П.И. Марков, Р.Р. Князев, И.Н. Онищенко, Г.В. Сотников
Представлены результаты численных исследований возбуждения кильватерных полей и динамики заря-
женных частиц в плазменно-диэлектрической прямоугольной замедляющей структуре. Основываясь на том,
что аналитика в линейном приближении для сверхплотной плазмы показывает, что при определенной плот-
ности плазмы суперпозиция плазменной и диэлектрической волн позволяет ускорять тестовый сгусток с его
одновременной фокусировкой, мы выполнили моделирование методом “частица в ячейке” возбуждения
кильватерных полей для нескольких случаев с разной плотностью плазмы. Проведенное численное модели-
рование подтвердило предсказания аналитической теории, продемонстрировав ускорение тестового сгустка
с одновременной его фокусировкой.
ФОКУСУВАННЯ ЕЛЕКТРОННИХ ЗГУСТКІВ У ПЛАЗМОВО-ДІЕЛЕКТРИЧНІЙ
ПРЯМОКУТНІЙ СПОВІЛЬНЮВАЛЬНІЙ СТРУКТУРІ
П.І. Марков, Р.Р. Князєв, І.М. Онiщенко, Г.В. Сотнiков
Представлено результати чисельних досліджень збудження кільватерних полів і динаміки заряджених
часток у плазмово-діелектричній прямокутній сповільнюваній структурі. Ґрунтуючись на тому, що аналіти-
ка в лінійному наближенні для надщільної плазми показує, що при певній щільності плазми суперпозиція
плазмової й діелектричної хвиль дозволяє прискорювати тестовий згусток з його одночасним фокусуванням,
ми виконали моделювання методом “частинка у гнізді” збудження кільватерних полів для декількох випад-
ків з різною щільністю плазми. Проведене чисельне моделювання підтвердило пророкування аналітичної
теорії, продемонструвавши прискорення тестового згустка з одночасним його фокусуванням.
ISSN 1562-6016. ВАНТ. 2016. №3(103) 61
INTRODUCTION
STATEMENT OF THE PROBLEM
GENERALITIES
RESULTS OF 3D-PIC CODE SIMULATION
Conclusions
acknowledgEmentS
references
ФОКУСИРОВКА ЭЛЕКТРОННЫХ СГУСТКОВ В ПЛАЗМЕННО-ДИЭЛЕКТРИЧЕСКОЙ ПРЯМОУГОЛЬНОЙ ЗАМЕДЛЯЮЩЕЙ СТРУКТУРЕ
ФОКУСУВАННЯ ЕЛЕКТРОННИХ ЗГУСТКІВ У ПЛАЗМОВО-ДІЕЛЕКТРИЧНІЙ ПРЯМОКУТНІЙ СПОВІЛЬНЮВАЛЬНІЙ СТРУКТУРІ
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