Reflection of normal incidence relativistic electron bunch from semi-bounded plasama
In [1] was obtained the model and analytic describing of the relativistic electron beam reflection from plasma boundary. This phenomenon was experimentally observed in paper [2]. Lack of experimental information compels us to make the new theoretical model. Numerical realisation of this one obtained...
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| Опубліковано в: : | Вопросы атомной науки и техники |
|---|---|
| Дата: | 2007 |
| Автори: | , |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Національний науковий центр «Харківський фізико-технічний інститут» НАН України
2007
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| Теми: | |
| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/110528 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Reflection of normal incidence relativistic electron bunch from semi-bounded plasama / S.V. Barchuk, V.I. Tkachenko // Вопросы атомной науки и техники. — 2007. — № 1. — С. 119-121. — Бібліогр.: 2 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1859916888367169536 |
|---|---|
| author | Barchuk, S.V. Tkachenko, V.I. |
| author_facet | Barchuk, S.V. Tkachenko, V.I. |
| citation_txt | Reflection of normal incidence relativistic electron bunch from semi-bounded plasama / S.V. Barchuk, V.I. Tkachenko // Вопросы атомной науки и техники. — 2007. — № 1. — С. 119-121. — Бібліогр.: 2 назв. — англ. |
| collection | DSpace DC |
| container_title | Вопросы атомной науки и техники |
| description | In [1] was obtained the model and analytic describing of the relativistic electron beam reflection from plasma boundary. This phenomenon was experimentally observed in paper [2]. Lack of experimental information compels us to make the new theoretical model. Numerical realisation of this one obtained in present work. Before numerical investigation the relations described reflection of a relativistic electron beam of finite length and small radius (Lb>>rb) from vacuum-plasma boundary and given in [1] are made more accurate. In particular, the influence of the posisitive volume charge in front of the high density electron beam is taken into account.
У [1] наведена модель і теоретичний опис відбиття релятивістського електронного пучка від межі плазми. Це явище досліджено експериментально в роботі [2]. Недостатність інформації про експеримент змусила створити нову теоретичну модель. У цій роботі наведена її чисельна реалізація. Перед чисельним вивченням були уточнені відношення, що описують відбиття релятивістського електронного пучка кінцевої довжини та малого радіуса (Lb>>rb) від межі вакуум-плазма, наведені в [1]. Зокрема був врахований вплив позитивного об'ємного заряду, що утворюється перед пучком.
В [1] приведена модель и теоретическое описание отражения релятивистского электронного пучка от границы плазмы. Это явление исследовано экспериментально в работе [2]. Недостаток информации об эксперименте вынудил создать новую теоретическую модель. В настоящей работе приведена ее численная реализация. Перед численным изучением были уточнены отношения, описывающие отражение релятивистского электронного пучка конечной длины и малого радиуса (Lb>>rb) от границы вакуум-плазма, представленные в [1]. В частности, было учтено влияние положительного объемного заряда, образующегося перед пучком.
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| first_indexed | 2025-12-07T16:06:00Z |
| format | Article |
| fulltext |
Problems of Atomic Science and Technology. 2007, 1. Series: Plasma Physics (13), p. 119-121 119
REFLECTION OF NORMAL INCIDENCE RELATIVISTIC ELECTRON
BUNCH FROM SEMI-BOUNDED PLASAMA
S.V. Barchuk, V.I. Tkachenko
NSC “Kharkov Institute of Physics and Technology”, 61108, Kharkov, Ukraine
In [1] was obtained the model and analytic describing of the relativistic electron beam reflection from plasma
boundary. This phenomenon was experimentally observed in paper [2]. Lack of experimental information compels us to
make the new theoretical model. Numerical realisation of this one obtained in present work. Before numerical
investigation the relations described reflection of a relativistic electron beam of finite length and small radius (Lb>>rb)
from vacuum-plasma boundary and given in [1] are made more accurate. In particular, the influence of the posisitive
volume charge in front of the high density electron beam is taken into account.
PACS: 52.27.Jt
In paper [1] it has been shown, that injected in plasma
from an insulated source the continuous beam of the
relativistic electrons is reflected from a monolithic double
layer, formed by it. In this paper the reflection of the
relativistic electron beam from plasma boundary is
considered. Similar reflection was experimentally
observed in [2]. Namely, the narrow relativistic electronic
beam of finite length, injected in plasma, is reflected at
certain conditions from semi-bounded plasma.
We investigate theoretically phenomena,
accompanying the injection of the relativistic electron
bunch in plasma with density, much greater the plasma
density ob nn >> .
Fig.1. The arrangement of the electron bunch, injected in
the plasma, and of area of the positive charge, screening
its, in a neighborhood of the plasma boundary
Outgoing from actual experimental conditions, we
consider the bunch, which length is greater than its radius,
bb rl >> . We consider that the effect of reflection is
realized on electron time scale, i.e. the ions have no time
to react on fields of the bunch, owing to their inertness.
The plasma electrons under effect of the electrical field of
the bunch are scattered in a transverse direction. As a
result of it around of the bunch the area of a positive
charge is formed, which scheme is introduced in Fig. 1 by
area, designated by "+". On the bunch electrons,
distributing in plasma, radial electrical scattering force
reE− and magnetic force of a self-focusing of the
relativistic electron bunch mfF act. We choose such
parameters of the bunch, that it’s self-focusing or increase
of its radius is not performed. Then following balance of
the radial forces ( ) ( ) 0=+− bmfobr nFnneE is
realized. Here e is the charge of the electron; rE is the
transversal component of an electrical field, created by
the bunch and plasma ions at its electron evacuation in a
radial direction from area of the bunch propagation. In
last ratio it is shown by brackets, that mfF depends on the
bunch density, and rE depends on the difference of
densities of the bunch and ambient plasma ions. For rE
and mfF we have following approximate expressions
( ) bbor rrrnneE <−≈ ,2π
ob
b
bor Rrr
r
rnrneE <<
−≈ ,2
2
π
b
b
bmf rr
c
vrneF <
≈ ,2
2
2π
(1)
From balance of radial forces with the help of these
expressions it is possible to receive for the relativistic
bunch 11
2
1
2
2
>>
−=
−
c
vb
bγ presented above condition
for densities
obob nnn >>= 2γ . (2)
Here bγ is the relativistic factor of the bunch. bv is
the bunch velocity, c is the velocity of the light, oR is
the radius of area, from which the plasma electrons are
escaped. From the condition that the electrical field,
scattering the plasma electrons, equals zero at oRr = we
receive, that around of the bunch the broad area of the
positive charge is formed
120
b
o
b
bo r
n
nrR >>
≈
2
1
. (3)
Below we will show that the spatial structure of the
electric potential, created by the bunch and the mentioned
above area of the positive charge at a separation of tail of
the bunch from the plasma boundary, can be the cause of
explained effect.
Let's consider distribution of the electrical field along
an axis z of the symmetry of the bunch in the case, when
the back from of the bunch was separated from plasma
boundary at its penetration in the plasma. The distribution
of the electrical potential of the bunch on the interval
between plasma boundary and back front of the bunch
oLz <<0 , and also between back and forward fronts of
the bunch, shown in Fig. 2. As it is visible from this
figure, the potential has a dip approximately in the center
of the bunch. As the strong inequality ob nn >> is
realized, then the distribution of the electric potential
between the plasma boundary and back front of the
electron bunch is flat in comparison with the potential
distribution in the region of the bunch.
Fig. 2. The distribution of the electric potential along an
axis of the electron bunch
The condition of reflection of electron bunch part
looks like: ( ) φγ ∆<− emc b 12
, where
( )minmax φφφ +=∆ , m is the electron mass. This
condition of reflection can approximately be presented as
follows:
( )
<−
b
b
bbb r
L
rnemc ln1 222 ψπγ . (4)
Let's present the following condition be γγ >⊥ ,
which is necessary that the plasma electrons do not have
time to retain behind the bunch and thus to neutralize the
positive charge. Here ⊥eγ is the relativistic factor of the
plasma electrons, accelerated by field of the bunch in a
transverse direction. Last condition can approximately be
presented as follows
<
o
b
bbb n
n
rnemc ln222 πγ . (5)
This condition is more easy executed in the case of the
large bunch density bn and not so large bγ . This
condition, in absence of a self-focusing or widening of the
bunch, receives the following kind
bbbb cr γγω 222 2ln > ,
m
ne b
b
2
2 4π
ω = ,
(6)
or through full quantity of charges bbb LnrQ 2π= of the
electron bunch
>
2
2 ln2
mc
e
LQ
b
bb
ε
ε
. (7)
Fig. 3. Region of the electron beam reflection from semi-bounded plasma
On Z-axis (Fig. 3) we have shown bunch energy in
GeV, on dim 1-axis – depth of beam penetration in
plasma in comparative units (“400” according to situation
where distance between back front of the bunch and
plasma boundary equal bL , and “1” - 0), on dim 2-axis –
ratio of beam and plasma densities plb nn / (“400” –
23,3×103, “1” – 14,88×103). Using this result we can say
that in borders of our model relativistic electron beam
reflection is strongly depend on plb nn / and bE but
almost independent from penetration depth.
We find out that in our model reflecting part of the
beam arrange not more than 50 % in whole investigated
scale of parameters and depend on relations of plasma and
the beam densities. Reflecting part of the beam depends
on beam density bn and its length bL .
REFERENCES
1. S.V. Barchuk, A.M. Egorov, V.I. Lapshin,
V.I. Maslov, G.A. Skorobagatko. Relativistic Electron
Beam Reflection from Plasma Boundary // Problems of
Atomic Science and Technology. Ser. “Plasma
Physics”(9). 2003, N 1, p. 109-110.
2. P. Muggli et al. Refraction of a particle beam //
Nature. 2001, v. 411, p. 43.
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[1]
. [2].
.
. ,
(Lb>>rb) ,
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.
. , .
[1] .
[2].
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,
(Lb>>rb) , [1].
, .
|
| id | nasplib_isofts_kiev_ua-123456789-110528 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1562-6016 |
| language | English |
| last_indexed | 2025-12-07T16:06:00Z |
| publishDate | 2007 |
| publisher | Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
| record_format | dspace |
| spelling | Barchuk, S.V. Tkachenko, V.I. 2017-01-04T18:16:14Z 2017-01-04T18:16:14Z 2007 Reflection of normal incidence relativistic electron bunch from semi-bounded plasama / S.V. Barchuk, V.I. Tkachenko // Вопросы атомной науки и техники. — 2007. — № 1. — С. 119-121. — Бібліогр.: 2 назв. — англ. 1562-6016 PACS: 52.27.Jt https://nasplib.isofts.kiev.ua/handle/123456789/110528 In [1] was obtained the model and analytic describing of the relativistic electron beam reflection from plasma boundary. This phenomenon was experimentally observed in paper [2]. Lack of experimental information compels us to make the new theoretical model. Numerical realisation of this one obtained in present work. Before numerical investigation the relations described reflection of a relativistic electron beam of finite length and small radius (Lb>>rb) from vacuum-plasma boundary and given in [1] are made more accurate. In particular, the influence of the posisitive volume charge in front of the high density electron beam is taken into account. У [1] наведена модель і теоретичний опис відбиття релятивістського електронного пучка від межі плазми. Це явище досліджено експериментально в роботі [2]. Недостатність інформації про експеримент змусила створити нову теоретичну модель. У цій роботі наведена її чисельна реалізація. Перед чисельним вивченням були уточнені відношення, що описують відбиття релятивістського електронного пучка кінцевої довжини та малого радіуса (Lb>>rb) від межі вакуум-плазма, наведені в [1]. Зокрема був врахований вплив позитивного об'ємного заряду, що утворюється перед пучком. В [1] приведена модель и теоретическое описание отражения релятивистского электронного пучка от границы плазмы. Это явление исследовано экспериментально в работе [2]. Недостаток информации об эксперименте вынудил создать новую теоретическую модель. В настоящей работе приведена ее численная реализация. Перед численным изучением были уточнены отношения, описывающие отражение релятивистского электронного пучка конечной длины и малого радиуса (Lb>>rb) от границы вакуум-плазма, представленные в [1]. В частности, было учтено влияние положительного объемного заряда, образующегося перед пучком. en Національний науковий центр «Харківський фізико-технічний інститут» НАН України Вопросы атомной науки и техники Plasma electronics Reflection of normal incidence relativistic electron bunch from semi-bounded plasama Відбиття нормально падаючого релятивістського електронного пучка напівобмеженою плазмою Отражение нормально падающего релятивистского электронного пучка полуограниченной плазмой Article published earlier |
| spellingShingle | Reflection of normal incidence relativistic electron bunch from semi-bounded plasama Barchuk, S.V. Tkachenko, V.I. Plasma electronics |
| title | Reflection of normal incidence relativistic electron bunch from semi-bounded plasama |
| title_alt | Відбиття нормально падаючого релятивістського електронного пучка напівобмеженою плазмою Отражение нормально падающего релятивистского электронного пучка полуограниченной плазмой |
| title_full | Reflection of normal incidence relativistic electron bunch from semi-bounded plasama |
| title_fullStr | Reflection of normal incidence relativistic electron bunch from semi-bounded plasama |
| title_full_unstemmed | Reflection of normal incidence relativistic electron bunch from semi-bounded plasama |
| title_short | Reflection of normal incidence relativistic electron bunch from semi-bounded plasama |
| title_sort | reflection of normal incidence relativistic electron bunch from semi-bounded plasama |
| topic | Plasma electronics |
| topic_facet | Plasma electronics |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/110528 |
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