Relativistic electron beam reflection from the plasma boundary
The spatial distribution of the electrical field, accompanying reflection of the relativistic electronic bunch from the plasma boundary, has been investigated. Теоретично досліджена просторова структура електричного поля при явищі відбиття релятивістського електронного пучка кінцевої довжини і малог...
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| Veröffentlicht in: | Вопросы атомной науки и техники |
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Національний науковий центр «Харківський фізико-технічний інститут» НАН України
2003
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| Zitieren: | Relativistic electron beam reflection from the plasma boundary / S.V. Barchuk, A.M. Egorov, V.I. Maslov, I.N. Onishchenko, G.A. Skorobagatko // Вопросы атомной науки и техники. — 2003. — № 1. — С. 109-110. — Бібліогр.: 3 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1860170636781944832 |
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| author | Barchuk, S.V. Egorov, A.M. Maslov, V.I. Onishchenko, I.N. Skorobagatko, G.A. |
| author_facet | Barchuk, S.V. Egorov, A.M. Maslov, V.I. Onishchenko, I.N. Skorobagatko, G.A. |
| citation_txt | Relativistic electron beam reflection from the plasma boundary / S.V. Barchuk, A.M. Egorov, V.I. Maslov, I.N. Onishchenko, G.A. Skorobagatko // Вопросы атомной науки и техники. — 2003. — № 1. — С. 109-110. — Бібліогр.: 3 назв. — англ. |
| collection | DSpace DC |
| container_title | Вопросы атомной науки и техники |
| description | The spatial distribution of the electrical field, accompanying reflection of the relativistic electronic bunch from the plasma boundary, has been investigated.
Теоретично досліджена просторова структура електричного поля при явищі відбиття релятивістського електронного пучка кінцевої довжини і малого радіуса від межі плазма-вакуум, що спостерігається експериментально.
Теоретически исследована пространственная структура электрического поля при экспериментально наблюдаемом явлении отражения релятивистского электронного пучка конечной длины и малого радиуса от границы плазма-вакуум.
|
| first_indexed | 2025-12-07T17:58:08Z |
| format | Article |
| fulltext |
RELATIVISTIC ELECTRON BEAM REFLECTION FROM THE PLASMA
BOUNDARY
S.V.Barchuk*, A.M.Egorov, V.I.Maslov, I.N.Onishchenko, G.A.Skorobagatko*
NSC Kharkov Institute of Physics and Technology,
Kharkov, Ukraine, E-mail: vmaslov@kipt.kharkov.ua;
*Karazin Kharkov National University, Kharkov,Ukraine
The spatial distribution of the electrical field, accompanying reflection of the relativistic electronic bunch from the
plasma boundary, has been investigated.
PACS: 52.40.-w; 52.40.Mj
INTRODUCTION
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 monotonic double
layer, formed by it. In this paper the experimentally observed
[2] and close to investigated in [1,3] the reflection of the
relativistic electron beam from plasma boundary is
considered, which, however, is implemented at other
conditions. Namely, the narrow relativistic electronic beam
of final length, injected in plasma, is reflected at certain
conditions from vacuum – plasma boundary.
We investigate theoretically phenomena,
accompanying the injection of the relativistic electron
bunch in plasma with density, much greater the plasma
density nb>>no. Outgoing from actual experimental
conditions, we consider the bunch, which length is greater
than its radius, Lb>>rb. 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 –eEr and magnetic force of a self-
focusing of the relativistic electron bunch Fmf act. We
choose such parameters of the bunch, that its self-
focusing or increase of its radius is not performed. Then
following balance of the radial forces eEr(nb-
no)+Fmf(nb)=0 is realized. Here e is the charge of the
electron, Er 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 Fmf
depends on the bunch density, and Er depends on the
difference of densities of the bunch and ambient plasma ions.
For Er and Fmf we have following approximate expressions
Er≈2πe(no-nb)r , r<rb;
Er≈2πe(nor-nbrb
2/r) , rb<r<Ro; (1)
Fmf≈2πe2nbr(Vb/c)2, r<rb
From balance of radial forces with the help of these
expressions it is possible to receive for the relativistic
bunch γb=(1-Vb
2/c2)-1/2>>1 presented above condition for
densities
nb=noγb
2>>no . (2)
Here γb is the relativistic factor of the bunch, Vb is the
bunch velocity, c is the velocity of the light, Ro 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 r=Ro we
receive, that around of the bunch the broad area of the
positive charge is formed
Ro≈rb(nb/no)1/2>>rb. (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 boundary plasma - vacuum, can be the
cause of explained effect.
REFLECTION OF THE ELECTRON BEAM
Let's consider distribution of the electrical field along
an axis z of the symmetry of the bunch in the case, when
the back front of the bunch was separated from boundary
plasma - vacuum at its penetration in the plasma. The
distribution of the electrical field along a symmetry axis
of the bunch on the interval between boundary plasma -
vacuum and back front of the bunch 0<z<Lo, and also
between back and forward fronts of the bunch
Lo<z<Lo+Lb looks like
Ez(z)=2πe{nb[µ+Lb+(rb
2+(z-Lo)2)1/2-(rb
2+(Lo+Lb-z)2)1/2 ]+
+no[2z-Lo-Lb+(Ro
2+(Lo+Lb-z)2)1/2-(Ro
2+z2)1/2]} (4)
µ≡0 , 0<z<Lo
µ≡2(Lo-z) , Lo<z<Lo+Lb
The distribution of the electric potential looks like
φ(z)=-2πe{no[z(z-Lo-Lb)-
-(Ro
2/2)ln[(z+(Ro
2+z2)1/2)(Lo+Lb-z+(Ro
2+(Lo+Lb-
z)2)1/2)/Ro[Lo+Lb+(Ro
2+(Lo+Lb)2)1/2]]-
-z(Ro
2+z2)1/2/2+(Lo+Lb)[Ro
2+(Lo+Lb)2]1/2/2- (5)
-(Lo+Lb-z)[Ro
2+(Lo+Lb-z)2]1/2/2]+
+nbα}
α≡Lb
2/4-(2Lo+Lb-2z)2/4+
+(rb
2/2)ln[(z-Lo+(rb
2+(z-Lo)2)1/2)(Lo+Lb-z+(rb
2+(Lo+Lb-
z)2)1/2)/rb[Lb+(rb
2+Lb
2)1/2]]+(z-Lo)(rb
2+(z-Lo)2)1/2)/2+
+(Lo+Lb-z)(rb
2+(Lo+Lb-z)2)1/2)/2-
-Lb(rb
2+Lb
2)1/2/2 , Lo<z<Lo+Lb
α≡(z-Lo)(rb
2+(Lo-z)2)1/2/2+
+Lb(z-Lo)-Lb(rb
2+Lb
2)1/2/2+
+(Lo+Lb-z)(rb
2+(Lo+Lb-z)2)1/2/2+
Problems of Atomic Science and Technology. 2003. № 1. Series: Plasma Physics (9). P. 109-110 109
+(rb
2/2)ln[rb(Lo+Lb-z+(rb
2+(Lo+Lb-z)2)1/2)/(Lo-z+(rb
2+(Lo-
z)2)1/2)(Lb+(rb
2+Lb
2)1/2)]+
+(z-Lo)(rb
2+(z-Lo)2)1/2)/2 , 0<z<Lo
here Lo is the distance from the plasma boundary to trailing
edge of the bunch, Lb is the length of the bunch.
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 boundary plasma - vacuum
Fig.2. The distribution of the electric potential along an
axis of the electron bunch
The function f(z) looks like, qualitatively 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 nb>>no 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.
Minimum and maximum values of the potential we
derive, using argument of the function (5), accordingly
Lo+Lb/2 and 0. Then we receive:
φmax≈-2πenb[-LbLo-Lb(Lb
2+rb
2)1/2/2-Lo(Lo
2+rb
2)1/2/2+
+(Lo+Lb)((Lo+Lb)2+rb
2)1/2/2-
-(rb
2/2)ln[(Lo+(rb
2+L2
o)1/2)×
×(Lb+(rb
2+Lb
2)1/2)/rb[Lo+Lb+(rb
2+(Lo+Lb)2)1/2]]≈
≈πenbrb
2ln(2LoLb/(Lo+Lb)rb) (6)
φmin≈-2πenb[Lb
2/4+Lb(Lb
2/4+rb
2)1/2/2-Lb(Lb
2+rb
2)1/2/2+
+(rb
2/2)ln[(Lo+Lb/2+(rb
2+L2
b/4)1/2)(Lb/2+(rb
2+Lb
2/4)1/2)/rb[Lo
+Lb+(rb
2+Lb
2)1/2]]≈
≈-πenbrb
2ln(Lo+Lb)Lb/(Lo+2Lb)rb (7)
The condition of reflection of electron bunch part
looks like: mc2(γb-1)<e∆φ, where ∆φ=(φmax+φmin), m
is the electron mass. This condition of reflection can
approximately be presented as follows
mc2(γb-1)<πe2nbrb
2ln(Lb/rb) . (8)
Let's present the following condition γe⊥>γb, which is
necessary that the plasma electrons do not have time to
retain behind the bunch and thus to neutralize the positive
charge. Here γe⊥ 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
πe2nbrb
2ln(nb/no)>mc2γb . (9)
This condition is more easy executed in the case of the
large bunch density nb and not so large γb. This condition,
in absence of a self-focusing or widening of the bunch,
receives the following kind
ωb
2rb
2lnγb>2c2γb. (10)
or through full quantity of charges Q=πrb
2nbLb of the
electron bunch
Q>Lbεb/2e2ln(εb/mc2). (11)
Here ωb
2=4πe2nb/m, εb is the energy of the electron bunch.
REFERENCES
1. V.I.Maslov // Plasma Physics Rep. 1992, v.18, p.676.
2. P.Muggli et al. // Nature. 2001, v. 411 p. 43.
3. N.Singh, W.Schunk. Plas. Phys. Contr. Fus. 26 1984.
v. 26, p. 859.
ВІДБИТТЯ РЕЛЯТИВІСТСЬКОГО ЕЛЕКТРОННОГО ПУЧКА ВІД МЕЖІ ПЛАЗМИ
С.В. Барчук, О.М. Єгоров, В.І. Маслов, І.М. Онищенко, Г.О. Скоробагатько
Теоретично досліджена просторова структура електричного поля при явищі відбиття релятивістського
електронного пучка кінцевої довжини і малого радіуса від межі плазма-вакуум, що спостерігається експериментально.
ОТРАЖЕНИЕ РЕЛЯТИВИСТСКОГО ЭЛЕКТРОННОГО ПУЧКА ОТ ГРАНИЦЫ ПЛАЗМЫ
С.В. Барчук, А.М. Егоров, В.И. Маслов, И.Н. Онищенко, Г.А. Скоробагатько
Теоретически исследована пространственная структура электрического поля при экспериментально
наблюдаемом явлении отражения релятивистского электронного пучка конечной длины и малого радиуса от
границы плазма-вакуум.
110
Z
Br
BL
0R
0R−
r
+
+
Z
MINϕ−
ϕ
MAXϕ
NSC Kharkov Institute of Physics and Technology,
Kharkov, Ukraine, E-mail: vmaslov@kipt.kharkov.ua;
INTRODUCTION
REFLECTION OF THE ELECTRON BEAM
|
| id | nasplib_isofts_kiev_ua-123456789-110543 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1562-6016 |
| language | English |
| last_indexed | 2025-12-07T17:58:08Z |
| publishDate | 2003 |
| publisher | Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
| record_format | dspace |
| spelling | Barchuk, S.V. Egorov, A.M. Maslov, V.I. Onishchenko, I.N. Skorobagatko, G.A. 2017-01-04T18:56:34Z 2017-01-04T18:56:34Z 2003 Relativistic electron beam reflection from the plasma boundary / S.V. Barchuk, A.M. Egorov, V.I. Maslov, I.N. Onishchenko, G.A. Skorobagatko // Вопросы атомной науки и техники. — 2003. — № 1. — С. 109-110. — Бібліогр.: 3 назв. — англ. 1562-6016 PACS: 52.40.-w; 52.40.Mj https://nasplib.isofts.kiev.ua/handle/123456789/110543 The spatial distribution of the electrical field, accompanying reflection of the relativistic electronic bunch from the plasma boundary, has been investigated. Теоретично досліджена просторова структура електричного поля при явищі відбиття релятивістського електронного пучка кінцевої довжини і малого радіуса від межі плазма-вакуум, що спостерігається експериментально. Теоретически исследована пространственная структура электрического поля при экспериментально наблюдаемом явлении отражения релятивистского электронного пучка конечной длины и малого радиуса от границы плазма-вакуум. en Національний науковий центр «Харківський фізико-технічний інститут» НАН України Вопросы атомной науки и техники Plasma electronics Relativistic electron beam reflection from the plasma boundary Відбиття релятивістського електронного пучка від межі плазми Отражение релятивистского электронного пучка от границы плазмы Article published earlier |
| spellingShingle | Relativistic electron beam reflection from the plasma boundary Barchuk, S.V. Egorov, A.M. Maslov, V.I. Onishchenko, I.N. Skorobagatko, G.A. Plasma electronics |
| title | Relativistic electron beam reflection from the plasma boundary |
| title_alt | Відбиття релятивістського електронного пучка від межі плазми Отражение релятивистского электронного пучка от границы плазмы |
| title_full | Relativistic electron beam reflection from the plasma boundary |
| title_fullStr | Relativistic electron beam reflection from the plasma boundary |
| title_full_unstemmed | Relativistic electron beam reflection from the plasma boundary |
| title_short | Relativistic electron beam reflection from the plasma boundary |
| title_sort | relativistic electron beam reflection from the plasma boundary |
| topic | Plasma electronics |
| topic_facet | Plasma electronics |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/110543 |
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