Peculiarities of a wake potential formation due to a polarization interaction of channeling electron with ionic crystal solid state plasma
Under the influence of electric and magnetic fields generated by a nonrelativistic electron moving in the regime of a plane channeling, the induced time dependent ion electric dipole moments of a crystal medium are calculated. Accounting the causality principle for this dipole system a general scala...
Збережено в:
| Дата: | 2015 |
|---|---|
| Автори: | , , |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Національний науковий центр «Харківський фізико-технічний інститут» НАН України
2015
|
| Назва видання: | Вопросы атомной науки и техники |
| Теми: | |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/82108 |
| Теги: |
Додати тег
Немає тегів, Будьте першим, хто поставить тег для цього запису!
|
| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Peculiarities of a wake potential formation due to a polarization interaction of channeling electron with ionic crystal solid state plasma / M.V. Maksyuta, V.I. Vysotskii, Ye.V. Martysh // Вопросы атомной науки и техники. — 2015. — № 1. — С.33-36. — Бібліогр.: 11 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
irk-123456789-82108 |
|---|---|
| record_format |
dspace |
| spelling |
irk-123456789-821082015-05-26T03:02:20Z Peculiarities of a wake potential formation due to a polarization interaction of channeling electron with ionic crystal solid state plasma Maksyuta, M.V. Vysotskii, V.I. Martysh, Ye.V. Магнитное удержание Under the influence of electric and magnetic fields generated by a nonrelativistic electron moving in the regime of a plane channeling, the induced time dependent ion electric dipole moments of a crystal medium are calculated. Accounting the causality principle for this dipole system a general scalar potential which can be named a “wake” one is found. It is shown that this potential in some crystallographic directions (for example, in ionic crystals) may lead to an essential reverse influence on the regime of the channeling particle motion. Под воздействием электрического и магнитного полей, создаваемых движущимся в режиме плоскостного каналирования релятивистским электроном, рассчитываются зависящие от времени наведенные электрические дипольные моменты ионов кристаллической среды. С учетом принципа причинности для этой системы диполей находится суммарный скалярный потенциал, который можно назвать “кильватерным потенциалом”. Показывается, что этот потенциал в некоторых кристаллографических направлениях (например, в ионных кристаллах) может приводить к существенному обратному влиянию на режим движения каналируемой частицы. Під дією електричного та магнітного полів, створених рухомим у режимі площинного каналювання релятивістським електроном, розраховуються залежні від часу наведені електричні дипольні моменти іонів кристалічного середовища. На підставі врахування принципу причинності для цієї системи диполів знаходиться сумарний скалярний потенціал, який можна назвати “кільватерним потенціалом”. Показується, що цей потенціал у деяких кристалографічних напрямках (наприклад, в іонних кристалах) може приводити до суттєвого зворотного впливу на режим руху канальованої частинки. 2015 Article Peculiarities of a wake potential formation due to a polarization interaction of channeling electron with ionic crystal solid state plasma / M.V. Maksyuta, V.I. Vysotskii, Ye.V. Martysh // Вопросы атомной науки и техники. — 2015. — № 1. — С.33-36. — Бібліогр.: 11 назв. — англ. 1562-6016 PACS: 61.85.+p; 41.75.Fr; 52.25.Vy http://dspace.nbuv.gov.ua/handle/123456789/82108 en Вопросы атомной науки и техники Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| topic |
Магнитное удержание Магнитное удержание |
| spellingShingle |
Магнитное удержание Магнитное удержание Maksyuta, M.V. Vysotskii, V.I. Martysh, Ye.V. Peculiarities of a wake potential formation due to a polarization interaction of channeling electron with ionic crystal solid state plasma Вопросы атомной науки и техники |
| description |
Under the influence of electric and magnetic fields generated by a nonrelativistic electron moving in the regime of a plane channeling, the induced time dependent ion electric dipole moments of a crystal medium are calculated. Accounting the causality principle for this dipole system a general scalar potential which can be named a “wake” one is found. It is shown that this potential in some crystallographic directions (for example, in ionic crystals) may lead to an essential reverse influence on the regime of the channeling particle motion. |
| format |
Article |
| author |
Maksyuta, M.V. Vysotskii, V.I. Martysh, Ye.V. |
| author_facet |
Maksyuta, M.V. Vysotskii, V.I. Martysh, Ye.V. |
| author_sort |
Maksyuta, M.V. |
| title |
Peculiarities of a wake potential formation due to a polarization interaction of channeling electron with ionic crystal solid state plasma |
| title_short |
Peculiarities of a wake potential formation due to a polarization interaction of channeling electron with ionic crystal solid state plasma |
| title_full |
Peculiarities of a wake potential formation due to a polarization interaction of channeling electron with ionic crystal solid state plasma |
| title_fullStr |
Peculiarities of a wake potential formation due to a polarization interaction of channeling electron with ionic crystal solid state plasma |
| title_full_unstemmed |
Peculiarities of a wake potential formation due to a polarization interaction of channeling electron with ionic crystal solid state plasma |
| title_sort |
peculiarities of a wake potential formation due to a polarization interaction of channeling electron with ionic crystal solid state plasma |
| publisher |
Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
| publishDate |
2015 |
| topic_facet |
Магнитное удержание |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/82108 |
| citation_txt |
Peculiarities of a wake potential formation due to a polarization interaction of channeling electron with ionic crystal solid state plasma / M.V. Maksyuta, V.I. Vysotskii, Ye.V. Martysh // Вопросы атомной науки и техники. — 2015. — № 1. — С.33-36. — Бібліогр.: 11 назв. — англ. |
| series |
Вопросы атомной науки и техники |
| work_keys_str_mv |
AT maksyutamv peculiaritiesofawakepotentialformationduetoapolarizationinteractionofchannelingelectronwithioniccrystalsolidstateplasma AT vysotskiivi peculiaritiesofawakepotentialformationduetoapolarizationinteractionofchannelingelectronwithioniccrystalsolidstateplasma AT martyshyev peculiaritiesofawakepotentialformationduetoapolarizationinteractionofchannelingelectronwithioniccrystalsolidstateplasma |
| first_indexed |
2025-07-06T08:15:13Z |
| last_indexed |
2025-07-06T08:15:13Z |
| _version_ |
1836884659165724672 |
| fulltext |
ISSN 1562-6016. ВАНТ. 2015. №1(95)
PROBLEMS OF ATOMIC SCIENCE AND TECHNOLOGY. 2015, № 1. Series: Plasma Physics (21), p. 33-36. 33
PECULIARITIES OF A WAKE POTENTIAL FORMATION DUE TO A
POLARIZATION INTERACTION OF CHANNELING ELECTRON
WITH IONIC CRYSTAL SOLID STATE PLASMA
M.V. Maksyuta, V.I. Vysotskii, Ye.V. Martysh
Taras Shevchenko National University of Kyiv, Ukraine
E-mail: maksyuta@univ.kiev.ua
Under the influence of electric and magnetic fields generated by a nonrelativistic electron moving in the regime
of a plane channeling, the induced time dependent ion electric dipole moments of a crystal medium are calculated.
Accounting the causality principle for this dipole system a general scalar potential which can be named a “wake”
one is found. It is shown that this potential in some crystallographic directions (for example, in ionic crystals) may
lead to an essential reverse influence on the regime of the channeling particle motion.
PACS: 61.85.+p; 41.75.Fr; 52.25.Vy
INTRODUCTION
Obviously, the motion of any particle in arbitrary
medium is accompanied by the mutual influence of
medium on a particle and a particle, in its turn, on
medium. This mutual influence in quite a complicated
way depends on medium characteristics, kind and
parameters of particles. For example, at the channeling
of relativistic electron (positron) its reverse effect on
crystal medium is negligible [1]. Just at the motion of a
heavy ion, on one hand, a polarization of crystal
medium occurs and on the other hand, a delayed in time
and space screening of a potential of an ion itself
appears [2]. It leads to an origination of so-called “wake
potential”. Note, that for the first time a qualitative
theory of a wake interaction for a charged particle
moving in plasma has been worked out in [3]. Similar
wake effects generate just in other cases. For example, a
wake potential which is possible at swift ions motion in
solids [4] is used for electron beams acceleration [5]. It
appears in carbon nanotubes [6], etc.
This paper deals with the investigation of the
channeling weak relativistic electron influence on
electron and nucleus subsystems of a crystal grid of an
ionic crystal which to some extent can be treated as
solid plasma. It should be emphasized that for the first
time the idea of the possibility of wake potential
generation at the channeling of relativistic electrons in
ionic crystals was stated in [7]. The case when a particle
effect on medium is not too strong is treated. Then the
problem can be solved by means of the successive
approaches (in the given paper a zero approach is
developed). In the opposite case when a particle effect
on medium may be compared with the effect of medium
on a particle (it is possible at the channeling of charged
particles along charged planes of some ionic crystals
and also at the motion along high indices directions in
many ionic and ionic covalent crystals) the problem,
evidently, should be solved in a self-consistent way by
means of a variation method.
Thus, supposing that crystal medium influence on a
moving electron is given (electron in a crystal is in the
states n x of a planar channeling with the
possibilities nw ), let’s come proceed to the
consideration of a reverse influence of the electron on a
crystal medium, i.е. let’s calculate the induced electric
dipole crystal moments.
1. CALCULATION OF ELECTRIC DIPOLE
MOMENTS OF CRYSTAL IONS
The expression for an electric charge density moving
with zv ve velocity of a relativistic electron (in
n x state) has a form
2,n nr t e x y z vt . (1)
In this case electric and magnetic field densities using
(1) and in the framework of the relativistic approach are
determined by the following expressions (see, for
example, [8]):
2
2 3
, ,
,
, ,
n n
R r te
E r t d
R r t
, (2a)
1
, , ,n nH r t v E r t
c
, (2b)
where is a Lorentz-factor, , , , ,R r t x y z vt
– radius-vector from e charge to , ,x y z field
observation point,
2 22 2 2, ,R r t x y z vt . The
induced electric dipole moment ,n np r t of a separate
crystal ion in the point with a radius-vector,
, ,n x x y y z zr n a n a n a (here , ,x y za are the crystal grid
periods along , ,x y z axes; , , 0, 1, 2,...x y zn ), is
calculated by means of the following equation of the
oscillation type:
2
0, , ,n n n n n np r t gp r t p r t
2 1
, , ,n n n
e
dr r r E r t v H r t
m с
,(3)
where m – an electron rest mass; r – the density of
an electron distribution in an ion; g – a fading constant
bound to electron and nucleus oscillations; 0 – the
density of dipole proper oscillations. To solve the
36 ISSN 1562-6016. ВАНТ. 2015. №1(95)
equation (3) one expands ,nE r t and ,nH r t fields
as it was done just in [3] into the following Fourier
integrals:
4
,,
exp
, ,2
nn
n n
E kE r t dkd
i kr t
H r t H k
, (4)
where Fourier-components of the expressions (2а) and
(2b) by means of [8] are represented in the form:
2
2
2
2
, 4n n x z
k v
c
E k ief k k v
k
c
, (5а)
2
2
2
,4
,n n x z
v kie
H k f k k v
c
k
c
. (5b)
Here
2 expn x n xf k ik d . Substituting
(4) into (3), the right side of the equation (3) is
transformed into the form
2
4
exp
2
1
, , , ,
n
n n
e
dkd k i kr t
m
E k v H k
с
(6)
where expk r ikr dr – a special Fourier-
component of r function. Substituting (5а) and (5b)
into the expression (6), from the expression (3) we find
a Fourier-component of ,n np r t electric dipole
moment:
3
2 2
2 2 2
0 2
4
,
n x z
n
kf k k k vie
p k
m
i g k
c
. (7)
At last, substituting the expression (7) into a Fourier
integral
4
, exp ,
2
n n n n
dkd
p r t i kr t p k ,
we come after long calculations to the expression for the
value ,n np r t :
2
2
2 2 2 2 2 2
0
,
n z n
n n z
z z
d dk
p r t C F k
k v k g v
,z z
x yn nz z
k kn
x n y n z zf e x e y e G k g (8)
where
2
20
2
sin cosz
z znz
k z
z n z z n
k g
f k k k
v v
,
2
20
2
cos sinz
z znz
k z
z n z z n
k g
g k k k
v v
,
1 1
0
4 2
,
2
n
zz n
z z n
zn
z n
z z
k rk
K K r
K r
F k
r
0 0
1
4 22
n
z n
z n n
zn
z
z z z
k r
K K r
r K r
G k ,
xn x xx n a ,
yn y yy n a ,
zn z zz n a ,
2 2
04z zk b ,
2 2
x y
n
n n
r x y ,
2 2 2 2
04z zk b , v c ,
z zn nz vt ,
3 2 2 2 2
016C e mv b , 0,1K x – MacDonald
functions. Note that calculating the expression (8) one
uses
2
2 2
032 4k k b function arising for
electron distribution density r , chosen in an
exponential form, namely
3
0 02 exp 2r b r b , where is a degree of
crystal atoms ionicity. Similar situation, for example,
takes place for negatively charged hydrogen ions H
in LiH , ionic crystal for which 0 016 11b a , where 0a
– a Bohr radius (see, for example, [9]). Analogous
situations are possible just in other ionic crystals.
2. CALCULATION AND ANALYSIS
OF A WAKE POTENTIAL
A wake potential, i.e. electrostatic potential,
generated by the system of electric dipoles induced, in
its turn, by a channeling particle, can be calculated by
means of the following expression:
3
,
, ,n n n n n
n n
r t p r t r r r r w . (9)
In particular, if we are restricted by the only
crystallographic plane ( 0xn ) and by the only one axis
( 0yn ) on this plane, the total scalar potential
accounting the expressions (8) and (9) is determined by
the formula
34
ISSN 1562-6016. ВАНТ. 2015. №1(95) 35
2
2
2 2 2 2 2 2
0 0 0
,4
,
n z z
z n
z n
z z
G k d dkC
w
a
k v k g v
2
20
2
3/2
22
sin cosz
z z zvt
k g
z k k k
vv
d
z
2
2
2 2 2 2 2 2
0 0 0
, , ,4 n z z z
z
z z
G k D k d dkC
a
k v k g v
, (10)
where
2
20
2
, , sin cosz
z z z z z z z
k g
D k k k k
vv
2 2
0
1 2 3/2
2 2
0
cos1 1 1
1; , ;
2 2 4 2
z
z z zz k I k k dk
F
2
20
2
sin cosz
z z z z z
k g
k k k
vv
0 3/2
2 2
0
sin
z
z
z z
k d
k K k ,
1 2
1 1
1; , ;
2 2
F x – a hypergeometric function; 0I x – a
modified Bessel function; vt , z z vt ,
2 2x y . In the formula (10) the causality
principle is accounted and the transition from the
summarizing by zn to integration
1 ...za d , has
been realized, where za is a distance between ions
along z axis.
In Fig. 1 the potential (10) is illustrated for the
example of nonrelativistic ( 2 ) channeling in ionic
LiH crystal when in H (111) planes with the potential
2
0 chU x U x b ( 0,22b A , 0 0,26eVU
[10]) pit the only one state with a wave function
1/2
0 2 2 B , chs sx b s s x b is realized,
where
1/2
2 2
02 1 4 1 2s m U b ( g and 0
were chosen on the basis of heuristic conformations: g
0v b , 0 0U ).
, А z, А
( , z), a. u.
0
-1
-2
-3
-2
0
0,4
0,2 -1
Fig. 1. The wake potential , z behavior, arising fo
non-relativistic electron channeling along H planes of
ionic LiH crystal (in arbitrary units) depending on the
distance and z
As it is clear from Fig. 1, the wake potential has the
reverse effect on the channeling particle. Let’s analyze
this phenomenon.
3. POTENTIAL WAKE REVERSE EFFECT
ON THE CHANNELING ELECTRON
The channeling electron interaction energy in a wake
potential (10), averaged by thermal oscillations can be
written down in the form
2 2
02
0
exp exp
22
V e I u d
uu
,(11)
where u is an amplitude of crystal ions thermal
oscillations, , 0z . Fig. 2 shows the
function
H HH
0U V V graph for the
above mentioned example (for H 0,26u A ions
[10]).
, A
UH
-
( )=V( )H
-
/V(0)H
-
0
0,2
0,4
0,6
0,8
1
0,5 1 1,5
Fig. 2. Interaction energy
H
U of the channeling
electron in a wake potential as a function of distance
from z axis
Numerical evaluations of dependence (11) show that
the wake potential can have a significant impact on
thecharacter of a channeling particle motion (especially
in anomalous cases).
36 ISSN 1562-6016. ВАНТ. 2015. №1(95)
CONCLUSIONS
Thus, in the paper it was shown that the channeling
of non-relativistic electrons in ionic crystals generates a
wake potential in the result of polarization of these
crystals. Besides, it is shown that a wake potential
affects a channeling particle. First, it is interesting from
the general scientific point of view since a certain
succession with analogous effects in many media is
traced, and second, it may be used in practice (for
example, at the investigation of the defects in crystals as
it is supposed in [11]).
REFERENCES
1. V.A. Bazylev, N.K. Zhevago. Fast particles radiation
in a substance and in external fields. Мoscow: “Nauka”,
1987 (in Russian).
2. Yoshi-Hiko Ohtsuki. Charged particles interaction
with solids. Мoscow: “Mir”, 1985 (in Russian).
3. J. Neufeld, R.H. Ritchie. Passage of charged particles
through plasma // Phys. Rev. 1955, v. 98, № 6,
p. 1632-1642.
4. R.H. Ritchie, W. Brandt, P.M. Echenique. Wake
potential of swift ions in solids // Phys. Rev. B. 1976,
v. 14, № 11, p. 4808-4812.
5. G. Shvets, N.J. Fish. Beam-channeled laser-wavefield
accelerator // Phys. Rev. E. 1997, v. 55, № 5,
p. 6297-6300.
6. D.J. Mowbray, Z.L. Miškovic, F.O. Goodman, Yon-
Nian Wang. Wake effect in interactions of fast ions with
carbon nanotubes // Physics Letters A. 2004, v. 329,
p. 94-99.
7. N.V. Maksyuta, V.I. Vysotskii. On the possibility of
screening manifestation and the origination of a wake
potential at the channeling of relativistic electrons in the
charged planes of ionic crystals // Тhesis of the reports
of XLII International Tulinov Conference on physics of
charged particles interaction with crystals / Edited by
prof. M.I. Panasyuk. Мoscow: “Universitetskaya
kniga”, 2012, p. 34 (in Russian).
8. L.D. Landay, E.M. Lifshitz. Theory of the field.
Moscow: “Nauka”, 1988 (in Russian).
9. V.I. Vysotskii, R.N. Kuz’min, N.V. Maksyuta.
Anomalous channeling and quasi-characteristic
radiation of non-relativistic electrons in ionic crystals //
Sov. Phys. JETP. 1987, v. 66, № 6, p. 1150-1152.
10. M. Maksyuta, V. Vysotskii. The peculiarities of
relativistic electron channeling in charged
crystallographic planes of LiH and LiD ionic crystals //
Visn. Kyiv. univ. Radiophysics and electronics. 2012,
№ 17, p. 4-14.
11. V. Epp, J. Janz. The inverse problem for the dipole
field // Nucl. Instr. and Meth. B. 2008, v. 266,
p. 3700-3702.
Article received 03.12.2014
ОСОБЕННОСТИ ФОРМИРОВАНИЯ КИЛЬВАТЕРНОГО ПОТЕНЦИАЛА ЗА СЧЕТ
ПОЛЯРИЗАЦИОННОГО ВЗАИМОДЕЙСТВИЯ КАНАЛИРУЕМОГО ЭЛЕКТРОНА
С ТВЕРДОТЕЛЬНОЙ ПЛАЗМОЙ ИОННОГО КРИСТАЛЛА
Н.В. Максюта, В.И. Высоцкий, Е.В. Мартыш
Под воздействием электрического и магнитного полей, создаваемых движущимся в режиме
плоскостного каналирования релятивистским электроном, рассчитываются зависящие от времени
наведенные электрические дипольные моменты ионов кристаллической среды. С учетом принципа
причинности для этой системы диполей находится суммарный скалярный потенциал, который можно
назвать “кильватерным потенциалом”. Показывается, что этот потенциал в некоторых
кристаллографических направлениях (например, в ионных кристаллах) может приводить к существенному
обратному влиянию на режим движения каналируемой частицы.
ОСОБЛИВОСТІ ФОРМУВАННЯ КІЛЬВАТЕРНОГО ПОТЕНЦІАЛУ
ЗА РАХУНОК ПОЛЯРИЗАЦІЙНОЇ ВЗАЄМОДІЇ КАНАЛЬОВАНОГО ЕЛЕКТРОНА
З ТВЕРДОТІЛЬНОЮ ПЛАЗМОЮ ІОННОГО КРИСТАЛА
М.В. Максюта, В.І. Висоцький, Є.В. Мартиш
Під дією електричного та магнітного полів, створених рухомим у режимі площинного каналювання
релятивістським електроном, розраховуються залежні від часу наведені електричні дипольні моменти іонів
кристалічного середовища. На підставі врахування принципу причинності для цієї системи диполів
знаходиться сумарний скалярний потенціал, який можна назвати “кільватерним потенціалом”. Показується,
що цей потенціал у деяких кристалографічних напрямках (наприклад, в іонних кристалах) може приводити
до суттєвого зворотного впливу на режим руху канальованої частинки.
|