Radiation electronics
Article is review of works on nonequilibrium electron distribution function formation at a presence of sources and sinks in momentum space. The analitical investigations and numerical simulation of the nonlineat collision integrals of Boltzmann and Landau-Fokker-Planck has been considered. The exper...
Збережено в:
| Дата: | 2007 |
|---|---|
| Автор: | |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Національний науковий центр «Харківський фізико-технічний інститут» НАН України
2007
|
| Назва видання: | Вопросы атомной науки и техники |
| Теми: | |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/110664 |
| 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: | Radiation electronics / V.I. Karas’ // Вопросы атомной науки и техники. — 2007. — № 2. — С. 172-181. — Бібліогр.: 42 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
irk-123456789-110664 |
|---|---|
| record_format |
dspace |
| spelling |
irk-123456789-1106642017-01-06T03:03:37Z Radiation electronics Karas, V.I. Физика радиационных и ионно-плазменных технологий Article is review of works on nonequilibrium electron distribution function formation at a presence of sources and sinks in momentum space. The analitical investigations and numerical simulation of the nonlineat collision integrals of Boltzmann and Landau-Fokker-Planck has been considered. The experimental study results of nonequilibrium electron distribution function formation in solid plasma at its irradiation by electromagnetic radiation or charged particles flows have been implemented. New type of radioisotope source of current based on others physical prince-ples was proposed. Огляд робіт по формуванню нерівноважних функцій розподілу електронів дії джерела та стоку у імпульсному просторі. Розглянуті як аналітичні дослідження, так і чисельне моделювання нелінійних інтегралів зіткнень Больцмана та Ландау-Фоккера–Планка. Наведені результати експериментальних досліджень формування нерівноважних функцій розподілу електронів у твердотільній плазмі при її опромінюванні потоками електромагнітного випромінювання або заряджених частинок. Описане оригінальне вторинно–емісійне радіоізотопне джерело струму, основане на нерівноважних розподілах електронів. Обзор работ по формированию неравновесных функций распределения электронов при наличии источника и стока в импульсном пространстве. Рассмотрены как аналитические исследования, так и численное моделирование нелинейных интегралов столкновений Больцмана и Ландау-Фоккера–Планка. Приведены результаты экспериментальных исследований формирования неравновесных функций распределения электронов в твердотельной плазме при облучении ее потоками электромагнитного излучения или заряженных частиц. Описан оригинальный вторично–эмиссионный радиоизотопный источник тока, основанный на неравновесных распределениях электронов. 2007 Article Radiation electronics / V.I. Karas’ // Вопросы атомной науки и техники. — 2007. — № 2. — С. 172-181. — Бібліогр.: 42 назв. — англ. 1562-6016 http://dspace.nbuv.gov.ua/handle/123456789/110664 533.9 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 |
Физика радиационных и ионно-плазменных технологий Физика радиационных и ионно-плазменных технологий |
| spellingShingle |
Физика радиационных и ионно-плазменных технологий Физика радиационных и ионно-плазменных технологий Karas, V.I. Radiation electronics Вопросы атомной науки и техники |
| description |
Article is review of works on nonequilibrium electron distribution function formation at a presence of sources and sinks in momentum space. The analitical investigations and numerical simulation of the nonlineat collision integrals of Boltzmann and Landau-Fokker-Planck has been considered. The experimental study results of nonequilibrium electron distribution function formation in solid plasma at its irradiation by electromagnetic radiation or charged particles flows have been implemented. New type of radioisotope source of current based on others physical prince-ples was proposed. |
| format |
Article |
| author |
Karas, V.I. |
| author_facet |
Karas, V.I. |
| author_sort |
Karas, V.I. |
| title |
Radiation electronics |
| title_short |
Radiation electronics |
| title_full |
Radiation electronics |
| title_fullStr |
Radiation electronics |
| title_full_unstemmed |
Radiation electronics |
| title_sort |
radiation electronics |
| publisher |
Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
| publishDate |
2007 |
| topic_facet |
Физика радиационных и ионно-плазменных технологий |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/110664 |
| citation_txt |
Radiation electronics / V.I. Karas’ // Вопросы атомной науки и техники. — 2007. — № 2. — С. 172-181. — Бібліогр.: 42 назв. — англ. |
| series |
Вопросы атомной науки и техники |
| work_keys_str_mv |
AT karasvi radiationelectronics |
| first_indexed |
2025-07-08T00:57:13Z |
| last_indexed |
2025-07-08T00:57:13Z |
| _version_ |
1837038289142415360 |
| fulltext |
UDC 533.9
RADIATION ELECTRONICS
V.I. Karas’
National Science Center “Kharkov Institute for Physics and Technology” of National Acade-
my of Sciences of Ukraine, Kharkov, Ukraine; E- mail: karas@kipt.kharkov.ua
Article is review of works on nonequilibrium electron distribution function formation at a presence of sources
and sinks in momentum space. The analitical investigations and numerical simulation of the nonlineat collision inte-
grals of Boltzmann and Landau-Fokker-Planck has been considered. The experimental study results of nonequilibri-
um electron distribution function formation in solid plasma at its irradiation by electromagnetic radiation or charged
particles flows have been implemented. New type of radioisotope source of current based on others physical prince-
ples was proposed.
1. INTRODUCTION
At present, the development of high-power particle
and radiation sources is stimulating great interest in the
properties of nonequilibrium systems. The presence of
sources and sinks in momentum space can lead to the
formation of nonequilibrium particle distribution func-
tions with power-law tails even in spatially uniform sys-
tems. The inapplicability of the local equilibrium ap-
proximation to such situations is related to the presence
of particle flows in phase space. In the second section of
this paper, the asymptotic properties of such nonequilib-
rium states are studied, their relation to the nonextensive
Tsallis’ thermodynamics is established, and the depen-
dence of the nonextensivity parameter on the intensity
of the particle flow in phase space (i.e., on the intensi-
ties of sources and sinks) is determined. The third sec-
tion is devoted to numerical simulations of the forma-
tion of a steady-state nonequilibrium dist-ribution of
particles with a long-range repulsion potential. The col-
lisional dynamics of such a system is studied using spa-
tially uniform nonlinear Landau and Fokker–Planck col-
lision integrals, which are model representations of the
Boltzmann collision integral. In numerical simulations,
completely conservative difference schemes are used. In
the fourth section, we consider the conduction and emis-
sion properties of a semiconductor plasma irradiated
with intense particle or laser beams. In the fifth section,
the formation of nonequilibrium electron distribution
functions (EDFs) in the plasmas of semiconductors and
of a Sb/CS cathode is studied experimentally. To study
these functions, the method of the secondary electron
emission induced by fast low- Z ions was employed.
The formed EDFs are measured, the coefficients of the
secondary ion-induced electron emission are deter-
mined, and their relationship to the source power in the
ion’s track is found.
2. STEADY NONEQUILIBRIUM STATES
OF SYSTEMS WITH STATIONARY PARTI-
CLE FLOWS IN PHASE SPACE
Quasi-steady nonequilibrium states of particle sys-
tems can be studied by solving kinetic equations with
allowance for sources and sinks. Power-law particle en-
ergy distributions were first predicted theoretically in
[1–4] and then observed experimentally in [5, 6]. In [1,
2], it was shown using a similarity transformation that
the kinetic Boltzmann equation for a spatially uniform
system has exact stationary power-law solutions. In [3,
4], it was shown by directly calculating the Boltzmann
and Landau collision integrals in kinetic equations that
the power-law distributions of the form sAEf −=
(where s is an exponent and A is a constant, are sta-
tionary solutions for which particle (or energy) fluxes in
phase space are nonzero constants. These particle states
are similar to turbulent Kolmogorov spectra of waves
and depend only on the integral characteristics of the
source and sink [4]. In particular, nonequilibrium spa-
tially uniform systems with a component obeying a
power-law distribution include electron subsystems of
semiconductors exposed to radiation with a photon en-
ergy on the order of the width of the forbidden zone [7]
or electron subsystems in metals that undergo ionization
caused by particles propagating in them [5]. In [1–4],
the exponent s of power-law solutions to the kinetic
Boltzmann equation depended only on the degree of ho-
mogeneity of the particle interaction potential. In those
papers, both the dispersion properties of a plasma with a
power-law electron distribution and the ionization equi-
librium in such nonequilibrium steady states were stud-
ied. In [8, 9], it was shown that plasma oscillations with
a linear dispersion can exist in a plasma with two com-
ponents of the distribution function, equilibrium and
nonequilibrium. These plasma oscillations could be of
importance for many interactions in semiconductor plas-
ma, in particular, for the plasmon mechanism of super-
conductivity [10]. As was mentioned above, steady-state
nonequilibrium distributions (SND) of particles in phase
space play the same role in spatially uniform systems as
Maxwellian distributions in Gibbs’ thermodynamics.
The presence of such great deviations from the expo-
nential dependence should significantly change the ther-
modynamic properties of a system. Note that, over the
last fifteen years, great progress has been achieved in
the thermodynamics of strongly nonequilibrium sys-
tems; the results obtained indicate the existence of non-
Gibbs (power-law) distributions in such systems.
So far, we have considered the formation of an SND
with sources and sinks localized in momentum space. It
should be noted that one often has to deal with systems
in which both the source and the sink are nonlocalized.
_________________________________________________________________________________
172 ВОПРОСЫ АТОМНОЙ НАУКИ И ТЕХНИКИ. 2007. № 2.
Серия: Физика радиационных повреждений и радиационное материаловедение (90), с. 172-181.
mailto:karas@kipt.kharkov.ua
In particular, wake ionization is a source that is not lo-
calized in momentum (energy) space. Moreover, the
source intensity is often insufficient to provide a univer-
sal nonequilibrium distribution throughout the interval
between the source and sink (see [11, 12]). In these cas-
es, it is necessary to resort to numerical simulations.
3. NUMERICAL SIMULATIONS
OF THE FORMATION OF STEADY-STATE
NONEQUILIBRIUM PARTICLE
DISTRIBUTIONS
A specific feature of systems of particles interacting
via the Coulomb potential is that the scattering cross
section increases without bound as the momentum
transferred tends to zero. For gaseous and semiconduc-
tor plasmas with a large Coulomb logarithm ( Λln =
10…15), one can restrict oneself to the expansion of the
integrand in the collision integral in small momenta
transferred (a diffusion approximation) and to represent
the collision integral in the Landau or Fokker–Planck
form [13, 14], which are model representations of the
Boltzmann collision integral. In this model [15–17], the
moments of the exact and model collision integrals co-
incide up to the third-order tensor moment and the
forth-order scalar moment. Conservation laws for ener-
gy and the number of particles, as well as the Boltz-
mann H theorem, are valid. The model collision integral
provides a correct representation of the equations for the
twenty-moment Grad approximation. Finally, the exact
solution to the Landau equation for Maxwellian
molecules ( β = 4) is the exact solution to the Boltz-
mann equation. Below, we will consider long range po-
tentials ( β−∝ rU , with 41 ≤≤ β ), where r is the dis-
tance between the interacting particles), for which a lo-
cal nonequilibrium particle distribution can form (see
[3]). Note that the dynamics of particles interacting via
the Coulomb repulsion potential ( β = 1) can be consid-
ered using kinetic equations in either the Landau or
Fokker–Planck form.
3.1. FORMULATION OF THE PROBLEM
In the case of an isotropic distribution function
),( tf υ , the Landau collision integral is
;)()()()(1
0
2
∂
∂−
∂
∂⋅
∂
∂Γ=
∂
∂ ∫
∞
w
wfffwwfdwQ
t
f υυ
υ
υ
υυυ
( )
( ) ( ) ,
62
44
+⋅+
−⋅++⋅
=
++
ηη
υυ ηη wbwa
Q ( ) ;/4 ββη −= (1)
,0,,0 ≥∞<≤ twυ ( )[ ]22 wwa +−= υυ ;
( )[ ]22 wwb ++= υυ , me /ln4 4 Λ=Γ π ,
where the symmetric kernel Q(v, w) = Q(w, v) in the
case of Coulomb potential has the form Q(v, w) = –
33/2 w− for υ≤w and Q(v, w) = 33/2 υ− for υ≥w .
The equilibrium solution to Eq. (1) is a Maxwellian dis-
tribution function
−= −
2
2
3
2
3exp4
T
TMaxw
V
nf υυ
π
, ,3
m
TkV B
T =
where n is the electron density, Bk is the Boltzmann
constant, m is the electron mass, and T is temperature. If
there are no sinks (so-urces), then the number of parti-
cles and the system energy do not vary over time: The
distribution function ),( tf υ is bounded at 0=υ and
quite rapidly decreases as ∞→t . Below, we use di-
mensionless variables: the velocity in units of the ther-
mal velocity TV and time in units of the electron–elec-
tron relaxation time eeτ , which is
( )Λ= ln/ 423 nemVTeeτ (where e is charge of electron)
in the case of Coulomb interaction. The function ),( tf υ
is normalized so that π4=n , the total energy
( ) 12 −=Ε mtot π ; consequently, in Eq. (1), the constant
Γ is equal to unity.
We consider the formation of a steady-state nonequi-
librium solution in the presence of particle or energy
flows in velocity space using the above modified ver-
sions of the Landau-Fokker–Planck collision integral in
form (1). In this case, the right-hand side of the kinetic
equation is added with the terms accounting for the
presence of a particle (energy) source +S (sink −− S ).
The source (sink) function was modeled by an expo-
nential function with a variable width in momentum
( ){ }2
1exp~ ±±± −− υυαIS ; a −δ function in the
form 2/)(~ υυυδ ±±± −IS ;
( ) ( )tfIS ,~
2 ±
±
±±
−
υ
υ
υυδ
(2)
The flow direction is determined by the positions of
+υ and −υ . Either a Maxwellian distribution or −δ
function was used as an initial distribution. In simula-
tions, we employed a fully conservative implicit differ-
ence scheme [15–17], for which discrete analogues of
conservation laws hold true and which allow one to per-
form long-run calculations without error accumulation.
An infinite velocity interval was replaced with the maxi-
mum interval TV1410 ⋅)...( , in which the distribution
function was set at zero. The initial distribution ( )0υυδ −
was approximated in the following way: the −δ function
was set at zero for all of the velocities except for one point
(usually, 10 =υ ).
Since the problem of relaxation is a kind of test, we
first consider the Cauchy problem for the initial distribu-
tion ( ) ( ) 20 /1 υυδυ −=f . In our calculations, we used
the kinetic equation with either Landau collision integral in
form (1) or the Fokker–Planck one, respectively. When
0=±S , these equations are analytically equivalent and, in
_________________________________________________________________________________
173 ВОПРОСЫ АТОМНОЙ НАУКИ И ТЕХНИКИ. 2007. № 2.
Серия: Физика радиационных повреждений и радиационное материаловедение (90), с. 172-181.
the limit ∞→t , lead to a Maxwellian distribution Maxwf .
Let us now discuss the results of numerical simulations.
3.2. DISCUSSION OF THE SIMULATION
RESULTS
In [15], the formation of a nonequilibrium distribu-
tion function was numerically simulated for the kinetic
equation with either the Landau or Fokker–Planck colli-
sion integral in the presence of energy and particle
flows in momentum space that were sustained by a so-
urce and a sink. For this purpose, the right-hand side of
kinetic equations (1) was supplemented with various
types of sources +S and sinks −S . First, solutions were
obtained for the case where the positions of a source and
a sink in momentum space were matched with the direc-
tion of a flow sustained by collisions. Note that analytic
consideration of equations for the case of a localized
source and sink gives a correct flow direction, namely,
from high to low velocities [3]. It was shown in [15]
that, within the interval between the source and sink, an
SND (of the Kolmogorov kind) of particles is estab-
lished with time. This distribution corresponds to the
presence of an energy flow in momentum space, where-
as beyond this interval, the distribution function is ther-
modynamically equilibrium.When using the Landau
equation, the particle distribution relaxes to an SND by
more than one order of magnitude faster than when the
Fokker–Planck equation is used. As was noted above,
the positions of the source and sink and the direction of
flow in momentum space should be matched with one
another. To make sure once again that this requirement
is important, we performed calculations with the inter-
changed positions of the source and sink in energy
space. It turned out that variations in the flow intensity
by several orders of magnitude did not influence the
equilibrium particle distribution when the source and
sink positions were not matched with the flow direction
[15]. It was shown that the behavior of the SND in most
of the interval between the source and sink does not de-
pend on the degree of the source (sink) localization; this
indicates the local (universal) character of the solution.
It is found also that, for low intensities of the source +I
(sink −I ), a universal nonequilibrium distribution is
formed in the velocity range +≤ υυ . This is due to (i) a
decrease in the cross section for Coulomb scattering
with increasing velocity ( 3~ −υ ) and (ii) the ever-
present flow of energy and particles (due to Coulomb
diffusion) toward the region of the main (“background”)
equilibrium distribution. Consequently, as the source
(sink) intensity increases, a universal nonequilibrium
particle distribution is formed that occupies a progres-
sively larger space between the source and sink. Such
behavior is related to a decrease in the fraction of the
flow transferred to the background plasma. It is worth
noting that the increase in intensity is accompanied by
an increase in the magnitude of the nonequilibrium dis-
tribution function in proportion to the flux magnitude
[3].
Let us examine the form of the distribution function
for power-law interaction potentials with the exponents
41 ≤≤ β . Note that β = 1 corresponds to the Coulomb
interaction potential, β = 2 corresponds to dipole inter-
action, and β = 4 describes the interaction of so-called
Maxwellian molecules. It was shown in paper [15] that,
for all these β values, the exponents of the formed
nonequilibrium power-law distribution functions are
close to one another, which agrees with the results of
[3]. The magnitude of the nonequilibrium part of distri-
bution function decreases with increasing β . These re-
sults are in qualitative agreement with the above analyt-
ic predictions.
4. FORMATION OF THE EDF
IN THE INTERACTION OF RADIATION
AND PARTICLE BEAMS
WITH SOLID-STATE PLASMA
In this section, we consider the conduction and emis-
sion properties of a semiconductor plasma irradiated
with intense particle or laser beams. A comparison of
the characteristic times of ionization and relaxation
shows that, in the case at hand, the steady-state EDF
should be determined mainly by electron–electron colli-
sions [3]. Hence, it can be obtained from the condition
that the Boltzmann collision integral (for a semiconduc-
tor plasma, the Landau or Fokker–Planck collision inte-
gral) be zero.
It follows from the analysis (see [4]) that, for a semi-
conductor plasma in the energy range FF EEE >− , a
power-law distribution with a nonzero flux of energy or
particles in momentum space can be established. This
distribution is formed due both to collisions with elec-
trons whose energy is in the range FF EEE >− and
background (equilibrium) electrons. It was shown in [4]
that a nonequilibrium electron distribution is close to a
universal distribution if the intensity of the flow produ-
ced by the source and sink in momentum space is suffi-
ciently high. Let us consider, as an example, the irradia-
tion of a solid-state plasma with a beam of fast ions
(with velocities higher than the velocities of atomic
electrons) [18] or high-power electromagnetic radiation
with the frequency ω satisfying the condition
Tk B>ω [19]. In both these cases, a great number of
high-energy electrons arise that, in accordance with the
above consideration, form a nonequilibrium steady-state
EDF [3]. When the distribution function is nonequilibri-
um, the emission current density is anomalously high
since the distribution function decreases very slowly
over the inertial interval.
The plasma conductivity is determined by the densi-
ty of current carriers. In the case of a nonequilibrium
EDF, the carrier density in semiconductor plasma is
very high in comparison to the case of an exponentially
decreasing equilibrium EDF. Therefore, when a semi-
conductor plasma is irradiated with intense radiation or
particle beams, an anomaly in the emission and conduc-
tion properties of plasma should be observed. elastic
losses are negligibly small, whereas the inelastic energy
losses, which are usually called ionization loss, are de-
scribed by the Bethe–Bloch formula (see for example
_________________________________________________________________________________
174 ВОПРОСЫ АТОМНОЙ НАУКИ И ТЕХНИКИ. 2007. № 2.
Серия: Физика радиационных повреждений и радиационное материаловедение (90), с. 172-181.
[20]). It follows from this formula that, at high energies,
the ionization loss decreases as 2~ −υ . The introduction
of an extra charge in a quasineutral equilibrium solid-
state plasma leads to the displacement of free electrons
with respect to their equilibrium positions and to the ex-
citation of plasma eigenmodes (plasmons) [21-23].
Thus, the energy lost by an ion due to its deceleration is
transferred to the target’s electrons in two ways: a cer-
tain fraction of the energy is spent on the excitation of
plasmons, while the rest energy is transferred to individ-
ual electrons in collisions (in particular, in collisions
with atoms, which then become ionized) [20-23]. Such a
nonequilibrium external action significantly changes the
distribution function of free electrons [4]. A fraction of
the nonequilibrium electrons that have proper magni-
tudes and momentum directions can escape from the tar-
get; i.e., these electrons can take part in the process of
secondary ion-induced electron emission (SIEE). The
emission proceeds in three stages: (i) origin of nonequi-
librium electrons, (ii) their collisions and motion (diffu-
sion) toward the surface of a solid, and (iii) overcoming
the potential barrier by these electrons and their escape
into vacuum. Such an approach is believed to most com-
prehensively account for the SIEE features and has been
widely used since the Sternglass study [24] (see also
[25,26]). Indeed, such an anomaly was observed, e.g., in
[18, 19]. Supplying additional kinetic energy to a solid-
state plasma results in the ionization of atoms and the
production of a rather large number of free electrons
with energies higher than the equilibrium (thermal) en-
ergy [20]. Under these conditions, nonequilibrium dis-
tributions of free electrons can form [3, 4]. It was shown
in a series of theoretical and experimental studies that,
when a solid-state plasma is irradiated with fast ion
beams, a steady-state nonequilibrium power-law EDF
sEIEf −= 2/1)( α (3)
is formed in the plasma due to the presence of a particle
(energy) flow produced by a source (ionization) and a
sink (electron emission) in momentum space. In Eq. (3),
α is the normalizing factor, I is the particle (energy)
flux, s is an exponent [4, 5], and E is the total electron
energy in a solid ( eUEE F ++= ϕ , where ϕ is the
work function and eU is the energy relative to the elec-
tron energy in vacuum). Power-law distributions are
characterized by a rather large fraction of high energy
electrons. For example, when a Be sample is irradiated
with 4.9-MeV −α particles, the fraction of electrons
with energies higher than pE = 18.9 eV (where pE is
the energy of plasma eigenmodes in beryllium) can ex-
ceed 37% [21]. An integral characteristic of SIEE is the
SIEE coefficient e∆ , often called the electron yield (see
[27]). The electron yield e∆ is defined as the ratio of
the num-ber of knocked-out secondary electrons eN to
the num-ber of incident ions iN . The SIEE coefficient
depends substantially on the energy of incident ions. It
has been shown both theoretically and experimentally
that, for low-Z ions, the electron yield e∆ is proportion-
al to the average specific ionization loss of ion energy in
matter, dxdE / [24, 27, 28]. A much more informative
characteristic of SIEE is the electron energy distribu-
tion. It has been shown experimentally that the energy
spectra of secondary electrons are of power-law charac-
ter [6, 29, 30]. When studying electron emission from
some metals, it was shown that the distribution func-
tions of the electrons knocked out by low-Z ions are
piecewise power-law functions with different exponents
s for different energy ranges [5, 6, 31]. As was shown in
[32], emissivity variations accompanying the irradiation
of a sample with intense charged particle beams can be
efficiently used to create new energy sources. One such
source is a secondary emission radioisotope current
source [33] that converts the energy of −α particles
into electrical energy using the nonequilibrium proper-
ties of the electron distributions. Since the efficiency of
this source is proportional to the difference between the
electron yields of the employed emitter materials ( 2e∆ -
1e∆ ) [33], it is necessary to use an emitter with the
maximum possible 2e∆ value to increase the source ef-
ficiency. At present, the available literature data on the
emission properties of materials irradiated with fast ion
beams mainly refer to metals. Note that no data are
available in the literature on the efficient electron emit-
ters widely used in the photoemission and electronic
techniques. Among the most widely used efficient emit-
ters of secondary electrons are emitters based on Sb/Cs
compounds. Due to the large coefficients of secondary
electron emission (SEE) and photoemission (this is usu-
ally related to the low potential barrier at the boundary
between the sample surface and vacuum), such com-
pounds have been widely used in manufacturing the
photocathodes and dynodes in photomultipliers and oth-
er devices [34]. To illustrate, the SEE coefficient eσ for
Sb/Cs compounds is 3–4 at low energies of primary
0.25 MeV. The cathode used as a target was a Sb/Cs
layer deposited on a massive nickel substrate. The layer
thickness was less than the mean free path of the inci-
dent ions in Sb/Cs. A 10-mm-diameter target fixed in a
copper mount was installed on a movable holder. The
ion beam collimated by a system of diaphragms was in-
cident onto the target and caused SIEE from its surface.
The target plane was normal to the beam axis. The beam
diameter on the target surface was 3 mm, and the ion
current density was no higher than 30 µA/cm2. The
chamber was evacuated with an NMD-0.4-1 magnetic-
discharge pump and an NVPR-16D backing pump with
a liquid nitrogen trap. In all our electrons (Ee ~ 100 eV)
and reaches its maximum value of = 8…10 at Ee =
500...600 eV [34]. Such large SEE coefficients are pre-
sumably explained not only by the low work function
for this material but also the formation of a power-law
nonequilibrium distribution function.
5. EXPERIMENT
This section is devoted to our experimental studies
aimed at revealing the main features of the EDFs for-
med during the irradiation of a Sb/Cs cathode and cer-
tain semiconductors with a beam of fast low-Z ions.
_________________________________________________________________________________
175 ВОПРОСЫ АТОМНОЙ НАУКИ И ТЕХНИКИ. 2007. № 2.
Серия: Физика радиационных повреждений и радиационное материаловедение (90), с. 172-181.
5.1. EXPERIMENTAL SETUP
An electrostatic Van de Graaf generator used as a
so-urce of primary particles provided beams of +H or
+He ions. Energy spectra of SIEE electrons were mea-
sured for +H beams with ion energies from 1.00 to 2.25
MeV and +He beams with ion energies from 1.75 to
2.25 MeV. The ion energy was varied with a step of
0.25 MeV. The cathode used as a target was a Sb/Cs
layer deposited on a massive nickel substrate. The layer
thickness was less than the mean free path of the inci-
dent ions in Sb/Cs. A 10-mm-diameter target fixed in a
copper mount was installed on a movable holder. The
ion beam collimated by a system of diaphragms was in-
cident onto the target and caused SIEE from its surface.
The target plane was normal to the beam axis. The beam
diameter on the target surface was 3 mm, and the ion
current density was no higher than 30 µA/cm2 . The
chamber was evacuated with an NMD- 0.4-1 magnetic-
discharge pump and an NVPR-16D backing pump with
a liquid nitrogen trap. In all our experiments, the residu-
al gas pressure in the vacuum chamber was no higher
than 10-6 torr. The electrons emitted from the target sur-
face were intercepted by a spherical collector consisting
of two 100-mm-radius hemispheres. The target and the
holder were set inside the collector. The gap between
the hemispheres was 15 mm. The diameter of the en-
trance window of the hemisphere was 10 mm. Besides
the collector current, we also measured the target cur-
rent tI , which was the sum of the beam ion current bI
and the current of the secondary electrons that reached
the collector: bCt III += . The measured CI and tI
currents amplified by electrometric amplifiers were ap-
plied to a PC through an analog-to-digital converter . To
calibrate the measurement system, a Faraday cup was
set behind the rear hemisphere. The Faraday cup al-
lowed us to directly measure the ion beam current FcI
when the target was removed from the beam path. The
diameter and length of the Faraday cup were 20 and 130
mm, respectively. The current from the Faraday cup
FcI was measured with an F303 current meter. The
SIEE coefficient was determined by the formula
( )./ CTCe III −=∆ (4)
By measuring the energy spectrum of SIEE electrons
with a spherical analyzer and assuming that emission is
produced by a point source, one can reconstruct the
EDF inside the target [21]. When the EDF is powerlaw
function (3), the derivative of the emission current with
respect to the electron energy, )(/ eUddI , can be writ-
ten as
,)(
)(
1s
F eUEB
eUd
dI +−++= ϕ (5)
where B is a constant. Hence, on a logarithmic scale, de-
pendence (5) is a straight line with a slope equal to –s +
1. The energy distributions of the secondary emission
electrons were measured with a spherical collector oper-
ating in the energy-analyzer regime with a retarding
field varied in the range 0...100 V with a step of 1 V.
The retarding electric potential was applied between
the target and two hemispheres. Since the radius of the
energy analyzer significantly exceeded the target size,
the field distribution was close to spherical. A 5-mm-di-
ameter ceramic tube with an outer surface covered with
a resistive layer served as a target holder. The specific
resistance of the layer Rc was varied nonlinearly along
the tube so that the holder potential did not disturb the
field inside the energy analyzer. One end of the resistive
layer was in contact with the target, whereas its other
end was grounded. The retarding potential was applied
to the target from a saw-tooth generator controlled by a
PC. Thus, the current flowing along the resistive layer
produced the needed potential distribution along the
holder. In experiments, the secondary electrons moved
along radial trajectories and reached the collector. When
the retarding voltage was applied to the target, only the
electrons whose energy was high enough to get through
the retarding field reached the collector. The computer
software for controlling the experiment allowed the
gathering of a 7-s-long time sample consisting of 100
measurements of the electron emission current for each
value of the retarding field. These 100 experimental
points were then averaged, and the resultant value of the
electron current was stored in the PC memory. By dif-
ferentiating the measured dependence of the collector
current on the retarding voltage (the so-called retarding
curves), one can deduce the energy spectrum of SIEE
electrons and then reconstruct the EDF. The exponents s
of power-law EDFs wereevaluated as follows. First, the
time samples of the elec
tron emission current were processed and the delay
curves were differentiated. Then, the dependences of
)(/ eUddI on the total electron energy eUEF ++ ϕ in
the compound under study, plotted on a logarithmic
scale, were approximated by straight lines. According to
formula (5), the slopes of these straight lines are equal
to –s + 1.
5.2. EXPERIMENTAL RESULTS
AND DISCUSSION
The measurements of the energy spectrum of SIEE
electrons show that, over the entire ion energy range un-
der study, the nonequilibrium EDF formed in the plas-
ma of a Sb/Cs cathode is a power-law function. A typi-
cal nonequilibrium EDF obtained for a sample bom-
barded with 1.75-MeV +He ions is shown in Fig. 1.
_________________________________________________________________________________
176 ВОПРОСЫ АТОМНОЙ НАУКИ И ТЕХНИКИ. 2007. № 2.
Серия: Физика радиационных повреждений и радиационное материаловедение (90), с. 172-181.
Fig. 1. Typical nonequilibrium EDF obtained for a
Sb/Cs sample bombarded with 1.75-MeV +He ions
The experimental points are quite well fit by two
straight lines corresponding to two different exponents,
1s and 2s , in the energy ranges of 5...30 eV and
30...100 eV, respectively. These exponents for the two
parts of the EDF in the above energy ranges measured
as functions of the energy of the incident +H and +He
ions. In our opinion, the exponent of a power-law distri-
bution function of secondary electrons could depend on
the energy (specific ionization loss) of fast ions. It
seems that it is the specific ionization loss that deter-
mines the intensity of the source of extra particles in
momentum space. It was shown in [4, 35] that, under
certain conditions, the exponent is independent of the
structure of the source and sink. In this case, it can be
said to be a universal power-law distribution function
with an exponent equal to –5/4 [35]. In our previous ex-
periments with a +He beam and thin metal films, in
which the exponents s were measured, it was shown that
the absolute value of the exponent 1s of a powerlaw dis-
tribution function in the first energy range correspond-
ing to slow electrons (E < 35 eV) decreases with in-
creasing specific ionization loss of ions in a substance
[31]. In [30], it was pointed out that the fraction of fast
electron increases with increasing energy of the incident
ions. It is shown that the exponents 1s for different inci-
dent ions and, accordingly, different specific ionization
losses in a Sb/Cs sample differ insignificantly, although,
for protons, the exponent increases with ion energy and
decreases with specific ionization loss. No such depen-
dence was observed for helium ions. It should be noted
that variations in the exponent do not exceed 10%; to
deduce the exact dependence of the exponent on the en-
ergy loss requires additional study. Fig. 2 shows the de-
pendence of the electron yield e∆ on the energy of the
incident +H and +He ions for a Sb/Cs cathode.
Fig. 2. Dependence of the electron yield e∆ on the ener-
gy of the incident +H and +He ions
It can be seen that, for the Sb/Cs compound under
study, the electron yield exceeds that for some metals
[35]. The reason could be as follows. As was mentioned
above, a fraction of the nonequilibrium electrons pro-
duced in a solid-state plasma under bombardment with a
beam of fast charged particles diffuse toward the surface
and escape into vacuum. Electron emission proceeds
from the surface layer, whose thickness is much less
than the depth to which the ions penetrate into the target
and is determined by the features of the electron motion
toward the surface. In metals, the generated electrons,
while diffusing toward the surface, interact mainly with
conduction electrons. This interaction may proceed via
pair collisions and collective effects—the excitation of
plasmons. Due to the large density of conduction elec-
trons in metals, the probability of electron–electron in-
teractions and, accordingly, the effective escape depth
of secondary electrons are small. In semiconductors, the
density of conduction electrons is low; hence, the es-
cape depth of secondary electrons can be quite large.
Since Sb/Cs compounds possess semiconductor proper-
ties [34], the escape depth of nonequilibrium electrons
can be larger than in metals. The higher (compared to
metals) value of the SIEE coefficient can be, to a certain
extent, explained by this factor. Sb/Cs compounds have
low work functions [36]. The relatively low potential
barrier at the boundary between such a compound and
vacuum may lead to an increase in the fraction of
nonequilibrium electrons leaving the solid. The work
function determines the cutoff energy for the nonequi-
librium power-law EDF formed in a solid-state plasma.
Since the exponent within the first energy interval is
fairly high and [6, 29–31]), even a slight decrease in the
work function leads to a significant increase in the SIEE
coefficient. Our experiments have shown that, for all of
the energies of +H and +He ions, the EDFs formed in
a semiconductor plasma are power-law functions. Fig. 3
shows (on a double logarithmic scale) a typical
nonequilibrium EDF formed in a GaAs sample bom-
barded with 1.25-MeV +He ions.
_________________________________________________________________________________
177 ВОПРОСЫ АТОМНОЙ НАУКИ И ТЕХНИКИ. 2007. № 2.
Серия: Физика радиационных повреждений и радиационное материаловедение (90), с. 172-181.
Fig. 3. Typical nonequilibrium EDF formed in a GaAs
sample bombarded with 1.25-MeV +He ions
The experimental points can be well fit by a single
straight line corresponding to the exponent s = 2.9
throughout the entire range of electron energies in vacu-
um (5…100 eV). It was shown in our early experiments
[12] that the EDFs formed in metal plasmas are piece-
wise powerlaw functions with different exponents in
different energy ranges. At least two such ranges were
revealed. In our opinion, the piecewise power-law shape
of the EDFs in experiments with metals, namely, the
presence of two characteristic energy ranges, could be
related to two different mechanisms for energy transfer
from a fast incident ion to the electron subsystem of a
solid. These mechanisms are (i) the excitation of collec-
tive plasma oscillations with a subsequent ionization in
the electric field of these oscillations and (ii) inelastic
collisions, resulting in the direct ionization of atoms.
The energy of the electrons produced due to ionization
via plasma oscillations cannot exceed the plasmon ener-
gy pE in a substance. In semiconductors, the energy of
plasmons related to conduction electrons is much lower
than the ionization potential of atoms. For this reason,
the distribution function in a semiconductor plasma is
characterized by one power-law segment throughout the
entire electron energy range under study. The measure-
ments of the energy spectrum of SIEE electrons have
shown that, for all of the ion energies under study, the
nonequilibrium EDFs formed in plasma are power-law
in character. As was mentioned above, the main integral
characteristic of SIEE is the electron yield e∆ . It is
shown that in germanium the measured values of e∆
plotted versus the ionization loss dxdE / for +He ions
are well fitted by a straight line; i.e., these quantities are
indeed proportional to one another.
6. APPLICATIONS
The solution of a lot of scientific and engineering
tasks requires use of autonomous source of the power
supplies of various devices. Those sources must satisfy
the such requirements: long service life; reliability; big
specific energy capacity; compact; ecology; explosion-
proof. Most commonly used are the chemical elements
of a feeds using as a primary source an energy of chem-
ical reactions. Historically such elements were first and,
for today most developed by the engineers. However, it
is necessary to notice, that they have a rather insignific-
ant specific power capacity hardly exceeding 0,1 KW×
hour/kg. Most perfect of them are lithium batteries but
they are very explosive.
6.1. THERMAL AND NONTHERMAL
RADIOISOTOPE CONVERTERS
A much higher power capacity and term of work
have the radioisotope sources of the power supplies, i.e.
devices,in which an energy of radioactive decay con-
verts in electrical one. The radioisotope sources of elec-
tricity have a general characteristics significantly better
than analogous ones of chemical batteries. They are
more preferable for the all-round utilization.
Now there is a significant amount of radioisotope
sources of an electricity based on various physical prin-
ciples. They are divided on two large classes:
- thermal radioisotope converters;
- nonthermal.
Nonthermal radioisotope converters manufacture an
electrical energy without application of a thermal cycle.
The sources with immediate gathering of electrical
charges (atomic batteries) are most commonly used
among such sources of a current. In these batteries the
electrical potency is elected at the expense of gathering
on a collector particles, which isotope emitted. A col-
lector and emitter in similar devices are isolated of elec-
tric from each other by vacuum gap or dielectric. Such
converter is a source of a current. Its voltage is determ-
ined by a resistance of loading. A residual of potentials
between the anode and cathode can be equal to an en-
ergy of particles. The large interior resistance of a
source, connecting with loading causes reduction of
voltage and, hence, increase of the part of the charged
particles energy, which goes to heat of a collector. In
outcome efficiency of the source is essentially reduced.
It is possible to specify some characteristic demerits re-
ducing service life of such source:
- necessity to have an additional source of voltage
for suppression of a second electronic emission from a
collector;
- the presence of δ-electrons in the α-particles
stream reduces a transferable current essentially.
Moreover, the high working voltage (about hundreds
kilovolt) of atomic batteries requires application of insu-
lators and vacuum conditions of very high level and
hampers use of these devices.
The devices using a contact residual of potentials
between the cathode and the anode are ones of varieties
of atomic batteries. The space between the anode and
the cathode is filled by gas, which is ionized by a radi-
ation of a radioisotope. The created charged particles
are accumulated on the cathode and the anode. Those
materials have various work function. The residual of
potentials, in this case, depends on work function of
used electrode materials and has magnitude about one
volt. First of all, the low efficiency of such device is due
to a small cross-section of gas atom ionization by the
char-ged particles. Insignificant increasing of efficiency
_________________________________________________________________________________
178 ВОПРОСЫ АТОМНОЙ НАУКИ И ТЕХНИКИ. 2007. № 2.
Серия: Физика радиационных повреждений и радиационное материаловедение (90), с. 172-181.
is possible by use of a mixture of radioactive and rare
gases at pressure some atmospheres. However, the in-
creased pressure in atomic battery, filled by high toxic
gas, creates hazard for the maintenence personnel and
equipment.
One of modes of transformation of an β-particles en-
ergy in electrical power is the generation of an electrical
current in a semiconductor mesh due to formation of
electron-hole pairs and their separation in p-n junction
area. The characteristic value of a current Is in this pro-
cess is determined as:
βmIeRlI s == ,
where R is factor of generation of a charge; l - diffusion
length; m - factor of multiplication of a current; Iβ - cur-
rent of a β-radiation. The maximum value of voltage
can be received from the following expression:
+= 1ln
0I
I
e
Tk
V sB ,
where 0I is inverse current of saturation. From these
expressions it is visible, that the characteristic value of
voltage on one semiconductor mesh is compared with
kT/e, i.e. rather small magnitude (less than one volt).
The weak place of such sources is p-n junction destroy-
ing under attack of a hard radiation. A long irradiation
of p-n junction by the β-particles causes the production
of radiation damages. If the life time of p-n junction in
the usual elements (transistors, chips etc.) makes up
some tens thousand hours, the life time of p-n junction
in the β-particles irradiation conditions will be signific-
antly less.
The most developed thermal converters are the ra-
dioisotope thermoelectric sources of the electric power.
In these devices the nuclear decay energy heats one
thermoelectric junction, whilst, another one is at tem-
perature of a refrigerator. The potential difference
beetwen thermoelectric junctions is arisen through ther-
moelectric effect. The modern thermoelectric converters
are made from semiconductor materials which have
transformation coefficient significantly more than
metals.
There are many various designs of thermoelectric
converters. The constructions of these devices have
thermocouples, which consist of some semiconductor
layers divided by insulators. It is necessary to notice,
that in conditions of high temperatures (about 1000 K)
and hard radiation insulation materials quickly will be
failed, causing the electrical break-downs and leakage .
However, the basic reason restricting service life of
such converter is the formation of many radiation dam-
ages in the semiconductor and ,consequence, modifica-
tion of the basic characteristics of the materials.
In thermoemission devices the transformation of the
nuclear particles energy in electrical one occurs through
thermoemission, which take place under heating of the
cathode by partiсles emitting from radioisotope. During
this, thermoemission current is an exponential function
of the ratio of the work function of the cathode materi-
al to its temperature and, therefore, the application as
high temperatures as materials with small work function
causes the increase of the efficiency of the converter.
The basic difficulty in using of these devices is destruct-
ive influence of temperatures about 1000...2000 K at
materials. Sometimes, cathode-anode space is filled by
gas, mostly by caesium (Cs), in order to reduce the work
function of the emitter. The presence of caesium steams
causes the formation of cathode film and reduction of
the work function (up to 1,81 eV, see for example, [6]).
At the same time, the constant presence of caesium re-
duces service life of such sources essentially and creates
problems of making operation safety available to main-
tenance personnel.
6.2. RADIOISOTOPE SECONDARY EMMISION
SOURCE OF CURRENT
A new type of radioisotope source of current based
on others physical principles was proposed in [37]. It is
well known that passing of fast ions through substance
initiates ionization of medium atoms. The some amount
of electrons break loose from atoms in result of ion ac-
tions. It may passed to vacuum if it have suitable value
and direction of momentum, i.e. secondary electron
emission induced by ions takes place. It was shown
earlier that in such situation it was possible to form
steady-state nonequlibrium electrons distribution with
power dependence of electrons energy. Based on the
studies the results, we proposed the radioisotope source
of the secondary-emission current [37]. The source con-
sists of a radioisotope layer placed inside a vacuum con-
tainer. Metallic emitters are positioned on each side of
the layer. The emitter thickness is less than the mean
path of the charged particle emitted by the radioisotope
in the emitter material. Each emitter consists of alternat-
ing layers of two different metals with different second-
ary-emission coefficients. The layers are electrically isol-
ated by vacuum gaps. A high efficiency of the radioiso-
tope current source of this type is determined by the fact
that the secondary electrons are produced along the entire
path of the charged particle in the metal; i.e., the charged
particle energy is directly transformed into electron en-
ergy; the amount and average energy of these electrons are
much above those for the thermal electron emission.
It was stated previously that the use of heavy particles
in electric-current sources leads to a high efficiency of
production of secondary electrons due to negligibly small
scattering of these particles (i.e., they move along almost
straight trajectories). The secondary-electron distribution
function is nonequilibrium; the average energy of the
emitted secondary electrons exceeds 10 eV. The source
efficiency increases as a result of an increase in the sec-
ondary emission under the action of δ-electrons. As a res-
ult, such a current source has high energetic parameters
that are proportional to the number of the emitter layers.
Since the total thickness of the emitter does not exceed
the mean path of the charged particle emitted by a ra-
dioisotope, the number of layers and, consequently, the
emitter efficiency can be increased only by making each
layer thinner. However, as the layer thickness decreases,
_________________________________________________________________________________
179 ВОПРОСЫ АТОМНОЙ НАУКИ И ТЕХНИКИ. 2007. № 2.
Серия: Физика радиационных повреждений и радиационное материаловедение (90), с. 172-181.
the construction loses the rigidity. This can break the elec-
tric insulation between layers. For example, if the layers
are bent, the vacuum gaps between them become narrow-
er.
We have also proposed the secondary-emission cur-
rent source with thinner emitter layers and, at the same
time, with a sufficiently high rigidity of the emitter.
This problem is solved by developing a radioisotope
source of the secondary-emission current in which a ra-
dioisotope and emitter with a thickness less than the
mean path of the charged particle emitted by the ra-
dioisotope are placed inside the hermetically sealed
case. The emitter consists of alternating electrically in-
sulated layers made of two different materials with dif-
ferent coefficients of secondary electron emission.
Dielectric grids are located between the emitter layers;
the grids serve to insulate the layers electrically from
each other and to improve the rigidity of the emitter
construction. The thickness of the dielectric grid is lar-
ger than the thickness of the emitter layers. To obtain a
better effect, the dielectric grid must be deposited dir-
ectly on one of the emitter layer. One of the version uses
the ceramic grid, and the other one uses the plastic grid.
In order to improve the efficiency of the proposed
current source, one of the alternating emitter layers can
be made of a metal, and the other one of the semicon-
ductor material with a secondary-emission coefficient
exceeding that of the metal layer. It is desirable to made
the semiconductor layer from silicon or gallium arsen-
ide. The energetic parameters of the proposed source
can be considerably improved by placing an additional
radioisotope inside the source case, so that the emitter
would be between the additional and the main radioiso-
topes, and the flows of particles emitted from radioiso-
topes be directed in opposite directions. By using all the
technical solutions presented above, it is possible to cre-
ate a radioisotope source of the secondary-emission cur-
rent with a substantially better energetic parameters and
smaller mass and sizes.
The new type of radioisotope source of current were
suggested on the basis of carried out investigations [38-
40]. Our source has considerably more specific energy
capacity than existing ones. Use of this source is most
advantageously there where it is necessary to apply
devices working without human intervention for a long
time. Above all, our source can be used very perspective
in such branches as: medicine and space researches.
This source can be very useful in the long space flights,
especially on the automatic station. The employment of
our source for the cardiastimulator supply is more
preferable than thermal radioisotope one. Our battery
can maintain it for a long time of operating and has not
high work temperatures as thermoelectric and thermion-
ic radioisotope sources. The wide perspectives are open
for using it for design of artificial heart because this
source almost satisfies all present requirements. It is ne-
cessary to note, other possibilities for using of our
source. It can be used as electricity source for devices in
hard accessible places (navigation buoys, magnitometric
station etc.). Moreover, it is advantageous to use our
source in the system of protection and obtaining of in-
formation.
7. CONCLUSIONS
In this paper, we have shown that the presence of
sources and sinks in a spatially uniform system leads to
the formation of SNDs with power-law tails. Numerical
simulations of the formation of SNDs show that, for
particles with Coulomb interaction, an SND is formed
between the source and sink. Starting from a certain in-
tensity of the source (sink), the powerlaw distribution
function has the same exponent; i.e., it is universal. A
radical change in the EEDF under nonequilibrium con-
ditions leads to an anomalous increase in the conductivi-
ty and emissivity of the substance. The experimental
data on the EEDFs formed in the solid-state plasma of a
Sb/Cs cathode irradiated with a beam of fast low-Z ions
are presented. In all of the experiments with +H and
+He ions, the nonequilibrium EEDFs in the energy
range from 5 to 100 eV are found to have a piecewise
power-law shape with different exponents in the energy
ranges of 5...30 and 30...100 eV. The power exponents
are expected to depend on the energy (specific ioniza-
tion loss) of fast ions, and this was indeed observed for
protons in the former energy range. The experimental
studies of the formation of nonequilibrium electron dis-
tributions in a semiconductor plasma exposed to ion
beams have shown that EEDFs have power-law asymp-
totes with one exponent. This is related to the low ener-
gy of the plasma oscillations carried by the conduction
electrons.
REFERENCES
1. A.V. Kats, V.M. Kontorovich, S.S. Moiseev and
V.E. Novikov. Preprint No. 42 (Institute of Radio-
electronics, Academy of Sciences of the Ukr. SSR,
Kharkov, 1974.
2. A.V. Kats, V.M. Kontorovich, S.S. Moiseev, and
V.E. Novikov //Zh. Eksp. Teor. Fiz. 1976, v. 71,
p. 177 [Sov. Phys .JETP. 1976, v. 44, p. 93].
3. V.I. Karas’, S.S. Moiseev and V.E. Novikov //Pis’-
ma Zh. Eksp. Teor. Fiz. 1975, v. 21, p. 525 [JETP
Lett. 1975, v. 21, p. 245.]
4. V.I. Karas’, S.S. Moiseev and V.E. Novikov //Zh.
Eksp. Teor. Fiz. 1976, v. 71, p. 1421 [Sov. Phys.
JETP. 1976, v. 44, p.744].
5. E.N. Batrakin, I.I. Zalyubovskiy, V.I. Karas’ et al.
//Zh. Eksp. Teor. Fiz. 1985, v. 89, p. 1098 [Sov.
Phys. JETP. 1985, v. 62, p. 633].
6. E.N. Batrakin, I.I. Zalyubovskioe, V.I. Karas’ et al.
//Poverkhnost. 1986. N 12, p. 82.
7. V.I. Karas’, S.I. Kononenko and V.I. Muratov //Vo-
pr. At. Nauki Tekh., Ser.: Yad. Fiz. Issled. 2001, v. 1,
71.
8. V.E. Novikov, A.V. Tur and V.V. Yanovskiy
//Problems of Theoretical Physics. Kiev: «Naukova
dumka», 1986.
9. V.E. Novikov, S.S. Moiseev and V.P. Seminozhen-
ko // Fiz. Tekh. Poluprovodn. (Leningrad). 1980, v.
_________________________________________________________________________________
180 ВОПРОСЫ АТОМНОЙ НАУКИ И ТЕХНИКИ. 2007. № 2.
Серия: Физика радиационных повреждений и радиационное материаловедение (90), с. 172-181.
14, p. 402 [Sov. Phys. Semicond. 1980, v. 14,
p. 236].
10. V.I. Karas’, V.E. Novikov, S.S. Moiseev and
V.P. Seminozhenko //Fiz. Nizk. Temp. 1977, v. 36,
p. 695 [Sov. J. Low Temp. Phys. 1977, v. 36, p. 336].
11. A.V. Bobylev, I.F. Potapenko, and V.A. Chuyanov.
//Zh. Vychisl. Mat. Mat. Fiz. 1980, v. 20, p. 993.
12. V.M. Balebanov, V.I. Karas’, I.V. Karas’ et al. //Fiz.
Plazmy. 1998, v. 24, p. 789 [Plasma Phys. Rep.
1998, v. 24, p.732].
13. B.A. Trubnikov //Reviews of Plasma Physics, Ed.
By M.A. Leontovich (Gosatomizdat, M., 1963; Con-
sultants Bureau, New York, 1966), V. 1.
14. V.P. Silin. Introduction to the Kinetic Theory of Gas
M.: «Nauka», 1971.
15. V.I. Karas’ and I.F. Potapenko //Fiz. Plazmy. 2002,
v. 28, p.908-917 [Plasma Phys. Rep. 2002, v. 28,
p. 837-846].
16. S.I. Kononenko, V.M. Balebanov, V.I. Karas` et al.
//Fiz. Plazmy. 2004, v. 30, p. 722–738 [Plasma
Phys. Rep. 2004, v. 30, p.671–686]
17. I.F. Potapenko, A. V. Bobylev, C. A. Azevedo and
A.S. Assis //Phys. Rev. E. 1997, v. 56, p. 7159.
18. I.F. Potapenko and V.A. Chuyanov //Zh. Vychisl.
Mat. Mat. Fiz. 1979, v. 19, p. 458.
19. A.S. Asseevskaya, E.B. Ivkin and B.G. Kolomi-ets
//Pis’ma Zh. Tekh. Fiz. 1976, v. 2, p. 116 [Sov.
Tech. Phys. Lett. 1976, v. 2, p. 44].
20. S.I. Anisimov, Ya.A. Imas, G.S. Romanov and
Yu.V. Khodyko. The Effect of High-Power Radia-
tion on Metals. M.: «Nauka», 1970.
21. N.P. Kalashnikov, V.S. Remizovich, and M. I.
Ryazanov. Collisions of Fast Charged Particles in
Solids. Moscow: «Atomizdat», 1980.
22. V.P. Zhurenko, S.I. Kononenko, V.I. Karas’ and
V.I. Muratov //Fiz. Plazmy. 2003, v. 29, p. 150
[Plasma Phys. Rep. 2003, v. 29, p. 130].
23. Yu.V. Gott, Particle Interaction with Substance in
Plasma Studies M.: «Atomizdat», 1978.
24. M.C. Steele and B. Vural. Wave Interactions in Sol-
id State Plasmas (McGraw-Hill, New York, 1969;
M.: «Atomizdat», 1973.
25. E.J. Sternglass //Phys. Rev. 1957, v. 108, p. 1.
26. H. Rothard, C. Caraby, A. Cassimi et al. //Phys. Rev.
A. 1995, v. 51, p. 3066.
27. B.A. Brusilovskiy. Kinetic Ion–Electron Emission
M.: «Energoatomizdat», 1990.
28. D. Hasselkamp, K. G. Lang, A. Scharmann et al.
//Nucl. Instrum. Methods Phys. Res. B. 1981, v. 180,
p. 349.
29. J. Schou //Phys. Rev. B. 1980, v. 22, p. 2141.
30. W. Meckbach, G. Braunstein and N. Arista //J.
Phys. B. 1975, v. 8, p. L344.
31. D. Hasselkamp, S. Hippler, and A. Scharmann
//Nucl. Instrum. Methods Phys. Res. 1987, v. B 18,
p. 561.
32. S. I. Kononenko //Dopovidi NANU. 2001, v. 1,
p. 87.
33. V. I. Karas’ and S. S. Moiseev //Ukr. Fiz. Zh. 1979,
v. 24, p. 1724.
34. V.M. Balebanov, S.S. Moiseev, V.I. Karas’ et al.
//At. Energ. 1998, v. 84, p. 398.
35. N.A. Soboleva and A.E. Melamid. Photoelectronic
Devices. M.: «Vysshaya shkola», 1974.
36. V.I. Karas’, S.S. Moiseev, and A. P. Shuklin //Ukr.
Fiz. Zh. 1980, v. 25, p. 820.
37. V. S. Fomenko and I. A. Podchernyaeva. Emission
andAdsorption Properties of Substances and Mate-
rials. M.: «Atomizdat», 1975.
38. V.I. Karas’, S.I. Kononenko, V.I. Muratov,
S.S. Moiseev. Secondary emission radioisotope
source of current USSR //Inventor's Certificate no.
1737559, class H01J45/00, from December 19,
1989.
39. V.M. Balebanov, V.I. Karas’, S.I. Kononenko,
V.I. Muratov, S.S. Moiseev, V.N. Pokrovskiy,
V.E. Storizhko. Secondary emission radioisotope
source of current //Russia Inventor’s Certificate
N1737559, 1992.
40. V.M. Balebanov, V.I. Karas’, S.I. Kononenko,
V.I. Muratov, S.S. Moiseev. Secondary emission ra-
dioisotope source of current //Patent of Russia
N2050625, 1995.
41. V.M. Balebanov, V.I. Karas’, S.I. Kononenko,
V.I. Muratov, S.S. Moiseev. Secondary emission ra-
dioisotope source of current /Patent of Russia,
N2054742.
42. V.M. Balebanov, V.I. Karas’, S.I. Kononenko,
V.I. Muratov, S.S. Moiseev. Multilayers emitter for
secondary emission radioisotope source of current
/Patent of Russia. N2050626, 1995.
РАДИАЦИОННАЯ ЭЛЕКТРОНИКА
В.И. Карась
Обзор работ по формированию неравновесных функций распределения электронов при наличии источника и стока в
импульсном пространстве. Рассмотрены как аналитические исследования, так и численное моделирование нелинейных
интегралов столкновений Больцмана и Ландау-Фоккера–Планка. Приведены результаты экспериментальных исследова-
ний формирования неравновесных функций распределения электронов в твердотельной плазме при облучении ее пото-
ками электромагнитного излучения или заряженных частиц. Описан оригинальный вторично–эмиссионный радиоизо-
топный источник тока, основанный на неравновесных распределениях электронов.
_________________________________________________________________________________
181 ВОПРОСЫ АТОМНОЙ НАУКИ И ТЕХНИКИ. 2007. № 2.
Серия: Физика радиационных повреждений и радиационное материаловедение (90), с. 172-181.
РАДІАЦІЙНА ЕЛЕКТРОНІКА
В.І. Карась
Огляд робіт по формуванню нерівноважних функцій розподілу електронів дії джерела та стоку у імпульсному про-
сторі. Розглянуті як аналітичні дослідження, так і чисельне моделювання нелінійних інтегралів зіткнень Больцмана та
Ландау-Фоккера–Планка. Наведені результати експериментальних досліджень формування нерівноважних функцій роз-
поділу електронів у твердотільній плазмі при її опромінюванні потоками електромагнітного випромінювання або заря-
джених частинок. Описане оригінальне вторинно–емісійне радіоізотопне джерело струму, основане на нерівноважних
розподілах електронів.
_________________________________________________________________________________
182 ВОПРОСЫ АТОМНОЙ НАУКИ И ТЕХНИКИ. 2007. № 2.
Серия: Физика радиационных повреждений и радиационное материаловедение (90), с. 172-181.
|