Transition radiation of the modulated electron beam in dusty plasma
Transition radiation of the modulated electron beam from the accidental inhomogeneities caused by the dust particles is calculated. This radioemission is proposed for the dust particles’ diagnostics. Numerical estimations show that the magnitude of this radioemission is much higher than thermal radi...
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Національний науковий центр «Харківський фізико-технічний інститут» НАН України
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| Цитувати: | Transition radiation of the modulated electron beam in dusty plasma / I.O. Anisimov, Eu.V. Martysh, I.M. Voronov // Вопросы атомной науки и техники. — 2002. — № 4. — С. 135-137. — Бібліогр.: 14 назв. — англ. |
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Anisimov, I.O. Martysh, Eu.V. Voronov, I.M. 2015-04-14T17:20:22Z 2015-04-14T17:20:22Z 2002 Transition radiation of the modulated electron beam in dusty plasma / I.O. Anisimov, Eu.V. Martysh, I.M. Voronov // Вопросы атомной науки и техники. — 2002. — № 4. — С. 135-137. — Бібліогр.: 14 назв. — англ. 1562-6016 PACS: 52.27.Lw https://nasplib.isofts.kiev.ua/handle/123456789/80299 Transition radiation of the modulated electron beam from the accidental inhomogeneities caused by the dust particles is calculated. This radioemission is proposed for the dust particles’ diagnostics. Numerical estimations show that the magnitude of this radioemission is much higher than thermal radioemission of the plasma core. en Національний науковий центр «Харківський фізико-технічний інститут» НАН України Вопросы атомной науки и техники Plasma electronics Transition radiation of the modulated electron beam in dusty plasma Article published earlier |
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Transition radiation of the modulated electron beam in dusty plasma |
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Transition radiation of the modulated electron beam in dusty plasma Anisimov, I.O. Martysh, Eu.V. Voronov, I.M. Plasma electronics |
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Transition radiation of the modulated electron beam in dusty plasma |
| title_full |
Transition radiation of the modulated electron beam in dusty plasma |
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Transition radiation of the modulated electron beam in dusty plasma |
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Transition radiation of the modulated electron beam in dusty plasma |
| title_sort |
transition radiation of the modulated electron beam in dusty plasma |
| author |
Anisimov, I.O. Martysh, Eu.V. Voronov, I.M. |
| author_facet |
Anisimov, I.O. Martysh, Eu.V. Voronov, I.M. |
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Plasma electronics |
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Plasma electronics |
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2002 |
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English |
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Вопросы атомной науки и техники |
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Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
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Article |
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Transition radiation of the modulated electron beam from the accidental inhomogeneities caused by the dust particles is calculated. This radioemission is proposed for the dust particles’ diagnostics. Numerical estimations show that the magnitude of this radioemission is much higher than thermal radioemission of the plasma core.
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1562-6016 |
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https://nasplib.isofts.kiev.ua/handle/123456789/80299 |
| citation_txt |
Transition radiation of the modulated electron beam in dusty plasma / I.O. Anisimov, Eu.V. Martysh, I.M. Voronov // Вопросы атомной науки и техники. — 2002. — № 4. — С. 135-137. — Бібліогр.: 14 назв. — англ. |
| work_keys_str_mv |
AT anisimovio transitionradiationofthemodulatedelectronbeamindustyplasma AT martysheuv transitionradiationofthemodulatedelectronbeamindustyplasma AT voronovim transitionradiationofthemodulatedelectronbeamindustyplasma |
| first_indexed |
2025-11-25T21:12:25Z |
| last_indexed |
2025-11-25T21:12:25Z |
| _version_ |
1850553347329753088 |
| fulltext |
TRANSITION RADIATION OF THE MODULATED ELECTRON BEAM
IN DUSTY PLASMA
I.O.Anisimov, Eu.V.Martysh, I.M.Voronov
Taras Shevchenko National University of Kyiv, Radio Physics Faculty,
64 Volodymyrska St., 01033, Kyiv, Ukraine
Transition radiation of the modulated electron beam from the accidental inhomogeneities caused by the dust particles is
calculated. This radioemission is proposed for the dust particles’ diagnostics. Numerical estimations show that the
magnitude of this radioemission is much higher than thermal radioemission of the plasma core.
PACS: 52.27.Lw
1. INTRODUCTION
It is well known that hot plasma part of
tokamaks exists up to the last closed magnetic surface.
This part is called the confinement region. Although at
the edge of the confinement region the plasma
temperature is lower than in the center of the plasma
torus, it seems still to be high for macro-particles (dust)
which may appear for some reason in this region to
survive for a long time [1]. Usually dust particles can
survive for a long time in plasma with temperature less
than 20eV. But there are regions behind the last magnetic
surface where the temperature of plasma is even lower
and these regions can influence the confinement of
plasma inside the last closed magnetic surface.
There are the experimental evidences that dust
exists in these regions inside the edge plasma and is not
located on the walls. This evidence is indirect since it
comes from analyses of the dust collected after the
discharge [2]. But the size and shape distributions of dust
particles and their material constitution indicate that
during the discharges dust must be confined in the low-
temperature parts of the edge plasma and it exposed to the
low-temperature plasma during the whole discharge.
The usual method for detection of dust particles
is Mie scattering by laser radiation. This method has not
been used in tokamaks for many reasons [1]. So, we have
a question - what kind of diagnostics of dust plasma
parameters is the best to use in a edge plasma? The idea
of this work is to use the transition radiation of the
modulated electron beam from the plasma
inhomogeneities caused by the dust particles. Electron
beams are already used for magnetic field configuration
diagnostics [3]. On the other hand registration of the
thermal radioemission in the microwave band was
traditionally used on the set of fusion devices [4]. The
charged dusty particles perturb the plasma concentration.
The charged particle (charged bunch) motion in such
plasma results to the transition radiation of the
electromagnetic waves. This effect was observed in the
laboratory experiments [5-6]. The magnitude of non-
resonant transition radioemission is directly proportional
to the bunch current and to the perturbations of the
plasma dielectric permittivity profile. Consequently the
information about the dust particles can be obtained in the
real time mode. The main types of the fusion plasma self-
radiation are the cyclotron radiation and recombination
radiation. Maximums of the spectrums of these types of
radiation lie in the short waves band relatively to the
transition radiation.
The non-resonant transition radiation of the
electron bunch in the planarly-stratified plasma with the
magnetic field parallel to the concentration gradient and
the resonant transition radiation of this bunch in the
planarly-stratified isotropic plasma were calculated in our
previous works [7-10]. The possibility to find out the
information about the plasma concentration profile from
the transition radiation spectrum was demonstrated. The
stability conditions of the electron bunch current and the
smallness of its influence on the plasma were found out
[11]. Formation of clusters from high-excited atoms near
border between fusion plasma and hard wall was
demonstrated in [12]. Role of recombination processes
with dusty particles was investigated in [13] to microwave
radiation from complex plasma.
2. MODEL DESCRIPTION AND BASIC
EQUATIONS
Charge compensated cylindrical modulated
electron beam of the radius a is injected into the cold
isotropic plasma. The plasma is considered to be
accidentally inhomogeneous. It is known [1] that
magnetic field in the edge plasma is much smaller than in
the plasma core. So in the zero-order approximation we
can neglect the effect of magnetic field on the electron
beam. Beam arises in the plane z=0 and moves along z
axis. Its alternating component of the current density can
be treated as a given function:
( )
<>
≥≤−−
=
,0,,0
;0,,exp)/exp(
),,(
zar
zarzitiLzmjze
tzrj
κω
(1)
where κ=ω/v0, v0 and ω are the beam velocity and
modulation frequency respectively (ω>ωp, ωp is the
Langmuir frequency of the background plasma), L is the
beam’s relaxation distance. Current density tends to zero
if z→+∞. Waves equations for electromagnetic field
excited by the current (1) in plasma with time
independent and spatially accidental dielectric
permittivity ε(φ,r,z) have the form:
=−−∆ 2
,2
2,
t
t),r,z(E
c
,r,z)ε(Egraddivt),r,z(E
∂
ϕ∂ϕϕ
t
j
c
π
∂
∂
2
4= ;
+−∆
2
,2
2
,
t
t),r,z(H
c
,r,z)ε(t),r,z(H
∂
ϕ∂ϕϕ
Problems of Atomic Science and Technology. 2002. № 4. Series: Plasma Physics (7). P. 135-137 135
[ ] =×+ t),r,z(Hrot,r,z)grad
,r,z)ε(
,(1 ϕϕε
ϕ
[ ]
−×= jrotj,r,z)grad
,r,z)ε(c
π
ϕε
ϕ
(14
. (2)
System’s solution (2) is based on infinitesimal
condition for relative permittivity alteration of the
background plasma:
( ) ( )zrzr ,,
10
,, ϕεεϕε
+= ,
( ) 0
)0(,,)1( εεϕε =< <zr . (3)
3. THE SPECTRAL INTENSITY OF THE
PLASMA INHOMOGENEITIES CAUSED BY
THE DUST PARTICLES
It is assumed that dust particles are equal and
distributed accidentally in the plasma volume. The
disturbances of the plasma dielectric permittivity caused
by the dust particles are treated as the small perturbations
(3).
The spatial spectrum intensity is estimated generalizing
the model of the accidental pulses’ sequence [14] (every
dust particle is located accidentally and independently
from other particles, spatial location point and dusty
particles’ total quantity are statistically independent):
2
)(2)( kdnkG Φ= π , (4)
where nd is the dust particles’ concentration, Φ is the
spatial spectrum density of separate dust particle.
The contribution of separate dusty particle into the
spatial disturbance of the plasma dielectric permittivity
vanishes exponentially at the characteristic Debye length
rd. After normalization the spatial spectrum intensity of
the dusty plasma inhomogeneities can be given in the
form:
( )
4
122
3216
+
=
drk
drkG
π
εσ
. (5)
Dispersion σε of the accidental function ε1(ϕ,r,z) can be
written through the parameters of the dust particles:
23
2
8
92
cndr
dnZ
=εσ , (6)
where Z is the dusty particle’s charge and nc(ω) is the
critical plasma concentration at the modulation frequency.
4. TRANSITION RADIATION CAUSED BY
THE DUST PARTICLES IN PLASMA
Non-resonant transition radiation is caused by the
scattering of the beam’s electromagnetic field on the
accidental inhomogeneties of the dusty plasma. This
radioemission can be calculated from the first-order
approximation equation (2) with the field of modulated
electron beam in the right side. The solution of this
equation was substituted in the form of Fourier series by
ϕ, Fourier integral by z and Fourier – Bessel integral by r.
Than the inverse transforms were carried out.
Due to the three-dimensional spatial inhomogeneity
radiated waves are both p- and s-polarized. The radial
component of the energy flux for these components can
be written in the form:
×∫
∞
Θ−
Θ
=ΘΠ
0
)cos,(
22/5
0
2)sin(2
),( krKGrdKrK
cR
amjL
R
p
R κ
ε
π
×∫
Θ+Θ−
Θ+Θ−
×
π
ψ
ψ
ψ
0 2sin2cossin22
)2sin2cossin22(2
1
krkKrK
akrkKrKJ
d
2
22cos2cossin22
)cos2sin)(22()cossin(cos
+Θ−Θ−
Θ+Θ−+Θ−Θ
×
κψ
κκψκ
krkKrK
kkkrKrK
×∫
∞
Θ−
Θ
=ΘΠ
0
)cos,(3
22/5
0
2)2sin(2
),( krKGrdKrK
cR
amkjL
R
s
R κ
ε
κπ
×∫
Θ+Θ−
Θ+Θ−
×
π
ψ
ψ
ψ
0 2sin2cossin22
)2sin2cossin22(2
1
krkKrK
akrkKrKJ
d
{ }
,222cos2cossin22
2sin
κψ
ψ
+Θ−Θ−
×
krkKrK
(7)
where k=ε0
1/2ω/c.
Transition radiation is determined by the overlapping
of the beam’s spatial spectrum and spatial spectral
intensity of the inhomogeneities. Its magnitude is directly
proportional to the product of the dust particles
concentration and their square average charge.
5. DISCUSSION
The radiation patterns for p- and s-polarised
components calculated for typical parameters are
presented on Fig.1a-d. The graphics show that radiated
power for p-polarized waves is mainly directed forward
and backward (Fig.1a-b). For s-polarized component it is
mainly directed perpendicularly to the beam velocity.
Position of maximum radiation point matches spatial
resonance condition for characteristic propagation vector
for radiated electromagnetic field, vector component for
modulation frequency and wave vector for spatial
spectrum intensity of the dusty plasma inhomogeneities.
Radiated power is more for p-polarized waves. Total
power is about 0.1-1 µW for radial component of p-
polarizated transition radioemission (s-polarizated
radiation is lower of 1-2 orders). This power is enough to
be detected by the radio receiver. Natural blackbody
thermal radiation is about 10-13 J/m2 and it is lower in
absolute comparison with transition radiation for typical
conditions.
For large velocities (v0>0.1c) the radioemission
intensity is decreased when the beam velocity is
increased. It is the result of growth of the transversal size
of the transition radiation formation zone. If this size is
large relatively to the average distance between the dust
particles, radioemission vanishes due to the averaging of
the contributions with the accidental phases. For small
velocities radioemission is decreased when the beam
velocity slow down.
Transition radioemission of the modulated electron
beam can be used for information obtaining about
complex plasma inhomogeneity caused by the strongly
charged dusty particles. So the diagnostics based on
transition radiation is possible method to study the
parameters of dusty plasma systems.
136
a
b
c
Fig.1. Radiation patterns of p-polarized (a - v0/c=0.1, b -
v0/c=0.9) and s-polarized (c - v0/c=0.1, d - v0/c=0.9)
transition radiation depending on the angle θ (radian)
for ωp=2⋅1010s-1, ω=6⋅1010s-1 jm=1А/cm2, rd=0.02cm,
a=0.5cm, L=1m, σε
2=5·10-8, Z=7⋅104.
In our calculation the effect of the beam on the
background plasma was negated. For plasma with the
typical parameters and beam of energy 100 KeV and
current 1 A it is possible for electron bunches of duration
less than 1 µs.
Of course the model treated in this article is very
simplified. More accurate treatment must take into
account real geometry of the system, influence of
magnetic field, dusty particles’ distribution on size, etc.
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137
1. INTRODUCTION
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