Ion-cyclotron absorption of fast waves in a cylindrical current-carrying plasma
Influence of a longitudinal stationary current on the absorption and the radial structure of fast waves in a cylindrical current-carrying plasma is discussed. To evaluate the dispersion equation for fast waves, there was used the dielectric tensor taking into account the radial current structure and...
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| Zitieren: | Ion-cyclotron absorption of fast waves in a cylindrical current-carrying plasma / N.I. Grishanov, N.A. Azarenkov // Problems of atomic science and tecnology. — 2021. — № 1. — С. 36-40. — Бібліогр.: 14 назв. — англ. |
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irk-123456789-1947272023-11-29T12:13:29Z Ion-cyclotron absorption of fast waves in a cylindrical current-carrying plasma Grishanov, N.I. Azarenkov, N.A. Basic plasma physics Influence of a longitudinal stationary current on the absorption and the radial structure of fast waves in a cylindrical current-carrying plasma is discussed. To evaluate the dispersion equation for fast waves, there was used the dielectric tensor taking into account the radial current structure and geometry of the confining helical magnetic field by the plasma safety factor. It is shown that the damping rate of fast waves in a non-equilibrium current-carrying plasma differ from those for an equilibrium plasma column in a homogeneous magnetic field nearby the cutoffs and resonances due to the rotational transformation (including shear-effects) of the helical magnetic field lines. Проаналізовано вплив стаціонарного струму на поглинання і радіальну структуру швидких хвиль у циліндричній струмонесучій плазмі. При отриманні дисперсійного рівняння швидких хвиль використано діелектричний тензор, який враховує радіальну структуру струму і геометрію утримуючого гвинтового магнітного поля через коефіцієнт запасу стійкості плазми. Показано, що дисперсійні характеристики швидких хвиль у нерівноважній плазмі зі струмом відрізняються від дисперсійних характеристик рівноважного плазмового шнура в однорідному магнітному полі поблизу точок відсічення і резонансів через облік обертального перетворення силових ліній гвинтового магнітного поля, включаючи шир-ефекти. Проанализировано влияние продольного стационарного тока на поглощение и радиальную структуру быстрых волн в цилиндрической токонесушей плазме. При получении дисперсионного уравнения быстрых волн использован диэлектрический тензор, учитывающий радиальную структуру тока и геометрию удерживающего винтового магнитного поля через коэффициент запаса устойчивости плазмы. Показано, что дисперсионные характеристики быстрых волн в неравновесной плазме с током отличаются от дисперсионных характеристик равновесного плазменного шнура в однородном магнитном поле вблизи точек отсечки и резонансов из-за учета вращательного преобразования силовых линий винтового магнитного поля, включая шир-эффекты. 2021 Article Ion-cyclotron absorption of fast waves in a cylindrical current-carrying plasma / N.I. Grishanov, N.A. Azarenkov // Problems of atomic science and tecnology. — 2021. — № 1. — С. 36-40. — Бібліогр.: 14 назв. — англ. 1562-6016 PACS: 52.50.Qt http://dspace.nbuv.gov.ua/handle/123456789/194727 en Вопросы атомной науки и техники Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
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Basic plasma physics Basic plasma physics |
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Basic plasma physics Basic plasma physics Grishanov, N.I. Azarenkov, N.A. Ion-cyclotron absorption of fast waves in a cylindrical current-carrying plasma Вопросы атомной науки и техники |
| description |
Influence of a longitudinal stationary current on the absorption and the radial structure of fast waves in a cylindrical current-carrying plasma is discussed. To evaluate the dispersion equation for fast waves, there was used the dielectric tensor taking into account the radial current structure and geometry of the confining helical magnetic field by the plasma safety factor. It is shown that the damping rate of fast waves in a non-equilibrium current-carrying plasma differ from those for an equilibrium plasma column in a homogeneous magnetic field nearby the cutoffs and resonances due to the rotational transformation (including shear-effects) of the helical magnetic field lines. |
| format |
Article |
| author |
Grishanov, N.I. Azarenkov, N.A. |
| author_facet |
Grishanov, N.I. Azarenkov, N.A. |
| author_sort |
Grishanov, N.I. |
| title |
Ion-cyclotron absorption of fast waves in a cylindrical current-carrying plasma |
| title_short |
Ion-cyclotron absorption of fast waves in a cylindrical current-carrying plasma |
| title_full |
Ion-cyclotron absorption of fast waves in a cylindrical current-carrying plasma |
| title_fullStr |
Ion-cyclotron absorption of fast waves in a cylindrical current-carrying plasma |
| title_full_unstemmed |
Ion-cyclotron absorption of fast waves in a cylindrical current-carrying plasma |
| title_sort |
ion-cyclotron absorption of fast waves in a cylindrical current-carrying plasma |
| publisher |
Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
| publishDate |
2021 |
| topic_facet |
Basic plasma physics |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/194727 |
| citation_txt |
Ion-cyclotron absorption of fast waves in a cylindrical current-carrying plasma / N.I. Grishanov, N.A. Azarenkov // Problems of atomic science and tecnology. — 2021. — № 1. — С. 36-40. — Бібліогр.: 14 назв. — англ. |
| series |
Вопросы атомной науки и техники |
| work_keys_str_mv |
AT grishanovni ioncyclotronabsorptionoffastwavesinacylindricalcurrentcarryingplasma AT azarenkovna ioncyclotronabsorptionoffastwavesinacylindricalcurrentcarryingplasma |
| first_indexed |
2025-07-16T22:12:11Z |
| last_indexed |
2025-07-16T22:12:11Z |
| _version_ |
1837843279337488384 |
| fulltext |
ISSN 1562-6016. ВАНТ. 2021. №1(131)
36 PROBLEMS OF ATOMIC SCIENCE AND TECHNOLOGY. 2021, №1. Series: Plasma Physics (27), p. 36-40.
https://doi.org/10.46813/2021-131-036
ION-CYCLOTRON ABSORPTION OF FAST WAVES
IN A CYLINDRICAL CURRENT-CARRYING PLASMA
N.I. Grishanov
1,2
, N.A. Azarenkov
1
1
V.N. Karazin Kharkiv National University, Kharkiv, Ukraine;
2
Ukrainian State University of Railway Transport, Kharkiv, Ukraine
Influence of a longitudinal stationary current on the absorption and the radial structure of fast waves in a cylindrical
current-carrying plasma is discussed. To evaluate the dispersion equation for fast waves, there was used the dielectric
tensor taking into account the radial current structure and geometry of the confining helical magnetic field by the
plasma safety factor. It is shown that the damping rate of fast waves in a non-equilibrium current-carrying plasma differ
from those for an equilibrium plasma column in a homogeneous magnetic field nearby the cutoffs and resonances due
to the rotational transformation (including shear-effects) of the helical magnetic field lines.
PACS: 52.50.Qt
INTRODUCTION
The fast waves (often referred as the fast magnetosonic
or compressional Alfvén waves) are interesting for
scientists both academically and in applications for fusion
plasmas. They can be used for an additional plasma heating
in tokamaks, stellarators and open mirror-traps in the
frequency range of ion-cyclotron resonances (ICR) and are
believed to be responsible for ion-cyclotron emission there.
Presently, the linear theory is very well developed [1] for
any plane waves in a uniform magnetized plasma confined
by a straight magnetic field. However, the plane waves are
not suitable for cylindrical and toroidal plasma models. In
this connection, the theory of fast waves was significantly
advanced at the end of 20th century using the models of
cylindrical and quasi-cylindrical waves in the cylindrical
[2-5] and toroidal [5-10] plasma configurations. It was
shown that the eigenfrequencies of fast waves are defined
by the contribution of bulk particles (mainly ions) to the
transverse dielectric tensor components. As some
restriction of these investigations is an assumption that the
dielectric tensor ik for waves in any cold current-carrying
magnetized plasma has the same (invariant) form, i.e., like
as for plane waves in a straight magnetic field [1].
However, the current-carrying plasma is not in the
stable equilibrium. Therefore, wave analysis in the current-
carrying plasmas should take into account the influence of
rotational transformation of the stationary magnetic field
lines (including the shear-effects) on the dielectric
properties of plasmas in the helical magnetic field. The
main goal of our paper is to describe the fast waves in the
cylindrical current-carrying plasmas using the approach
developed in Refs. [3, 11-14].
1. PLASMA MODEL
The simplest model of tokamaks is a magnetized
plasma cylinder (radius a) with identical ends in the
helical magnetic field, where the ohmic current j0
generates the poloidal magnetic field eH 00 H in
addition to the longitudinal zzz H eH 00 , where re ,
e ,
and ze
are the unit vectors along the axis r, and z of
the cylindrical
coordinates. In this case, the length of plasma cylinder
is equal to 02 R , where 0R corresponds to a major
tokamak radius. As a result, the stationary field
z000 HHH becomes helical with a rotational
transformation, allowing to take into account the shear-
effects and the radial profiles of ohmic current by the
radial dependence of plasma safety factor
q(r)=rH0z/(R0H0) and its derivatives
Describing such plasma model [11-14] we assume
that the steady-state current 0 0( || )j H is created by
electrons having the velocity
0 0e , whereas
0 0i
for heavy ions. In this case, according to Ampere’s law,
0 0 0 0
4 4
ej N e
c c
H h , (1)
where
0
0H
H
h , 2 0
0
04 e
H c
n e
. (2)
Here n0e is the electron density, e is the elementary
charge, and magnetic field parameter 2 is equal to
2 2 1
2
zh h r dq
r q dr
. (3)
To evaluate the dispersion relations for eigenmodes
in the current-carrying plasma, as usual, we should
resolve the Maxwell’s equations for perturbed electric
field (E), magnetic field (H) and current density (j)
components. Further, we use the normal An, binormal Ab
and parallel Ah projections relative to 0H for the vector
values , , n b hA A A A E H j n b h :
1 nA A A n ,
2 bA A A b ,
3 hA A A h , (4)
where n, b, h are the normal, binormal and parallel unit
vectors relative to 0H :
0 0/ z zH h h h H e e ,
r n b h e , (5)
z zh h b h n e e ,
accounting for that 0r rb h ,
zb h and
zb h .
2. WAVE’S EQUATIONS
Assuming the smallness of a poloidal magnetic field,
h<< hz, the differential Maxwell’s equations for short
wave perturbations, proportional to
ISSN 1562-6016. ВАНТ. 2021. №1(131) 37
0, , ~ exp( i i i / i )rt m nz R k dr E H j , (6)
can be reduced, in the geometric optic approximation, to
the set of linear algebraic equations
1 3 || 2bH N E N E ,
2 || 1 1 2 3rH N E iN E N E ,
3 1 2 2 3b rH N E N E iN E , (7)
|| 2 3 11 1 12 2 13 3bN H N H E E E ,
|| 1 1 2 3 21 1 22 2 23 3rN H iN H N H E E E ,
1 2 2 3 31 1 32 2 33 3b rN H N H iN H E E E .
Here r
r
k c
N
, b
b
k c
N
,
k c
N
are the radial
(normal), binormal and parallel refractive index
components, corresponding to the radial (kr), binormal
0
z
b
nhmh
k
r R
and parallel
0
z
mh nh
k
r R
wave-
numbers; m and n are the poloidal and toroidal
eigenmode numbers;
1
1
c
N
, 2
2
c
N
, 1
zh h dq
q dr
, (8)
where 1 – parameter is defined by the shear of
magnetic field lines (~dq/dr) in the explicit form.
Deriving Eqs. (7) the perturbed current density
components were excluded by the connection
4iji/=(ik-ik)Ek, where subscribed indexes i,k=1,2,3
numerate the n, b, h projections of the vector values,
Eqs. (4); ik are the Kronecker symbols.
Contribution of cold particles in the current-carrying
plasma to the dielectric tensor ik for waves in the
frequency range below the electron-cyclotron frequency
(<<|e|) can be expressed as [11,12]:
1 2 1 2
2 2, , ,.. , ,..
11 2 2 2 2
1 1
e i i i i
p p
,
22 1 2N N , (9)
1 2
1 2
2, , ,..
12 21 22 2
2, ,..
22 2
i i
( )
i i ,
( )
e i i
p
i i
p
N N
N N
13 31 2i bN N ,
23 32 2i rN N ,
1 2
2 2, , ,...
33 2 2
1 1
e i i
p pe
.
Here 2 2
04 /p N q M is the squared Langmuir
frequency of -kind particles,
0 /q H M c is the
cyclotron (Larmor) frequency of ions (single or multiple
species,
1 2, ,...i i , 0i ) and electrons ( e ,
0e ); M, N0 and q are the mass, density and
charge of -kind plasma particles; 2 2
0 0 0zH H H is
the stationary magnetic field module; c is the speed of
light. As we see, the transverse component
11 is
defined mainly by the contribution of plasma ions; the
longitudinal 33 and off-diagonal 13 , 31 , 23 , 32
components – by the current-carrying electrons;
22 and
gyrotropic components
12 and
21 – by both the ions
and electrons. Of course, if j0=0, h=0, hz=1, 1 0 ,
2 0 , this dielectric tensor can be reduced to ik for
waves in a cold equilibrium collisionless plasma in a
uniform magnetic field [1].
Excluding the magnetic field components by the
Faraday’s law [first three equations in (7)], we obtain
the following wave equations for E1, E2, and E3:
2 2
|| 1 2 3i 0b r b rN N Е N N g Е N N E ,
2 2
1 0 1 2
1 3
i
0,
r b r b
b r
N N g Е N N N N Е
N N iN N E
(10)
2 2 2
1 1 2 2 3i 0r b r r bN N E N N N N Е N N N Е ,
where the additional designation
1 2
2, ,..
02 2( )
i i
p
g N N
(11)
is introduced instead of 12 1i iN N g . Note, the new
parameter
0 2 1N N N is independent from the
magnetic shear. Moreover, the term
0N N can be
comparable and larger than the ion contribution to g for
low frequency waves (<<i) far from the rational
magnetic surfaces, where m+nq(r)>>1.
3. DISPERSION RELATIONS
As usual, the squared radial refractive index 2
rN of
eigenmodes in the current-carrying plasma cylinder can
be derived from the corresponding biquadratic
dispersion equation [i.e., when the determinant of Eqs.
(10) is equal to zero]:
4 2 0r rAN BN C , (12)
where
A , (13)
2 2 2 2
2 1 2
2 2 2
1 12 2 ,
b
b
B N N g N N N
N N N gN N
2 2 2 2 2 2
2 0 1
2 2 2 2 .
b b
b b
C N N N N N N N g
N N N N
This dispersion equation allows us to determine the
radial structure of eigenmodes (by kr, as a boundary
value problem) in dependence on the given m, n and
at the considered magnetic surface [by r=const under
the given radial profiles of (r) and q(r)]. The shear
corrections
0 1N N in C are smaller than , but they
can be comparable with 2N , e.g., nearby the rational
magnetic surfaces, where ( ) 0m nq r . It should be
noted, that assuming N0=N1=N2=0 into B and C
coefficients, Eq. (12) can be easily reduced to the
dispersion equation in Ref. [7] suitable for plane (and
cylindrical) slow and fast waves in the equilibrium
magnetized plasmas held by a uniform magnetic field,
where h=0, kr=kx, k||=n/R0=kz, kb=km/r=ky.
Two roots of Eq. (12) are equal to
2
2 4
2
r
B B AC
N
A
, (14)
38 ISSN 1562-6016. ВАНТ. 2021. №1(131)
corresponding [7] to slow waves ( 2 2
rSW rN N ) and fast
waves ( 2 2
rFW rN N ), respectively. Using inequalities
| |,| | | |g , Eqs. (14) can be simplified to
2 2 2
rSW bN N N
, (15)
2 2 2 2
0 12
2
b
rFW
N N N N N g
N
N
. (16)
4. ICR ABSORPTION OF FAST WAVES
As is well known [1], the growth/damping rate of
any waves is determined by the anti-hermitic part of
dielectric tensor elements in the considered plasma
models. Since the dielectric tensor jk in Eqs. (9) is
hermitic, the slow and fast waves in our cold current-
carrying plasma cylinder must be pure harmonic-
periodic. However, we should remember about the
possible two principal collisional and collisionless wave
dissipation mechanisms in any plasma model.
The collisional mechanism is connected with
resistive (ohmic) conductivity of cold plasma models
due to electron-ion friction as a result of effective
electron-ion collisions. Resistive absorption both the
fast and slow waves in magnetized plasmas usually is
small. It can be substantial [7] only for slow waves at
the plasma periphery under the conditions where the
particle density is quite large and temperature is very
law. The detailed analysis of influence of collisional
effects on the cyclotron wave-particle interactions in
magnetized plasmas of tokamaks and stellarators has
been done at Ref. [8].
Other collisionless wave dissipation mechanisms are
connected with the resonance wave-particle interactions
in the high-temperature plasmas when collisional
(resistive) wave damping become ineffective. In this
case, the kinetic wave theory should be used to estimate
the contribution of resonant particles to the anti-hermitic
parts of jk. As one can easily verify in section 4, the
collisionless damping rate of slow waves (i.e.,
imaginary part of radial refractive index,
Im ~ ImrSWN ) in a high-temperature plasma can be
defined by the contribution of resonant electrons to the
imaginary part (or anti-hermitic part) of the parallel
dielectric tensor element :
2
,
2 2
2
2 2
2
1 1 i ( )
2
1 i ( ) .
e i
p
Ts
pe
e e
Te
W
k
W
k
(17)
Here
2 2
0
2i
( ) e 1 tW e dt
(18)
is the probability integral for the complex arguments
0
e
Te
k
k
, (19)
where the thermal velocity of hot electrons is
defined by their temperature
0eT , 02 /Te e eT M , and
the current velocity is determined in Eq. (2). The
corresponding resonance conditions for waves with
phase velocity / k and particles having the same
parallel velocity / k are known as the Cherenkov
resonance conditions: k . In this case, the field-
aligned electric field component E h E of waves
effectively interacts with plasma particles moving along
the H0 field lines, and the wave absorption mechanism
itself is named as the electron (or ion) Landau damping.
However, as was mentioned above, in a magnetized
collisionless plasma there is another wave dissipation
mechanism connected with cyclotron wave-particle
interactions under the conditions when the transverse
electric field components (
1 2iE E ) can effectively
interact with plasma particles moving along the
magnetic field lines with the parallel velocities
|| ~ / k , where the indices =e, =i mark the
cyclotron frequencies of electrons and ions, and the
integer values 1, 2,... correspond to the numbers
of cyclotron resonances. The corresponding single
wave-particle resonance conditions in magnetized
plasmas confined by the uniform (straight) magnetic
field are well-known:
|| ||k , where
|| zk k ,
since h=0. Considering the cylindrical magnetized
current-carrying plasmas (in the helical magnetic field)
we should take into account that the cyclotron wave-
particle resonance conditions there have some another
form [13,14]:
|| || ||sk . (20)
A specific feature of current-carrying plasmas is the -
shift,
2 1
4
zh h r dq
r q dr
, (21)
in the parallel projection of the wave vector, ||k , due to
the curvature of the external magnetic field lines in the
plasma with ohmic current. This -shift is responsible
for the difference between the resonance conditions in
the plasmas with straight and helical magnetic fields.
Evidently, if =0 or h=0, i.e., in the absence of ohmic
current, the cyclotron resonance conditions
automatically reduce to the expression
|| ||k ,
for plasmas in a uniform magnetic field, where
|| zk k .
In this section we consider the ion-cyclotron
resonance absorption of fast waves in a cylindrical
current-carrying plasma nearby the first (principal,
fundamental, 1 ) cyclotron frequency harmonic.
Unfortunately, there are no correct expressions of jk
elements suitable for waves with ~ (under
2 ) in the current-carrying plasma models. As for
case of 1 , the contributions of resonant ions to jk
can be derived by solving [14] the Vlasov equation
for
perturbed distribution functions of plasma particles in a
cylindrical current-carrying plasma under the arbitrary
values of parameter || / ( )ik . In this case, we
obtain [13]
the following dielectric tensor elements
( )i
jk :
ISSN 1562-6016. ВАНТ. 2021. №1(131) 39
2
( ) ( )
11 22
i ( ) 1
2
pii i i
iTi
W
k
,
2
( ) ( )
12 21
( ) i
2
pii i i
iTi
W
k
,
2
( ) ( )
13 23 2
||
i
1 i ( )
2
pii i r b
i i
k k
W
k
, (22)
2
( ) ( )
31 32 2
||
i
1 i ( )
2
pii i r b
i i
k k
W
k
,
2
( )
33 2
pii
.
Here the ion argument of ( )iW – function, E q. (18), is
||| |
i
i
Tik
, (23)
where the thermal velocity of resonant ions is defined
by their temperature
0iT : 02 /Ti i iT M .
To estimate the ICR absorption of fast waves on the
fundamental cyclotron frequency ( 1 , so that
~ i ), we can use the dispersion equations (14)
and/or (16), where the transverse and gyrotropic
dielectric tensor components (after summation over ions
and electrons) have the following form:
2 2
11 22
i ( )
1
2 ( ) 2 ( )
pi pi i
i Ti
W
k
22
2
i ( )
2 ( )4
pi i
TiA
Wc
k
, (24)
2 2
12 21
(2 ) i ( )
2 ( ) 2 ( )
pi i pi i
i i Ti
W
g i i
k
22
2
i ( )
2 ( )4
pi i
TiA
Wc
k
.
As one can see these dielectric characteristics under the
given (real) wave frequency and eigenmode numbers
m and n have the equal anti-hermitic parts
a :
2 2
11 22
exp( )
Im Im Im
2 ( )
pi i
a
Ti
g
k
, (25)
responsible [1] for the ICR absorption of both the slow
and fast waves.
Assuming that 2
0 1 2, ,g N N N N N for fast
waves with ~ i , the dispersion equation (16) can be
reduced to
2 2
2 2 2 2
FW r b
g
N N N N
. (26)
Here /N kc is the refractive index of fast waves
(FW), 2 2 2 2 2 2 2 2
0/ /r b rk k k k k n R m r is the
value of their wave vector. The dispersion
characteristics of fast waves (the real and imaginary
parts of the radial refractive index under the given
~ i , m and n at the considered by r magnetic
surface):
Re i Im Re (1 i )r r r rN N N N (27)
can be estimated from Eq. (26) using the smallness of
ICR damping rate:
Im Im
1
Re Re
r r
r r
N k
N k
. (28)
As a result, the spectrum of fast waves in the ICR
frequency range is defined by the expressions for these
waves in the case of a uniform magnetic field:
2
2 2 2
2
Re rFW b
A
c
N N N
. (29)
As we see, the radial refractive index of fast waves has a
finite value for ~ i , whereas g in this
frequency range. Since the transverse electric field
component of fast waves and resonant ions rotate
relatively H0-field lines in the opposite directions, the
damping rate of fast waves should be small and can be
estimated by the expression
2
2
exp( )
4 ( )
Ti i
FW
i i
k
W
. (30)
Neglecting the-corrections to k in Eq. (30), we
obtain the well-known result for ICR fast wave damping
rate in Ref. [7]. However, these -corrections are not
important only for perturbations with /k h r , i.e.,
in the case, when the pitch of the 0H -line screw is
greater than the wavelength along H0. If ~ /k h r , the
-corrections should be accounted in the current-
carrying plasmas, including the tokamaks, or other
devices, where the magnetic field is helical. The main
difference between our results and the well-known ones
is that fast waves propagating strictly across the uniform
magnetic field (kz=0) are not absorbed by plasma ions,
whereas if magnetic field is helical, the absorption of
these waves with 0k (under ~ i ) can be nonzero
due to corrections connected with the magnetic shear
and curvature of the magnetic field lines in the wave-
particle resonance condition (20). In this case, the
damping rate of fast waves propagating along the
normal n to the magnetic surface in the current-carrying
plasma is estimated by the formula
||
2
20
0
exp1
1
4 4 ( )
Ti i
FW k
i i
dq
R q q d W
. (31)
This feature of the ICR absorption of fast waves should
be accounted analyzing their stability, excitation and
dissipation in cylindrical and toroidal plasmas near the
so-called rational magnetic surfaces, where the
longitudinal wave number changes sign, i.e., ( ) 0k r .
CONCLUSIONS
In conclusion, let us summarized the main results of
our paper related to the penetration of fast waves with
fixed longitudinal and poloidal mode numbers (n and m)
in the frequency range below the electron cyclotron
frequency ( e ) at the considered by r magnetic
surface in the cylindrical current-carrying plasma with
one and/or two ion species.
40 ISSN 1562-6016. ВАНТ. 2021. №1(131)
It is shown that the dielectric characteristics of
electromagnetic waves in the current-carrying plasmas
depend on the structure of the steady-state magnetic
field configuration and plasma particle distribution
functions. Spectra of fast and slow waves in a current-
carrying plasma are determined (as in a straight uniform
magnetic field case) by the contribution of bulk particles
to the dielectric tensor components jk. However, the jk-
components in the current-carrying plasma (where 0H
is helical), Eqs. (9), (22), (24), differ from ones for
plasmas confined in the uniform magnetic field.
It is easily verify that, neglecting the poloidal
magnetic field 0h , i.e., if
1 2 0 0 ,
the dispersion characteristics (ReNr and ImNr) of fast
waves in the cylindrical current-carrying plasmas can be
reduced to the well-known results for magnetized
plasmas in a uniform magnetic field.
As in the case of a uniform magnetic field the cold
plasma approximation for jk becomes incorrect nearby
the Alfvén, cyclotron and hybrid resonances, where the
wave phase velocity can be comparable with thermal
velocities of ions and/or electrons. It means that kinetic
theory should be used analyzing the wave penetration,
wave excitation and wave dissipation in the current-
carrying plasmas in the range of resonant frequencies
and resonant surfaces.
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Article received 15.10.2020
ИОННО-ЦИКЛОТРОННОЕ ПОГЛОЩЕНИЕ БЫСТРЫХ ВОЛН В ЦИЛИНДРИЧЕСКОЙ ПЛАЗМЕ
С ТОКОМ
Н.И. Гришанов, Н.А. Азаренков
Проанализировано влияние продольного стационарного тока на поглощение и радиальную структуру быстрых
волн в цилиндрической токонесушей плазме. При получении дисперсионного уравнения быстрых волн
использован диэлектрический тензор, учитывающий радиальную структуру тока и геометрию удерживающего
винтового магнитного поля через коэффициент запаса устойчивости плазмы. Показано, что дисперсионные
характеристики быстрых волн в неравновесной плазме с током отличаются от дисперсионных характеристик
равновесного плазменного шнура в однородном магнитном поле вблизи точек отсечки и резонансов из-за учета
вращательного преобразования силовых линий винтового магнитного поля, включая шир-эффекты.
ІОННО-ЦИКЛОТРОННЕ ПОГЛИНАННЯ ШВИДКИХ ХВИЛЬ У ЦИЛІНДРИЧНІЙ ПЛАЗМІ
ЗІ СТРУМОМ
М.І. Гришанов, М.О. Азарєнков
Проаналізовано вплив стаціонарного струму на поглинання і радіальну структуру швидких хвиль у
циліндричній струмонесучій плазмі. При отриманні дисперсійного рівняння швидких хвиль використано
діелектричний тензор, який враховує радіальну структуру струму і геометрію утримуючого гвинтового
магнітного поля через коефіцієнт запасу стійкості плазми. Показано, що дисперсійні характеристики швидких
хвиль у нерівноважній плазмі зі струмом відрізняються від дисперсійних характеристик рівноважного
плазмового шнура в однорідному магнітному полі поблизу точок відсічення і резонансів через облік
обертального перетворення силових ліній гвинтового магнітного поля, включаючи шир-ефекти.
https://iopscience.iop.org/journal/0029-5515
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