Particle transport: model of non-stationary fluctuations
Particle dynamics in non-uniform magnetic field for a slab and a cylinder is presented. The presence of electric field with low frequency drift (LFD) and lower hybrid drift (LHD) waves is considered. Drift waves as the possible cause of an anomalous transport in plasma are used in calculations. Non-...
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| Опубліковано в: : | Вопросы атомной науки и техники |
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| Дата: | 2002 |
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Національний науковий центр «Харківський фізико-технічний інститут» НАН України
2002
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Particle transport: model of non-stationary fluctuations / V.I. Khvesyuk, S.V. Ryzhkov, A.V. Kovalev // Вопросы атомной науки и техники. — 2002. — № 5. — С. 60-62. — Бібліогр.: 14 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1859946041799868416 |
|---|---|
| author | Khvesyuk, V.I. Ryzhkov, S.V. Kovalev, A.V. |
| author_facet | Khvesyuk, V.I. Ryzhkov, S.V. Kovalev, A.V. |
| citation_txt | Particle transport: model of non-stationary fluctuations / V.I. Khvesyuk, S.V. Ryzhkov, A.V. Kovalev // Вопросы атомной науки и техники. — 2002. — № 5. — С. 60-62. — Бібліогр.: 14 назв. — англ. |
| collection | DSpace DC |
| container_title | Вопросы атомной науки и техники |
| description | Particle dynamics in non-uniform magnetic field for a slab and a cylinder is presented. The presence of electric field with low frequency drift (LFD) and lower hybrid drift (LHD) waves is considered. Drift waves as the possible cause of an anomalous transport in plasma are used in calculations. Non-stationary fluctuations of the electrostatic field of the plasma waves are modeled. The stochastization of the particles is studied numerically.
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| first_indexed | 2025-12-07T16:14:15Z |
| format | Article |
| fulltext |
PARTICLE TRANSPORT: MODEL OF NON-STATIONARY
FLUCTUATIONS
V.I. Khvesyuk, S.V. Ryzhkov, A.V. Kovalev
Bauman Moscow State Technical University, 2nd Baumanskaya Street, 5,
Moscow, 105005 Phone: (095) 263-65-70, e-mail: khves@power.bmstu.ru
Particle dynamics in non-uniform magnetic field for a slab and a cylinder is presented. The presence of electric field
with low frequency drift (LFD) and lower hybrid drift (LHD) waves is considered. Drift waves as the possible cause of
an anomalous transport in plasma are used in calculations. Non-stationary fluctuations of the electrostatic field of the
plasma waves are modeled. The stochastization of the particles is studied numerically.
PACS numbers: 52.25.Fi, 52.35.Hr
INTRODUCTION
Anomalous transport is a result of complex processes
of interactions of the particles with electrostatic and/or
electromagnetic field produced by waves propagating in
plasma.
Investigation of anomalous transport includes two
problems: examination of wave fields and action by one
on particles. Rigorous mathematical set of equations for
reconstruction of the closed to real picture of the field in
plasma is lacking. Consequently different models of wave
fields on a base both experimental data and theoretical
considerations are formulated.
The most known model is so-called quasi-linear
theory [1,2]. In this theory one model of the wave field
with some assumptions has been formulated [3]. Under
these assumptions the Vlasov-Maxwell equations may be
reduced to MHD set of equations including the
convective anomalous transport terms (mass and energy)
as well as dispersion relations [4,5]. In this theory
anomalous transport properties as a function of the
imaginary part of ion or electron contribution to
dispersion relation are expressed.
Recently W. Horton and his team [6,7] have
proposed a new model of wave field in plasma. First of all
arising of electrostatic fluctuations as a result of the
summing up of wave modes is taken into account.
Therefore any charged particle perceives separated
fluctuations as strong single perturbation against a
background of a weak noise. This interaction is the main
reason of anomalous transport within the context of this
model. This very important feature demands especial
careful investigation. The mentioned papers contain only
initial ideas. The main purpose of one is to calculate the
motion of the separate particles in the collisionless plasma
of tokamak. The similar works for field reversed
configuration (FRC) and tandem mirror made in [8,9].
But investigations of anomalous transport for toroidal
systems are confronted by the big difficulties (compare
with open end systems). This problem has been
demonstrated clearly at the recent paper [10]. In contrast
of tokamak FRC system allows to solve the problem of
anomalous transport completely.
Wave - soliton-like wave interaction and other
phenomena must be included in the model of anomalous
transport. But existing theories of the nonlinear wave
processes in plasma are too complicated and they cannot
be the base for calculations of anomalous processes in
plasma.
The main purpose of our work is developing an
approach taking into account the field fluctuations for the
high plasma beta.
This problem is divided into following three parts.
a) Derivation of the dispersion relation in the
range close to lower hybrid drift frequencies.
b) Analysis of fluctuations produced by
simultaneously propagating wave modes.
c) Working out of the approach taking into
account non-uniformity both plasma parameters and
magnetic field.
Calculations were carried out for the model of the
stochastic processes of particle-particle interaction and
electrostatic fluctuations. These fluctuations are packets
of waves propagating along azimuthal direction of the
non-uniform cylindrical plasma. The above mentioned
approximations allow to obtain stochastic motion and
orbits of charged particles. The calculations have shown
that the short-wave fluctuations render the weak influence
on the energetic particle (the velocity vastly exceeds the
thermal velocity).
A NEW APPROACH
A new approach to examine the transport properties
of the plasma observed in the experiments is developed.
Field fluctuations and particles transfer in plasma with
strong inhomogeneity of density and magnetic field is
presented. Proposed theoretical analysis takes into
account the real spatial structure of plasma and non-
uniform magnetic field. Influence of magnetic field and
plasma density profiles on diffusion is studied. Non-
stationary electromagnetic field of the waves propagated
in plasma is modeled.
This paper aims to study a new model of transport
plasma. The most important distinction of this model
from the transport model [5] is taking into account the
real structure of plasma geometry and magnetic field.
Influence of complex radial dependence of magnetic field
B(r) and density n(r) on confinement time may be
investigated by this approximation and resolved for
various plasma areas where different types of instabilities
are arising.
60 Problems of Atomic Science and Technology. 2002. № 5. Series: Plasma Physics (8). P. 60-62
Space localization of electrostatic oscillations is
considered and wave spectrum influence on the transport
properties is studied at first time. Feature of the proposed
system is the supposition of the wave-harmonics with the
formation of two regions on the time scale: soliton-like
impulses with peak shape and noises dividing impulses. It
is important that transport processes may be appeared by
action of impulses only. It is shown that the intensity of
the electric field in noise region is significant less than
maximum values of field in impulse (see Figure). Form of
the impulse, its duration, and interval between impulses
are defined by number of harmonics in packet, its
amplitude, frequency, and wave length.
Presence of dispersion in plasma is also takes into
consideration. Dispersion of the electrostatic waves has
essential influence on the plasma particle transport
because leads to decay of impulses cause of the different
phase velocites of independent harmonics. Therefore,
taking into account dispersion leads to non-stationary of
electrostatic field and besides the non-stationary is
determined not only by motion of soliton with group
phase velocity of packet, but its decay and formation of a
new soliton.
Electric field fluctuations (LHD oscillations) vs azimuthal
angle. For both figures the number of layers in the
plasma volume is equal 10, 20 harmonics in each one
Electric field intensity is shown in the Figure.
Harmonics have Gaussian transversal profile, its
dispersion is equal to layers width so that fringes of
profile intersect two adjacent layers. Amplitude/energy of
oscillations is about 2,5% of thermal energy.
MODEL OF THE WAVE FIELD
The main features of the wave field are the following.
1) The occurrence of the weak background
oscillations in plasma: their averaged values a such that
they exert negligible action on particles.
2) On the background of weak wave oscillations the
wave packets are formed.
3) The different parameters of the wave modes (e.g.
phase velocity) depend on coordinate directed along
transport flows.
4) The reason of anomalous transport is the influence
of the big field fluctuations on the particles.
5) As the main types of oscillations that are
responsible for anomalous transport the lower hybrid and
low frequency drift oscillations are considered.
Therefore in general the wave field is complex three-
dimensional non-stationary formation.
Analysis of the particles motion is reused to
calculations of interactions particles with the big
fluctuations.
Such model provides stochastic behavior of the
particles motion automatically.
The important question of magnetic configuration is
resonance conditions for plasma oscillations. The
formation of the wave field depends on these conditions.
In toroidal systems discrete conditions occur [11]. For
cylindrical plasma with straight magnetic force lines the
resonance conditions are continuous if azimuthal
propagation of waves is considered. Therefore wave
modes can be excited in any radius where corresponding
type of wave is instable.
So-called local and global models of wave fields for
toroidal systems in sense of above mentioned works of
W. Horton et al. are not adequate for cylindrical systems
because of indicated differences of resonance conditions.
In cylindrical plasma different wave modes can be excited
at arbitrary radius r. The common picture of wave field in
this case presents the set of many wave modes localized
in different areas of cylindrical plasma. The neighboring
wave modes are overlapped. Therefore in the whole
plasma area where conditions of instability for the waves
of certain type are satisfied these waves consist of
continuous wave field. In this cense this model is global.
Dynamics of formation and decay of the wave
packets is a separate problem of our investigation.
Naturally this problem is connected with form of
dispersion relation F(ω,k)=0 and the corresponding area
of occurrence certain kind of waves. Fluctuation
parameters in different conditions vary within wide range
(frequencies, amplitude values, forms of fluctuations).
CONCLUSIONS
Numerical investigation of particle transport in non-
uniform plasma with electrostatic waves is carried out.
Diffusion is generated by drift in magnetic field, confined
plasma and field of electrostatic oscillations, propagated
in plasma. Diffusion passing perpendicular to magnetic
field and has influence on energy and plasma confinement
time. Results of the research may be used for method
providing the suppression of transport processes and
enhancement of confinement properties.
Mathematical models obtained can be used for full
analysis of transport processes for wide class of magnetic
confinement systems (spheromak, tandem mirror, gas
dynamic trap, spherical tokamak). Including, diffusion
and particle transfer properties. Moreover, last
experimental data on the stellarator L-2M [12] shown a
61
good agreement between our theoretical predictions and
field fluctuations observed in the experiments.
Instabilities with variable gradients are taken into
account when the particle transport in plasma is
considered. Calculations are carried out for the range of
plasma parameters, reached in experiments. Non-local
approach [13,14] is used in the analysis and dispersion
relation is obtained. The possible suppression of drift
wave turbulence is shown.
The main features of this model are taking into
account complex field of drift waves propagating in
plasma and analysis of motion of the particles interacting
with field fluctuations.
The major conclusions of the study are summarized
as follows:
1) model of anomalous transport in plasma with drift
waves was developed in detail and main ideas of its are
presented in this article;
2) plasma geometry/shape and particles energy (in the
view of wave-particle interaction) have influence on the
transport processes;
3) it is also found that the external electric field may be
applied to control the particle transport and suppress the
instablity.
ACKNOWLEDGEMENTS
This work was supported by Grant # 1260 of
International Science and Technology Center.
REFERENCES
1. A.A.Vedenov, E.P.Velikhov, R.Z.Sagdeev // Nucl.
Fusion 1961, v.1, p.82.
2. W.E.Drummond, D.Pines // Nucl. Fus. Suppl. 1962,
v.3, p.1094.
3. B.B.Kadomtsev, Plasma turbulence, Academic Press,
New York, 1965.
4. R.C.Davidson, N.T.Gladd // Phys. Fluids 1975, v.18,
p.327.
5. R.C.Davidson, N.A.Krall // Nucl. Fusion 1977, v.17,
p.1313.
6. W.Horton et al // Phys. Plasmas 1998, v.5, p.3910.
7. J.M.Kwon et al // Phys. Plasmas 2000, v.7, p.1169.
8. V.I.Khvesyuk, A.Yu.Chirkov // Proceedings of the
US-Japan Workshop and The Satellite Meeting of
ITC-9 on Physics of High Beta Plasma Conf. in
Innovat. Fusion Syst. 1997, NIFS-Proc.-41, p.19.
9. V.I.Khvesyuk, A.Yu.Chirkov, A.A.Pshenichnikov //
J. Plasma Fusion Res. SERIES 2000, v.3, p.150.
10.J.B.Taylor et al // Plasma Phys. and Contr. Fusion
1996, v.38, p.243.
11.J.W.Connor, J.B. Taylor // Phys. Fluids 1987, v.30,
p. 3180.
12.G.M.Batanov, O.I.Fedianin, N.K.Kharchev, et al //
Plasma Phys. Control. Fusion 1998, v.40, p.1241.
13.V.I.Khvesyuk, A.Yu.Chirkov, S.V.Ryzhkov,
“Nonlocal Modeling of Anomalous Transport in FRC
Plasma” // Proc. 29th EPS Conference on Plasma
Physics and Controlled Fusion in Montreux,
Switzerland June 16-23, 2002 (on CD).
14.V.I.Khvesyuk, A.Yu.Chirkov, A.V.Kovalev //
Plasma Physics Reports 2002, v.28, № 9, p.854.
62
INTRODUCTION
A new approach
model of the wave field
CONCLUSIONS
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| id | nasplib_isofts_kiev_ua-123456789-77880 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1562-6016 |
| language | English |
| last_indexed | 2025-12-07T16:14:15Z |
| publishDate | 2002 |
| publisher | Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
| record_format | dspace |
| spelling | Khvesyuk, V.I. Ryzhkov, S.V. Kovalev, A.V. 2015-03-08T20:25:43Z 2015-03-08T20:25:43Z 2002 Particle transport: model of non-stationary fluctuations / V.I. Khvesyuk, S.V. Ryzhkov, A.V. Kovalev // Вопросы атомной науки и техники. — 2002. — № 5. — С. 60-62. — Бібліогр.: 14 назв. — англ. 1562-6016 PACS numbers: 52.25.Fi, 52.35.Hr https://nasplib.isofts.kiev.ua/handle/123456789/77880 Particle dynamics in non-uniform magnetic field for a slab and a cylinder is presented. The presence of electric field with low frequency drift (LFD) and lower hybrid drift (LHD) waves is considered. Drift waves as the possible cause of an anomalous transport in plasma are used in calculations. Non-stationary fluctuations of the electrostatic field of the plasma waves are modeled. The stochastization of the particles is studied numerically. This work was supported by Grant # 1260 of International Science and Technology Center. en Національний науковий центр «Харківський фізико-технічний інститут» НАН України Вопросы атомной науки и техники Basic plasma physics Particle transport: model of non-stationary fluctuations Article published earlier |
| spellingShingle | Particle transport: model of non-stationary fluctuations Khvesyuk, V.I. Ryzhkov, S.V. Kovalev, A.V. Basic plasma physics |
| title | Particle transport: model of non-stationary fluctuations |
| title_full | Particle transport: model of non-stationary fluctuations |
| title_fullStr | Particle transport: model of non-stationary fluctuations |
| title_full_unstemmed | Particle transport: model of non-stationary fluctuations |
| title_short | Particle transport: model of non-stationary fluctuations |
| title_sort | particle transport: model of non-stationary fluctuations |
| topic | Basic plasma physics |
| topic_facet | Basic plasma physics |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/77880 |
| work_keys_str_mv | AT khvesyukvi particletransportmodelofnonstationaryfluctuations AT ryzhkovsv particletransportmodelofnonstationaryfluctuations AT kovalevav particletransportmodelofnonstationaryfluctuations |