Calculation of the dielectric tensor elements of microwave produced plasma in the presence of a strong magnetic field

M. Ghorbanalilu∗ and B. Shokri†
∗Physics Department of university of Tarbiat Moallem, Tabriz, Iran
†Laser and Plasma Research institute of shahid beheshti university, Tehran, Iran
Abstract. The plasma produced by interaction between microwave (MW) field weaker than the atomic field with circular
polarization with a dilute gas in the presence of a strong static magnetic field is studied. Solving the Vlasov equation with
proper approximations the electron distribution function (EDF) obtained for produced plasma in the non-relativistic case. The
obtained EDF shows that, the created plasma completely non-equilibrium and anisotropic. Making use of the EDF the all
elements of the dielectric tensor investigated.
Keywords: Discharges,Microwave, breakdown, instability, Weibel
PACS: 52.40.Db,52.35.Hr
There are various ways to supply the necessary energy for plasma generation to a neutral gas. 1 Electrons and ions are
produced in the gas phase when electrons with sufficient energy collide with the neutral atoms and molecules in the
feed gas. The most widely used method of generating and sustaining a low-temperature plasma for technological and
technical application is by applying a microwave electric field to a neutral gas. Any volume of a neutral gas always
contains a few electrons and ions that are formed, for example, as the result of the interaction of cosmic rays or radio
active radiation with the gas. These free charge carriers are accelerated by the MW field and new charge particles
may be created when these charge carriers collide with atoms and molecules in the gas. Charge carriers accelerated
in the MW field couple their energy into the plasma via collisions with other particles. Electrons retain most of their
energy in elastic collision with atoms and molecules because of their small mass and transfer their energy primarily in
inelastic collisions. This leads to an avalanche of charged particles that is eventually balanced by charge carrier loss, so
that a steady state plasma develops. In breakdown physics one deals with a medium ranging from an essentially neutral
gas with very small densities of charge particles to a weakly ionized plasma with a small fraction of charge particles
together with a bulk of neutral particles. Although the charged species only make up a small fraction of the total number
of particles or particle density of the medium, their charge, and the concomitant force and conductivity, give the plasma
properties completely different from those of a neutral gas. The interaction between intense MW fields and a neutral
gas opens new possibilities for studying the fundamental plasma properties. In such plasmas the electron distribution
is non-equilibrium and may give rise to various plasma instabilities. 2−7The main feature of this interaction is the gas
ionization mechanism. When MW field amplitude is comparable to the atomic field strength E a ≈ 5.1×109 V cm−1
the tunneling ionization becomes an important mechanism for direct ionization of the gas atoms. 8−10 However, the
MW fields generated by the present day pulsed duration sources are weaker than the atomic field. The kinetic effects
associated with the specific features of the electron distribution are the key role in the plasma processes. These features
are completely governed by the pulse parameter of theMWfield due to the short interaction time. It is well-known that
MW fields are capable of manifesting weakly relativistic behavior of electrons produced because relativistic effects
come into play when the kinetic energy of oscillating electron in an electromagnetic field is comparable to the electron
rest mass energy.5 In the previous work we have been studied the breakdown phenomenon when the strongMW field
with linear and circular polarization interact with a dilute gas and generate the plasma in the non-relativistic regime.
It was shown that this kind of plasma completely anisotropic and the dielectric tensor elements found for such kind of
plasma.2 In the present paper we wish to obtain the dielectric tensor elements in the non-relativistic regime in the case
of that the plasma generated with circularly polarized MW field frequency around ω 0  2×109−2×1010 s−1 by
the presence of a strong static magnetic field perpendicular to the MW field.
The thermal velocity of the electrons in a discharge plasma can be neglected in comparison to the electron oscillation
velocity in theMWradiation field. Since the collision frequency is much smaller than theMWfield frequency, we can
ignore the collisional stochastization of the forced electron oscillation as well. Furthermore, if plasma density n e(t)
produced by the field during gas breakdown, is less than the critical density (that is ω 2
0 > ω2
Le = 4π ne2/m) we can
neglect the effect of the polarization field. Moreover, the plasma density is assumed to be less than the neutral gas
density n0 so that the latter can be considered constant. We also suppose that the field was adiabatically switched on
in the infinite past. Furthermore, we can assume that the MW radiation electric field amplitude E is constant during a
single field period. Therefore, the kinetic SUMMERY AND CONCLUSION
In analyzing the interaction between high frequency MW field by circular polarization with a dilute neutral gas we
obtain the EDF of the produced plasma in the presence of the strong static magnetic field perpendicular the MW field.
Making use of this EDF we found the all dielectric tensor elements. This tensor shows that the plasma anisotropic and
may give rise to various instability. In the feature work we wish to study the Weibel instability for produced plasma.
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