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Besides the relation between the wave vector $bm k$ and the complex frequency $omega$, wave polarization is useful for characterizing the properties of a plasma wave. The polarization of the electromagnetic fields, $delta bm E$ and $delta bm B$, have been widely used in plasma physics research. Here, we derive equations for the density and velocity perturbations, $delta n_s$ and $delta{bm v}_s$, respectively, of each species in the electromagnetic kinetic plasma dispersion relation by using their relation to the species current density perturbation $delta {bm J}_s$. Then we compare results with those of another commonly used plasma dispersion code (WHAMP) and with those of a multi-fluid plasma dispersion relation. We also summarize a number of useful polarization quantities, such as magnetic ellipticity, orientation of the major axis of the magnetic ellipse, various ratios of field energies and kinetic energies, species compressibility, parallel phase ratio, Alfven-ratio, etc., which are useful for plasma physics research, especially for space plasma studies. This work represents an extension of the BO electromagnetic dispersion code [H.S. Xie, Comput. Phys. Comm. 244 (2019) 343-371] to enhance its calculation of polarization and to include the capability of solving the electromagnetic magnetized multi-fluid plasma dispersion relation.
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We present the first observation of instability in weakly magnetized, pressure dominated plasma Couette flow firmly in the Hall regime. Strong Hall currents couple to a low frequency electromagnetic mode that is driven by high-$beta$ ($>1$) pressure profiles. Spectroscopic measurements show heating (factor of 3) of the cold, unmagnetized ions via a resonant Landau damping process. A linear theory of this instability is derived that predicts positive growth rates at finite $beta$ and shows the stabilizing effect of very large $beta$, in line with observations.
Wave properties and instabilities in a magnetized, anisotropic, collisionless, rarefied hot plasma in fluid approximation are studied, using the 16-moments set of the transport equations obtained from the Vlasov equations. These equations differ from the CGL-MHD fluid model (single fluid equations by Chew, Goldberger, and Low, 1956) by including two anisotropic heat flux evolution equations, where the fluxes invalidate the double polytropic CGL laws. We derived the general dispersion relation for linear compressible wave modes. Besides the classic incompressible fire hose modes there appear four types of compressible wave modes: two fast and slow mirror modes - strongly modified compared to the CGL model - and two thermal modes. In the presence of initial heat fluxes along the magnetic field the wave properties become different for the waves running forward and backward with respect to the magnetic field. The well known discrepancies between the results of the CGL-MHD fluid model and the kinetic theory are now removed: i) The mirror slow mode instability criterion is now the same as that in the kinetic theory. ii) Similarly, in kinetic studies there appear two kinds of fire hose instabilities - incompressible and compressible ones. These two instabilities can arise for the same plasma parameters, and the instability of the new compressible oblique fire hose modes can become dominant. The compressible fire hose instability is the result of the resonance coupling of three retrograde modes - two thermal modes and a fast mirror mode. The results can be applied to the theory of solar and stellar coronal and wind models.
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The tearing mode instability is one important mechanism that may explain the triggering of fast magnetic reconnection in astrophysical plasmas such as the solar corona and the Earths magnetosphere. In this paper, the linear stability analysis of the tearing mode is carried out for a current sheet in the presence of a guide field, including the Hall effect. We show that the presence of a strong guide field does not modify the most unstable mode in the two-dimensional wave vector space orthogonal to the current gradient direction, which remains the fastest growing parallel mode. With the Hall effect, the inclusion of a guide field turns the non-dispersive propagation along the guide field direction to a dispersive one. The oblique modes have a wave-like structure along the normal direction of the current sheet and a strong guide field suppresses this structure while making the eigen-functions asymmetric.
A two-fluid flowing plasma model is applied to describe the plasma rotation and resulted instability evolution in magnetically enhanced vacuum arc thruster (MEVAT). Typical experimental parameters are employed, including plasma density, equilibrium magnetic field, ion and electron temperatures, cathode materials, axial streaming velocity, and azimuthal rotation frequency. It is found that the growth rate of plasma instability increases with growing rotation frequency and field strength, and with descending electron temperature and atomic weight, for which the underlying physics are explained. The radial structure of density fluctuation is compared with that of equilibrium density gradient, and the radial locations of their peak magnitudes are very close, showing an evidence of resistive drift mode driven by density gradient. Temporal evolution of perturbed mass flow in the cross section of plasma column is also presented, which behaves in form of clockwise rotation (direction of electron diamagnetic drift) at edge and anti-clockwise rotation (direction of ion diamagnetic drift) in the core, separated by a mode transition layer from $n=0$ to $n=1$. This work, to our best knowledge, is the first treatment of plasma instability caused by rotation and axial flow in MEVAT, and is also of great practical interest for other electric thrusters where rotating plasma is concerned for long-time stable operation and propulsion efficiency optimization.
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