The viscosity of a plasma in a strong magnetic field

The viscosity of a plasma is studied under conditions in which a magnetic field influences particle collisions. The expressions obtained for the viscosity coefficients differ significantly from those obtained in the normal theory. It is shown that in sufficiently strong magnetic fields a temperature difference arises between the electron and ion plasma components which is proportional to the drift velocity and depends logarithmically on the magnetic field strength.     

Stabilization of plasma flow in a transverse magnetic field

Results are given of a theoretical and experimental investigation of the intensive interaction between a plasma flow and a transverse magnetic field. The calculation is made for problems formulated so as to approximate the conditions realized experimentally. The experiment is carried out in a magneto-hydrodynamic (MHD) channel with segmented electrodes (altogether, a total of 10 pairs of electrodes). The electrode length in the direction of the flow is 1 cm, and the interelectrode gap is 0.5 cm. The leading edge of the first electrode pair is at x = 0. The region of interaction (the region of flow) for 10 pairs of electrodes is of length 14.5 cm. An intense shock wave S propagates through argon with an initial temperature T_o = 293 °K and pressure p_o = 10 mm Hg. The front S moves with constant velocity in the region x < 0 and at time t = 0 is at x = 0. The flow parameters behind the incident shock wave are determined from conservation laws at its front in terms of the gas parameters preceding the wave and the wave velocity W_S. The parameters of the flow entering the interaction region are as follows: temperature T ₀ ¹ = 10,000 °K, pressure P ₀ ¹ = 1.5 atm, conduction ₀ ¹ = 3000 ^–1·m^–1, velocity of flow u ₀ ¹ = 3000 m·sec^–1, velocity of sounda ₀ ¹ = 1600 m·sec^–1, degree of ionization = 2%, 0.4. The induction of the transverse magnetic field B = [0, B_y(x), 0] is determined only by the external source. Induced magnetic fields are neglected, since the magnetic Reynolds number Re_m 0.1. It is assumed that the current j = (0, 0, jz) induced in the plasma is removed using the segmented-electrode system of resistance R_e. The internal plasma resistance is R_i = h(A)^–1 (h = 7.2 cm is the channel height; A = 7 cm² is the electrode surface area). From the investigation of the intensive interaction between the plasma flow and the transverse magnetic field in [1–6] it is possible to establish the place x* and time t* of formation of the shock discontinuity formed by the action of ponderomotive forces (the retardation wave R_T), its velocity W_T, and also the changes in its shape in the course of its formation. Two methods are used for the calculation. The characteristic method is used when there are no discontinuities in the flow. When a shock wave R_T is formed, a system of nonsteady one-dimensional equations of magnetohydrodynamics describing the interaction between the ionized gas and the magnetic field is solved numerically using an implicit homogeneous conservative difference scheme for the continuous calculation of shock waves with artificial viscosity [2].Translated from Izvestiya Akademiya Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 112–118, September–October, 1977.     

Kelvin-Helmholtz instability of a compressible plasma in a magnetic field

The Kelvin-Helmholtz instability of a compressible plasma in a uniform magnetic field with respect to disturbances propagating along the flow is considered. First, the case with the magnetic field parallel to the direction of streaming is considered. The result given by Sen [4] that the compressibility effects destabilize an otherwise neutrally stable system even in the hydrodynamic limit is apparently erroneous. Re-examination of the dispersion relation in the limit of small compressibility effects shows that the latter reduce the growth rate of an otherwise unstable disturbance. Attention is also drawn to errors in the calculations of Fejer [2] in the limit of small compressibility effects. Next, the case with the magnetic field transverse to the direction of streaming is considered. It is found that the transverse magnetic field does influence the stability of the system when the compressibility effects are present, contrary to the result given by Chandrasekhar [1] for the case of an incompressible plasma. However, interestingly enough, the compressibility effects are effectively reduced if a transverse magnetic field is present! It is further shown that the transverse magnetic field reduces the stability of the system.     

Time-of-flight probing of a plasma jet in a magnetic field

Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 1, pp. 8–11, January–February, 1991.     

Dispersion of a plasma cloud in a uniform magnetic field

The numerical solution of the two-dimensional gasdynamical problem of the dispersion of a plasma cloud in a magnetic field which is uniform to infinity is described. The disturbance of the field and the deformation of the cloud are taken into account self-consistently.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 4, pp. 146–148, July–August, 1974.In conclusion the authors thank A. I. Barchenkov, G. V0 2harova, S. A. Kuchai, V. G. Rogachev, and V. P. Statsenko for valuable advice and assistance in the work.     

Hydrodynamic stability of dense plasma in a corrugated magnetic field

The hydrodynamic stability of plasma in a corrugated magnetic field is considered. A stability criterion is established for flute oscillations; it is valid for arbitrary values of β = 8πp/B². In a fairly long system unstable flute perturbations with a wavelength much greater that the period of corrugation always exist. The equations of motion are solved for these most dangerous perturbations, and the instability increments are derived for the case of an ideal plasma and also with due allowance for viscosity. The viscosity is considerable for large β and may lead to a reduction by a factor of ～ √β in the increments.     

Convective instability in a rapidly rotating fluid layer in the presence of a non-uniform magnetic field

Magnetoconvective instabilities in a rapidly rotating, electrically conducting fluid layer heated from below in the presence of a non-uniform, horizontal magnetic field are investigated. It was first shown by Chandrasekhar that an overall minimum of the Rayleigh number may be reached at the onset of magnetoconvection when a uniform basic magnetic field is imposed. In this paper, we show that the properties of instability can be quite different when a non-uniform basic magnetic field is applied. It is shown that there is an optimum value of the Elsasser number provided that the basic magnetic field is a monotonically decreasing or increasing function of the vertical coordinate. However, there exist no optimum values of the Elsasser number that can give rise to an overall minimum of the Rayleigh number at the onset of magnetoconvection if the imposed basic magnetic field has an inflexion point. The project supported by the National Natural Science Foundation of China (40174026 and 40074041)     

Magnetohydrostatic behaviour of a plasma column in a decreasing external axial magnetic field

A study is made of the magnetohydrostatic behaviour of a plasma column in a decreasing external axial magnetic field by exploiting its analogy with the behaviour of a vortex tube embedded in a decelerating irrotational flow. The theory that considers only the initial and the final static states, ignoring the dynamics of the transition, predicts that the increased expansion of the plasma column in a decreasing external axial magnetic field becomes catastrophic and the column would burst at a critical value of the latter.     

Linear response of a plasma in a magnetic field to localized initial vorticity

It is established that for three-dimensional disturbances the long-range effect is observed even in the absence of boundaries. The problem of the evolution of the electrodynamic and gas dynamic disturbances created by a localized vorticity source is considered. It is shown that acoustic disturbances of a nonlocal nature are formed. The spatial structure of the electric potential and the nonlocal electric field created by localized initial vorticity at a finite value of the Hall parameter is investigated.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 109–114, March–April, 1990.     

Analysis of the transient thermal field and heat flux in circular plates, heated rapidly by a fast-decaying magnetic field

The rapid heating of a circular conducting plate by a magnetic field decaying exponentially with time and its transition to a final steady-state is studied for the cases of both isolated and non-isolated plates. Analytic expressions are derived for the thermal field, the heat flux and the relaxation times. Both the ’‘thin” and the “thick” aspects of the problem are investigated. Emphasis is placed upon some characteristic parameters arising from the analytical solution. Attention is paid to the time constants, related to the combined (conduction and convection) thermal process. In fact, the ratio of these time constants determines the transition process up to the final steady-state of each region of the plate.