Magnetohydrodynamic instabilities in a weakly ionized, radiating plasma

Abstract

A unified, linear theory is formulated for MHD waves at low magnetic Reynolds number, propagating transverse to the magnetic field in a weakly ionized, radiating plasma. The set of equations obtained from a two-fluid model yields a fifth-order dispersion relation whose roots correspond to four waves: magnetoacoustic (a paired wave), thermal, electrothermal, and "ionization-rate." To bring out the physics of each of these waves, simplifying assumptions are made, and "simple" analytical wave solutions are found. By taking advantage of the wide separation of the roots in the complex plane, "distinct" wave solutions are obtained in which many limitations of the "simple" wave solutions are absent and which are in excellent agreement with the roots of the full dispersion relation, obtained numerically. Both thermal and magnetoacoustic waves are shown to require a two-fluid model for proper description. In particular, the latter mode requires the inclusion of the rate of change of electron enthalpy for wavelengths < 0.1 m, at typical MHD generator conditions. The electrothermal wave instability region is much larger than previously thought, whereas the "ionization rate wave" is always stable.

Plasma Behavior in a High‐Temperature Noble Gas Plasma Disk‐Shaped MHD Power Generator

“…The shape and the rotation direction seem to be the same as with nonuniform structure that occurs at weak ionization of noble gas in seed-plasma scheme [17]. from dispersion equations that variation of plasma parameters occurs mostly without relative speed with respect to fluid [18]. Figure 5 shows the detailed distribution of electron temperature at 90 μs and θ = 0°.…”

“…This is consistent with the conclusion drawn by Hougen and colleagues. from dispersion equations that variation of plasma parameters occurs mostly without relative speed with respect to fluid [18]. Here, there is one wave of ionization degree and two waves of electron temperature, and the one wave of ionization degree propagates between the two waves of electron temperature.…”

Radio-frequency power assistance on a compact magnetohydrodynamic electrical power generator under high-density magnetic flux

“…Local steady-state analysis taking the linear theory of ionization instability into account 3-6 ͓Figs. [11][12][13] In comparison with the case of previous larger-scale MHD generators using lower-density magnetic flux, 14-18 the control of the plasma state is more vital for the compact MHD generator owing to the narrow plasma stable region under high-density magnetic flux. However, a nonequilibrium plasma will be conditionally unstable if the Hall parameter exceeds its critical value.…”

Behavior of magneto‐acoustic waves in a nonequilibrium subsonic disk MHD generator

“…Research on nonequilibrium MHD generators using linear perturbation analysis has confirmed that four types of waves exist in the plasma and electric fluid inside a generator: an electrothermal wave, an ionization-rate wave, a magneto-acoustic wave, and a thermal wave [1]. The electrothermal (E.T.)…”