The problem of arbitrary test current sources embedded in an infinite spatially homogeneous Vlasov plasma is considered. By computing the rate at which the test sources do work on the plasma, the energy emission into transverse and longitudinal waves is obtained. A variety of radiation problems can be handled by appropriate choice of the current sources. Use of the time varying dipole moment due to encounters between shielded electrons and ions leads to expressions for the bremsstrahlung spectra. If the currents are produced by the interaction of waves with density fluctuations, the scattering and coupling of waves is obtained. By equating the rate of emission of longitudinal or transverse waves to their rate of absorption, expressions for the steady‐state energy densities of such waves are obtained.

Radiation Processes in Plasmas

The nature of oscillations in the 1 kHz–60 MHz frequency range that have been observed during operation of Hall thrusters is quantitatively discussed. Contours of various plasma parameters measured inside the accelerating channel of a typical Hall thruster are used to evaluate the various stability criteria and dispersion relations of oscillations that are suspected to occur. A band by band up-to-date overview of the oscillations is carried out with a description of their observed behavior and a discussion of their nature and dependencies through comparison of the calculated contours to reported observations. The discussion encompasses the excitation of low frequency azimuthal drift waves that can form a rotating spoke, axially propagating “transit-time” oscillations, azimuthal drift waves, ionization instability-type waves, and wave emission peculiar to weakly ionized inhomogeneous plasmas in crossed electric and magnetic fields.

Plasma oscillations in Hall thrusters

The most intense, F region irregularities in the high-latitude ionosphere appear to be produced by convective plasma processes and in particular, by the fluid (gradient drift) interchange instability. Such irregularities are produced by convectively mixing plasma across a mean plasma density gradient with the transport of higher-density plasma into regions of lower-density plasma (and vice versa) leading to the development of an irregularity spectrum that extends in scale from about 10 km down to the ion gyroradius. The mean plasma density gradient that must be present to allow irregularity production by this interchange process appears to be associated with larger-scale (>10 km) plasma structure produced by other means. Because much of the recent progress on this research topic stems from this recognition, a significant portion of this review is dedicated to a description of the characteristics and processes of 10-km plasma structure and their relationships to those of smaller-scale irregularities. From this review, we synthesize a descriptive model of plasma structures in the high-latitude F layer that unifies most of the diverse and independent observations. For the large-scale plasma processes, the model includes (1) the formation of 1000-km-scale “patches” in the polar cap from solar-produced plasma that is transported poleward from lower latitudes; (2) the reconfiguration of patches as they convect into the auroral region and become the latitudinally confined, but longitudinally extended, plasma density enhancements near the equatorward auroral boundary; and (3) the production of localized enhancements and depletions along the poleward auroral boundary by soft-particle precipitation and large but localized electric fields. In the model, the most intense, smaller-scale irregularities are in spatial proximity to these large-scale plasma features, the implication being that the presence of the latter allows formation of the former. The irregularity characteristics are consistent with production by the instability and a morphology controlled by (1) a “slip” velocity (i.e., plasma drift relative to the neutral gas) that is moderately small except in regions of nonuniform plasma convection or under time-varying conditions (e.g., substorms, pulsation events) and (2) a highly conducting auroral E layer that damps irregularity growth and enhances decay. The final irregularity spectrum appears to be produced by (1) global convective processes acting on solar-produced plasma at the largest scales (>50 km), (2) particle precipitation at scales greater than 10 km, (3) perhaps some form of wave activity around 10 km, and (4) the instability at the smaller scales (<10 km).

High-Latitude F-Region Irregularities: A Review and Synthesis

The Z-pinch, perhaps the oldest subject in plasma physics, has achieved a remarkable renaissance in recent years, following a few decades of neglect due to its basically unstable MHD character. Using wire arrays, a significant transition at high wire number led to a great improvement in both compression and uniformity of the Z-pinch. Resulting from this the Z-accelerator at Sandia at 20 MA in 100 ns has produced a powerful, short pulse, soft x-ray source >230 TW for 4.5 ns) at a high efficiency of ~15%. This has applications to inertial confinement fusion. Several hohlraum designs have been tested. The vacuum hohlraum has demonstrated the control of symmetry of irradiation on a capsule, while the dynamic hohlraum at a higher radiation temperature of 230 eV has compressed a capsule from 2 mm to 0.8 mm diameter with a neutron yield >3 × 1011 thermal DD neutrons, a record for any capsule implosion. World record ion temperatures of >200 keV have recently been measured in a stainless-steel plasma designed for Kα emission at stagnation, due, it was predicted, to ion-viscous heating associated with the dissipation of fast-growing short wavelength nonlinear MHD instabilities. Direct fusion experiments using deuterium gas-puffs have yielded 3.9 × 1013 neutrons with only 5% asymmetry, suggesting for the first time a mainly thermal source. The physics of wire-array implosions is a dominant theme. It is concerned with the transformation of wires to liquid-vapour expanding cores; then the generation of a surrounding plasma corona which carries most of the current, with inward flowing low magnetic Reynolds number jets correlated with axial instabilities on each wire; later an almost constant velocity, snowplough-like implosion occurs during which gaps appear in the cores, leading to stagnation on the axis, and the production of the main soft-x-ray pulse. These studies have been pursued also with smaller facilities in other laboratories around the world. At Imperial College, conical and radial wire arrays have led to highly collimated tungsten plasma jets with a Mach number of >20, allowing laboratory astrophysics experiments to be undertaken. These highlights will be underpinned in this review with the basic physics of Z-pinches including stability, kinetic effects, and finally its applications.

A review of the dense Z-pinch

Physics and technology of magnetron sputtering discharges

A weakly ionized plasma in a uniform magnetic field is considered. Application of a potential across the magnetic field results in a steady current flow, owing to the finite conductivity. It is shown that this steady state is unstable if the plasma density is nonuniform in the direction of the applied electric field and if the applied potential is large enough. It is necessary that the sign of the product of the electric field and the density gradient be positive.

Instability of a Partially Ionized Plasma in Crossed Electric and Magnetic Fields

Plane parallel flow between rigid plates of an incompressible inviscid fluid is considered. A necessary and sufficient condition for infinitesimal stability is derived in the special case where w″ has only a single zero and w′ > 0 where w(x) is the velocity profile between the plates. A general sufficient condition for instability is also obtained.

Necessary and Sufficient Condition for the Stability of Plane Parallel Inviscid Flow

A set of equations are derived for the amplitudes of the oscillating modes which arise in a slightly unstable weakly ionized plasma The plasma is initially in a time‐independent but spatially dependent and linearly stable equilibrium It becomes unstable upon a small fractional increase Δ of some external parameter The amplitudes of the final steadily oscillating states, the frequency shifts of these states, and the transport rates are determined in terms of Δ

Nonlinear Transport in Weakly Ionized Plasma

A weakly ionized plasma in a nonuniform magnetic field exhibits an instability analogous to the well‐known flute instability of a fully ionized plasma. The instability sets in at a critical magnetic field. When this external field is slightly increased above the critical value by the fractional amount Δ, to begin with only one mode goes unstable and it grows in amplitude to a finite limiting value. Using a general theory of the nonlinear behavior derived in an accompanying paper, we evaluate the mode amplitude and frequency shift as functions of Δ, as well as the corresponding enhanced particle transport. The results are first obtained in the quasilinear approximation, but it is then shown that the mode‐coupling contribution is negligible and hence that the result is generally valid for small Δ.

Convection of Weakly Ionized Plasma in a Nonuniform Magnetic Field

The starting point is the Liouville equation for the density in phase space of a system of charged particles and a denumerably infinite set of field oscillators. By integrating out the coordinates of all but a finite number of particles and oscillators one obtains a chain of equations relating the reduced distribution functions. A complete solution to the chain is obtained by a generalization of the expansion method of Rosenbluth and Rostoker. In lowest order, a coupled set of self‐consistent field equations in the one‐particle and one‐oscillator distributions is obtained. These are partially decoupled to give the usual Vlasov equation and a companion equation for the oscillator distribution. In first order one obtains a similar set of equations for the two‐particle and the particle‐oscillator correlation functions. An entirely similar pair of equations then relates the first‐order distribution functions themselves. It appears that the general solution is obtained by the steady unfolding of higher correlation functions in terms of higher and higher self‐consistent field equations. The first‐order equations can be regarded as a ``Fokker‐Planck'' equation for particles and a ``Fokker‐Planck'' equation for radiation.

Kinetic Equations for Plasma and Radiation

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