This paper presents an investigation of the excitation of an upper hybrid wave in a hot collisionless magnetoplasma by a Gaussian EM beamm propagation perpendicular to the static magnetic field and having its electric vector polarized along the direction of the static magnetic field (ordinary mode). On account of the Gaussian intensity distribution of the EM beam the ponderomotive force becomes finite and the electorns are redistributed. The amplitude of the upper hybrid wave, which depends on the background electron concentration, is thus nonlinearly coupled with the EM wave. When the initial power of the EM wave is between the two critical powers Pcr1 and Pcr2 (Pcr1 < Pcr2) self-focusing occurs. On the other hand, for very low powers (P < Pcrl) and high powers (P > Pcr2), monotonic and oscillatory defocusing of the EM wave occurs. The dynamics of the excitation of the upper hybrid wave in these different power domains of the pump wave is accordingly modified. Moreover it is seen that the effect of changing the strength of the static magnetic field on the nonlinear coupling, and hence on the dynamics of the excitation of the upper hybrid wave, is significant.

The enhanced effective collision frequency in a turbulent plasma produced by a strong electric field is studied using a small toroidal device. The collision frequency is presented as a function of the electric field E and the average electron drift velocity. Two collision frequency regimes are identified. In the regime I where v ∝ E½, the current driven ion-acoustic turbulence is considered responsible.

The parametric decay of an intense electromagnetic ordinary wave, propagating perpendicular to a uniform static magnetic field, into an extraordinary wave and a backscattered ordinary wave is investigated. Formulae are derived for the growth rate and threshold power associated with the instability in a homogeneous plasma. An analysis of the spatial amplification of the decay waves in an inhomogeneous plasma is presented. The effects of the uniform static magnetic field on the backscattering in both homogeneous and inhomogeneous plasmas are studied numerically.

Propagation of waves in inhomogeneous, hot, isotropic plasma is described, assuming that the wavelength is much smaller than the scale-length of the plasma. The effect of the magnetic field topology on properties of waves is discussed in some detail. Coupling between the modes of oscillations is always present in an inhomogeneous ‘hot’ plasma. It is particularly strong for magneto- dynamic and sound waves propagating essentially along the fleidlines in the vicinity of a point where the phase velocities of the two modes are equal.

The resistive evolution of a magnetic field through force-free states is discussed, and some unusual features described.

A canonical distribution function is proposed to describe the instantaneous state of a single nonlinear wave–plasma system as it evolves quasi-statically in time. This function is based on two single particle constants of motion for a charged particle in a zero-frequency transverse magnetic wave and determines a wavenumber condition and two system energy constants. In the case of a onecomponent bi-Maxwellian plasma with T⊥/T‖>1, these relations are particularly simple and yield expressions for the energy in the magnetic wave field, the wavenumber, the temperatures, and the entropy of the system in terms of one unknown parameter, chosen to be the instantaneous temperature ratio, T⊥/T‖ The maximum value of the field energy is expressed in terms of only the initial temperature anisotropy, and is shown to be always less than of the system's total energy. The results are in good agreement with computer simulations of the electron Weibel instability.

Following Dungey's original magnetohydrodynamic formulation, a solution is obtained for the nonlinear evolution of a current discharge in the vicinity of a magnetic neutral line. For an ideal gas with constant conductivity and uniform mass density we obtain a particular exact solution in the limit of an initial, nearly sheet-like configuration. This particular solution implies special boundary conditions for the pressure and electric field at the surface of the conductor. If These conditions are not met, then the solution eventually breaks down before the current density becomes infinite. The time required for complete breakdown is determined by the wave propagation times from the surface of the fluid to the neutral line and by the diffusion time for the magnetic field through the fluid. For large conductivity and a small sound speed, the maximum current density achieved at the time of the solution's complete breakdown depends upon the ratio of the characteristic diffusion time to the Alfvén wave propagation time. In the limit of infinite conductivity or infinite extension of the fluid, the current density along the neutral line becomes infinite at π/23/2 times the Alfvénic scale time. At this same time the inflow Alfvenic Mach number approaches 21/2i while the outflow Alfvenic Mach number approaches infinity.

The definition of the generalized antipotential four-vector makes it possible to give a relativistically covariant variational formulation in the dynamics of ideal charged fluids. A special relativistically covariant form of Maxwell's equation is given. The antipotential four-vector does not explicitly appear in the Lagrangian density. The derivation of the equation of motion of a single charged particle is given, to illustrate the theory.

When an electron distribution drifts relative to the ions along a d.c. magnetic field, it is known that, above some critical drift velocity, a nearly field-aligned electromagnetic ion cyclotron instability may be excited. We extend the study of this instability over wide variations in plasma parameters, ion β in particular, and beyond marginal stability.Above threshold the most unstable waves propagate very obliquely to the ambient d.c. magnetic field at wavenumbers of the order of an inverse ion Larmor radius. At low ion β the critical electron drift normalized to the ion thermal velocity scales inversely as β i- ½ while, for β i>10-2, the critical drift scales as the ion thermal velocity. For the Te≈Tielectromagnetic ion cyclotron instabifity begins to have a lower threshold than the corresponding electrostatic instability at β i≈me/Mi. In a moderately high β i, homogeneous, collisionless plasma the electromagnetic ion cyclotron instability appears to have the lowest threshold of any current driven instability.

A pulse-power-driven, heavy-ion beam, ignition and inertial confinement system for thermonuclear microexplosions is proposed. The proposed method depends on already developed and tested techniques and has the potential of a high repetition rate, one of the requirements for a thermonuclear microexplosion reactor. In the proposed method, a space charge neutralized ion beam of modest intensity is projected into a long drift tube where it is radially confined by an applied axial magnetic field and axially compressed by a programmed variation of the diode voltage with time. Because the beam consists of a space charge neutralized flow of heavy ions, it behaves like a high atomic number plasma and, as such, rapidly looses internal energy by radiation during its axial compression. The axial compression proceeds isothermally until the beam becomes optically opaque where it reaches its maximum density. The axial beam compression greatly amplifies the final beam power over its initial value at the beam producing diode. In typical cases the initial beam power is ≃ 1010 W, and in a drift tube ≃ 100 meters long can be amplified ≃ 104 fold up to ≃ 1014 W; but much larger beam powers are also possible. The accelerating voltage is typically in the range of several 106V and the diode current several 103A. Because the collision mean free path in the beam is smaller than the beam length, some unavoidable deviation from the programmed diode voltage will not lead to a dispersion of the beam. For typical cases the beam has, at its maximum compression, an atomic number density of ≃ 1018 cm−3 and a radius of ≃ 1 cm. After being compressed to its final maximum density the beam can, from there on, be easily focused on to the thermonuclear target. The use of singly ionized heavy ions in combination with an accelerating voltage of several 106V has the further advantage that the ion velocities are of the order of several 108 cm sec−1, ideally matching the required optimal implosion velocity for the microexplosion target and thus implying a high beam energy conversion efficiency for ignition and confinement. For a final beam power of ≃ 1014W the diode cross-section is ≃ 102 cm2. With a diode cross-section ≃ 103 times larger, that is ≃ 10 m2, final beam powers up to ≃ 1017 W will be possible, opening the prospect for igniting the DD and perhaps the HB11 thermonuclear reactions.

Expressions for the conductivity tensors of all orders are obtained, for both relativistic and unrelativistic magnetized Vlasov–Maxwell plasmas, closely related to the well-known formula for the linear conductivity tensor. Thus the unperturbed orbit integrations and the ø-integration in velocity space have been performed and each conductivity tensor is expressed as an infinite series with terms involving ordinary Bessel functions. Jα(K⊥V⊥/ωc) and denominators of type ω–KzVz–αωc for integers.α a. The symmetries related to the Manley-Rowe relations are explicitly seen in the formulae presented. These conductivity tensor formulae provide a much better starting point than the basic equations for many nonlinear investigations.

Following a prescription invoked by Clemmow for cold plasma, we show how the method can be extended for a warm plasma so that self-consistent, large-amplitude, nonlinear waves can be obtained in an otherwise homogeneous, stationary system. Results are given for situations in the presence of an imbedded constant magnetic field. The relationship of phase and amplitude for such waves is more complex than in the cold plasma since the resultsobtained depend to a surprising degree on the form of the distribution functions invoked for the warm plasma, as we demonstrate by specffic example. We have pursued this problem for two reasons: first, Clemmow has noted that the need has arisen for a detailed investigation of the behaviour of large amplitude waves in plasma; secondly, the self- consistent, large-amplitude waves catalogued by Clemmow in the case of a cold plasma, have recently been shown to be highly unstable. The question then arises of a possible stabilizing influence in the case of a warm plasma. In this paper we investigate the first part of this problem: construction of self-consistent waves in warm plasma.

The methods of thermodynamic quantum field theory are used to obtain the equation of state and other thermodynamic properties of a plasma. Electrons may be partially degenerate, while ions are treated classically and restricted to charge number Z = 1 or 2. Results are obtained for densities in the range 1026–1034 m−3and for temperatures of 105–108 K.

For a high β screw pinch it is shown explicitly how the perturbation theory distorts the spectrum of ideal magnetohydrodynamics and guiding centre plasmas. In particular it is seen why the Cauchy integrals (present in the nonperturbative linearized guiding centre plasma model, and which are necessary for the isotropic pressure guiding centre plasma eigenvalue problem to differ from that for magnetohydrodynamics) are absent in the perturbation theory. This result holds also for axially and helically symmetric systems. The distortions in the m = 1 growth rates are also presented.

The jump conditions for MHD shock waves in partly ionized gases and for transverse ionizing shock waves in neutral gases are obtained in explicit forms suitable for calculation. The fractional ionization behind the shook front is determined by assuming the plasma reaches Saha ionizational equilibrium. Solutions to the MHD jump equations are calculated for geometries ranging from transverse to switch-on. Switch-on shock jump solutions are compared with experimental observations of switch-on shock waves in partly ionized hydrogen plasmas. Numerical solutions are presented for transverse ionising shock waves in hydrogen, using the pre-shock electric field as a variable parameter, and the modes of propagation of such shook waves are examined in detail. Ionization is found to play a significant role in medium shock speed behaviour, particularly in determining the density jump.

The resonant nonlinear interaction between three waves in a non-uniform rotating plasma is considered. The coupling coefficients are calculated for the case where the axis of rotation is parallel to an external magnetic field. Owing to similarities between this plasma and a gas of gravitating particles, it is likely that these coefficients can also be useful in the theory of galactic density waves.

The perturbation solution of the ordinary differential equations that describe exact nonlinear travelling plane waves leads to asymptotic expansions in powers of the (small) wave amplitude for both the proffle and the frequency of the waves. This paper shows how the Padé approximant method can be used to extend the validity of those expansions to larger amplitudes. The method is applied to the Duffing equation and to two types of nonlinear waves in a cold electron plasma: longitudinal oscillations and coupled transverse–longitudinal relativistic waves.

Finite Larmor radius corrections may be significant in plasma stability theory, and the geometry of the cylindrical pinch is appropriate for theoretical development. The study presented here is limited to calculation of the perturbation of the energy of a particle by a normal mode disturbance. This is found to be complicated when terms proportional to the square of the Larmor radius are retained. It is concluded that stability theory becomes identical with drift wave theory in complex geometry.

It is shown that Dupree's resonance function has a negative real asymptotic tail, so that the dispersion relation of the renormalized weak turbulence theory leads to unstable high phase velocity waves, even when the average distribution is a Gaussian. A possible explanation of this paradox is proposed.

The cylindrical MHD equilibrium equation is formulated in a manner suitable for numerical computations which require the application of a constraint. In this formulation a uniqueness theorem is proved for a free boundary equilibrium with a specified total current. Uniqueness is independent of the details of the current density and merely requires that the total current is compatible with the current density. Two uniqueness theorems for diffuse plasmas are also presented. Four free boundary examples are studied with a variety of constraints applied.