Electrostatic instabilities excited by an energetic ion beam are examined as a possible plasma heating mechanism. The dielectric properties of electrostatic waves in a uniform magnetized plasma are studied for a warm ion beam propagating at an arbitrary angle with respect to the magnetic field. The instability threshold and growth rate are calculated for the resonant ion-beam and ion- acoustic modes. The quasi-linear moment equations are used to follow the self-consistent evolution of the macroscopic plasma properties. A comparison is made with the collisional slowing-down rate of the beam. For the fastest growing modes it is found that the quasi-linear slowing-down time is significantly shorter than the coffisional slowing-down time.

Three-dimensional plots of dispersion in a cold anisotropic plasma are presented. The ω(κ, θ) surfaces provide a clear picture of the behaviour of cold plasma waves as the direction of propagation is varied. The group velocity (dω/dκ) has a simple geometrical interpretation on the surfaces.

Kinetic theory for the nonlinear propagation of quasi-monochromatic extraordinary waves is presented. It reveals that propagation of an envelope of the extraordinary carriers is described by the nonlinear Schrödinger equation. In the cold plasma limit, a detailed analysis is carried out of the behaviour of the envelope of the upper- and the lower-hybrid waves at their respective resonant frequency ranges.

We discuss the possible magnetohydrodynamic configurations that can be realized as ‘most probable’ states compatible with the existence of certain constraints. These constraints can be either experimentally imposed constraints such as constant total electric current or magnetic flux, or constants of the motion, or both.

The concept of merging tokamak plasmas is proposed. It has potential applications for solving the problems of pseudo steady-state tokamak operation, refuelling, impurity removal and plasma heating. The currents in the two merging tokamak plasmas are in the same direction so that the columns attract each other. A model for the merging process is given.

An inverstigation is made of the transverse instability of plane soliton solutions of the nonlinear Schrödinger equation, including the case of an exponential nonlinearity. The analysis is based on a variational method, where specific trial functions are applied for the perturbations. Explicit expressions for the growth rates are given, showing good agreement with numerical results.

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.

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.

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.

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.

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.

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.

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.

Complex-variable, hodograph methods are used to solve the free-boundary problem of a plasma confined by its own skin currents and the field due to two parallel external conductors. In one extreme case the external field is a quadrupole field in the vicinity of the plasma; another extreme case describes the local perturbation of a large plasma by a single, nearby conductor.

A second-order theory for electrostatic instabilities driven by the free energy in the relative drifts of plasma components in an infinite homogeneous, Vlasov plasma is constructed. General expressions for the wave–particle exchange rates of momentum, energy and heat flux are derived. Under the boundary condition of constant current, new terms arise which significantly modify the conventional quasi-liner results. The theory is applied to the B = 0 ion-acoustic heat flux instability, and exchange rates are obtained which are suitable for inclusion in electron fluid models of thermal transport.

This paper (Hirose 1978) appears to contain an error. The space averaged beam kinetic energy density is, to second order where n and V are the space averaged beam density and velocity, ñ and V are the oscillating quantities. The last term is significant, as will be shown, but it has been omitted by Hirose.

The points raised by Schmidt (1979) are irrelevant and do not invalidate my paper (Hirose 1978). He has overlooked the beam deceleration and consequent obvious relationship, where V (t) is the beam drift velocity at arbitrary time, V(0) is the initial beam velocity, nb1, is the perturbed beam density and vb1 is the perturbed beam velocity. It is obvious that V(t) < V(0) due to beam deceleration caused by the instability as shown by Shapiro (1963) and also in the subject paper (Hirose 1978).