Using a perturbation technique, we derive Modified Korteweg—de Vries (MKdV) equations for a mixture of warm-ion fluid (γ i = 3) and hot and non-isothermal electrons (γ e> 1), (i) when deviations from isothermality are finite, and (ii) when deviations from isothermality are small. We obtain stationary solutions for these equations, and compare them with the corresponding solutions for a mixture of warm-ion fluid (γ i = 3) and hot, isothermal electrons (γ i = 1).

The paper discusses the dispersion relation for longitudinal electron waves propagating in a collisionless, homogeneous isotropic plasma, which contains both Maxwellian and suprathermal electrons. It is found that the dispersion curve, known to have two separate branches for zero suprathermal energy spread, depends sensitively on this quantity. As the energy half-width of the suprathermal population increases, the branches approach each other until they touch at a connexion point, for a small critical value of that half-width. The topology of the dispersion curves is different for half-widths above and below critical; and this can affect the use of wave-propagation measurements as a diagnostic technique for the determination of the electron distribution function. Both the distance between the branches and spatial damping near the connexion frequency depend on the half-width, if below critical, and can be used to determine it. The theory is applied to experimental data.

We consider two non-parallel beams, each of width a, that interact in a plasma and excite a wave that travels across their region of intersection. We determine the dependence of the amplitude of the excited wave on a for the limiting cases of large and small values of the ratio of the initial beam intensities.

The normal modes of oscillation of a cold dielectric plasma ring are analysed in the quasi-electrostatic approximation. An exact dispersion relation is derived, valid for all aspect ratios. Its solutions are shown to be extremely close to those of an infinite cylindrical plasma with cross-section equal to the minor cross-section of the ring, when the cylinder is considered as a wavelength-preserving limit of the toroidal geometry.

This paper considers the steady two-dimensional problem of regular reflexion and symmetric intersection of oblique magnetogasdynamic shock waves. It is assumed that the fluid medium is a non-viscous, non-heat-conducting, ideal gas of infinite electrical conductivity, and that the applied magnetic field is parallel to the velocity of the approaching stream. In view of the complexity of the shock relations, a graphical method is presented for determining the orientation and strength of the reflected shock wave in terms of the Laval number M*1 (flow speed divided by critical sound speed), the Alfvén number A1 (flow speed divided by Alfvén speed), and the shock angle ϑ 1 ahead of the incident shock. Moreover, the possible ranges of M*1, A1, and ϑ 1, for which regular reflexion may occur, are calculated and illustrated graphically for the case of a monatomic gas.

We investigate second-harmonic resonance for weakly nonlinear hydromagnetic waves travelling in a cold collisionless plasma by the method of multiple scales. We find that the second-harmonic resonance can occur between the magneto-acoustic modes; but it can occur neither between the magneto-acoustic and the Alfvé n modes, nor between the Alfvé n modes. The resonant frequency of the magneto-acoustic modes is characterized by the geometric mean of the ion and electron Larmor frequencies. We obtain steady-state solutions to the dynamical equations governing the second-harmonic resonance. The result of analysis shows that the envelopes of the two resonant waves are composed of two periodic wave- trains, two solitary pulses or a solitary pulse and a phase jump. We also extend the problem to more general dispersive wave systems.

This paper reports calculations of the collision-free expansion of a semi-infinite plasma. It is shown that the ion front is accelerated to velocities comparable with the thermal velocity of the electrons.

Equilibrium properties of linear theta-pinch plasmas are studied within the framework of the steady-state (∂ / ∂ t = 0) Vlasov– Maxwell equations. The analysis is carried out for an infinitely long plasma column aligned parallel to an externally applied axial magnetic field Bzext ê 2. Equilibrium properties are calculated for the class of rigid-rotor Vlasov equilibria, in which the jth component distribution function f j(H⊥, Pθ, υ 2) depends on perpendicular energy H⊥ and canonical angular momentum Pθ, exclusively through the linear combination H⊥ – ω jPθ, where ω j = const. = angular velocity of mean rotation. General equilibrium relations that pertain to the entire class of rigid-rotor Vlasov equilibria are discussed; and specific examples of sharp- and diffuse-boundary equilibrium configurations are considered. Rigid-rotor density and magnetic field profiles are compared with experimentally observed profiles. A general prescription is given for determining the functional dependence of the equilibrium distribution function on H⊥−ωjPθg in circumstances, where the density profile or magnetic field profile is specified.

A new systematic method of analysis of three-wave interactions is proposed, and applied to a description of interactions of waves (0, 1 and 2) in a homogeneous electron plasma, in which Landau damping is insignificant. Transverse, linearly polarized wave 0, which may represent an external (‘ pump’ ) wave, is assumed to be in resonance with longitudinal and transverse waves 1 and 2 already existing in a weakly-turbulent plasma. The rate (d W/ dt)j, at which energy is transferred from wave j to the others, is calculated, assuming that directions of propagation of resonating waves are restricted by conditions of three-wave resonance only. Conditions of the form (dW/dt)j = 0 constitute threshold criteria for amplification of wave j to occur. There is a brief discussion of processes during which the energy of one of the resonating waves remains constant, although energy is transferred between the other two waves. The relation between energy absorbed by the plasma and energy transferred between waves is evaluated.

The paper considers the two scattering instabilities photon decays into photon plus plasmon (t → t' + l) and photon decays into photon plus phonon (t → t' + s) and the two absorptive instabilities photon decays into plasmon plus plasmon (t → l + l' ) and photon decays into plasmon plus phonon (t → l + s). The corresponding growth rates and thresholds are determined for a homogeneous, unmagnetized plasma. The regimes of weak and moderately strong pump fields are examined, together with the possibility of purely-growing instabilities for the decays t → t' + s and t→ l + s.

A collisional electromagnetic dispersion relation is derived from two-fluid theory for the interchange mode coupled to the Alfvé n, acoustic, drift and entropy modes in a partly-ionized plasma. The fundamental electromagnetic nature of the interchange mode is noted: coupling to the intermediate Alfvé n mode is strongly stabilizing for finite k2. Both ion– viscous and ion–neutral stabilization are included; and it is found that collisions destroy the FLR cutoff at short perpendicular wavelengths.

The structure of the drift instability is examined in several density regimes. Let λ e be the total electron mean free path, kz the wave-vector component along the magnetic field, and ν ⊥ / ν ∥ the ratio of perpendicular ion diffusion to parallel electron streaming rates. At low densities (kz ν e > 1), the drift mode is isothermal, and should be treated kinetically. In the finite heat conduction regime

the drift instability threshold is reduced at low densities (v⊥/v‖<0·1) and increased at high densities (v⊥/v‖>0·1), as compared with the isothermal threshold. Finally, in the energy transfer limit (kzλe<(m/M)½), the drift instability behaves adiabatically in a fully-ionized plasma, and isothermally in a partly-ionized plasma, for an ion-neutral to Coulomb collision frequency ratio vin/vii>2(m/M)½ at Ti = Tc = Tn.

The stability of a bounded, homogeneous, neutralized plasma with counter- streaming electron beams is analysed. A water-bag model is used to describe the electron distribution in velocity space, so that finite beam temperature and a background plasma are included in the theory. For boundary conditions, the absorber– source wall (the diode boundary) and the reflecting wall are considered. For the former, growth-rate calculations indicate that the instability is a combination of charge bunching (counter-streaming) and diode circuit effect. As the diode length increases, the growth rate of all modes in the system approaches the maximum growth rate. For the reflecting wall, as the length increases, the maximum growth rate transfers to higher and higher order modes with shorter wavelength, while the growth rate of the lower-order modes goes to zero.

In this paper, we derive a kinetic equation and discuss its validity for a stationary turbulent plasma. We use, for this purpose, the Dupree— Weinstock model in the weak-coupling approximation, and take into account ballistic streams. Frictional effects appear, in addition to the velocity diffusion. The diffusion causes a resonance broadening, the friction causes a frequency shift. Our model is a generalization of the dressed test particle model, and leads to a kinetic equation formally similar to Balescu— Lenard' s. A comparison between our model and the Dupree ‘clump’ theory is developed. Physical quantities are conserved, the H theorem is satisfied; but the asymptotic solution is not necessarily a Maxwellian distribution function.

An attempt is made to trace the physical origin of the complex roots of the dispersion relation for a Maxwellian, non-relativistic, homogeneous, magnetized Vlasov plasma. For simplicity, the identification process is performed for the case of propagation perpendicular to the magnetic field. For a given real ω, there are infinitely many complex roots, in addition to a finite number of propagating solutions. The propagating waves correspond (in addition to the cold-plasma waves) to either the extraordinary Gross— Bernstein mode propagating just above the harmonics, or the pair of Dnestrovskij— Kostomarov modes (one ordinary and the other extraordinary) propagating just below the harmonics. The hot-plasma solutions asymptotically approach the harmonic frequencies as k‖→∞, and analytically continue across the harmonics as complex waves. These complex waves, originating in groups of three from each cyclotron harmonic, apparently remain distinct, giving rise to an infinity of complex roots for a given frequency (since there are an infinite number of cyclotron harmonics). Detailed analysis reveals that, for the ordinary and the extraordinary Dnestrovskij-Kostomarov modes, electric displacement and magnetic induction, respectively, are the dominant field components.

The exact surface-wave dispersion relation is expressed in terms of elementary functions for a plasma characterized by a ‘resonance’ velocity distribution function. An approximate form of the relation is derived for the case when the thermal velocity spread is much less than c. The pure surface wave obtained by dropping the term responsible for Landau damping is compared with that predicted on the basis of a fluid model of the plasma. The effect of Landau damping is then investigated, both by analytic approximations and by computation. Two branches of the solution to the dispersion relation are found; and it is shown that the surface wave suffers increasingly severe damping as the frequency grows beyond 1/ √ 2 times the plasma frequency. It is argued that qualitatively similar damping would be present were the plasma to have a Maxwellian equilibrium distribution function.