Dispersion relations for first-order oscillations in an infinite homogeneous two- component plasma, in response to an externally applied constant magnetic field and a right-hand circularly polarized external electric field, and with propagation vector parallel to the magnetic field, has been obtained. The external electric field, assumed to be spatially homogeneous, is perpendicular to the applied magnetic field. It has been shown that the left-hand mode is excited and is unstable when its frequency ≃ ν–ωρ, where ν is the frequency of the external electric field and ωρ is the characteristic plasma frequency. When the applied magnetic field is large, both the left- and right-hand modes are excited and may be unstable when their frequencies ≃ Ωic – ωρ where Ωic represent the electron (i = 1) and the ion (i = 2) cyclotron frequencies. The principal criterion for the validity of these results is the condition of spatial homogeneity of the external electric field.

The propagation of small monochromatic disturbances in a stable ideal magnetohydrodynamic fluid is treated by the method of geometric optics. The medium is trirefringent and requires six systems of rays. The problem of a point radiator is solved in the small wave-length limit where the theory holds.

It is shown that the relativistic Vlasov–Maxwell equations admit a solution very much like the transverse Alfvén wave of magnetohydrodynamic theory. This wave propagates as a plane electromagnetic wave of arbitrary amplitude, is noncompressive, is associated with fluctuations in direction (but not magnitude) of magnetic field, is characterized by a non-linear ‘dispersion relation’, and reduces in the limit of small amplitude to the transverse Alfvén mode of linearized plasma wave theory. The dispersion relation yields a criterion for the firehose instability which turns out to be the same as that derived from linearized theory.

The effect of stochastic high-frequency fields on the stability of electrostatic plasma oscillations in a magnetostatic field is studied. The stabilizing effect can be provided by diffusion in configuration co-ordinates, as well as in the longitudinal and transverse velocities. The parameters of the stochastic field for effective stabilization are estimated, as well as the influence of the accompanying escape of particles due to the stochastic fields.

The effects of ion-ion collisions, described by a Fokker-Planck operator in the kinetic equation, on an ion-acoustic plasma pulse, are studied. Our investigations show that the coffisions give a broadening of the pulse, and reduce the effect of interaction between the main plasma and the pulse.

The propagation and stability of drift waves is examined, by means of a perturbation technique, in geometries where the magnitude of the magnetic field varies periodically along the field lines. Two sets of modes are found which can be driven unstable by resonant particles trapped in the magnetic field non-uniformity. One set of modes consists of standing waves with wavelength twice that of the magnetic field non-uniformity. The other set of modes consists of standing waves composed essentially of the sum of a component which does not vary along the line and a component which is a standing wave with wavelength equal to the wavelength of the magnetic field non-uniformity. The advantage of this method is that it predicts simply and pictorially the real frequency of oscillation for these modes.

Jeans's criterion for instability is found to be changed only for the case of perturbations perpendicular to the magnetic field and rotation parallel to it, when rotation and finite Larmor radius effects tend to stabilize the plasma.

The problem of the linear stability of a plasma with density profiles

in a homogeneous magnetic field B = îzB0 has been solved exactly. The dispersion relation leads to stability criteria less severe than those obtained in the local approximation. As examples, we consider Bernstein waves and the low-frequency drift instability. In the second example the marginal stability curve

is given for different values of the parameters kx, Ri, Ri n′/n, with Ti = Te. Further, the same method is applied to a plasma with equilibrium distribution function in a linear electric potential φ = αx and a homogeneous magnetic field B = îxB0.

The observed response of a low-density magnetoplasma column to a pair of RF pulses near the cyclotron frequency is a series of pulses known as two-pulse echoes. A similar three-pulse echo train may be obtained by applying a third pulse. This behaviour involves some type of non-linearity, and for a low-density plasma the most promising mechanism appears to be velocity-dependent electron-neutral collisions. This gives velocity-dependent decay to induced currents, and velocity-dependent diffusion. The latter may be important in three-pulse echo formation. In this paper computations from these theories are compared with experimental data with these findings: (1) diffusion is not primarily responsible for three-pulse echoes; (2) the predictions of the collisional current decay theory are in reasonable agreement with the experimental results.

This paper considers the non-linear interaction between three resonant, modified ordinary electromagnetic waves, which propagate perpendicular to a constant magnetic field in a spatially homogeneous electron plasma. The coupling coefficients are calculated and discussed. Finally, a general formula, describing the interaction between three waves propagating at arbitrary angles to the static field, is derived.

The oscillations, excited by a pulsed dipole antenna at the upper hybrid resonance in a weakly inhomogeneous plasma, are investigated by the Wentzel—Kramers—Brillouin (WKB) approximation. In addition to a direct component, the field at a given distance from the transmitter is shown to consist in two obliquely reflected rays when the upper hybrid frequency WT is less than twice the electron gyro-frequency WH. The analytical expressions of the frequencies of the echoes intercepted by a moving receiver are given and the influence of the reception time t, the velocity VS of the receiver and the parameters of the plasma are thus pointed out.

As distinct from previous studies, the static magnetic field B0, the velocity of the receiver, and the gradient of the electron density ∂N/∂X, are here vectors of arbitrary directions. The choice of such a general model makes it possible to interpret most of the experimental data concerning the upper hybrid resonance in the ionosphere.

The effect of a test particle, moving through a two-dimensional Maxwellian plasma, has been studied both analytically and by computer simulation. For a stationary test particle, Debye shielding occurs. When the velocity of the test particle approaches the electron thermal velocity, there is a concentration of electrons several Debye lengths downstream, an effect which is essentially a heavily damped plasma oscillation. The analytic results agree closely with the computer simulation. As the velocity of the test particle increases, it is shown analytically that the damping diminishes, and eventually a fully developed plasma oscillation is established in the wake of the particle.

Inside any symmetrical double-humped plasma velocity distribution, all growing waves with real wave-number have zero phase velocity. Growth rates of such plasma oscillations are calculated for distributions made up of resonance functions and of Gaussian functions. The results are compared with an earlier calculation made with less realistic distribution functions with no infinite tails.

Stable, phase coherent ion plasma oscillations are found superimposed on the d.c. potential and current of positive coaxial corona discharges in air at pressures of the order of 1/100 of one atmosphere. The frequency of these oscillations, typically several hundred kHz, is a function of air density, and varies with the concentration of gaseous trace contaminants.

Waves, propagating transverse to the direction of the streaming of a plasma in the presence of a uniform external magnetic field, are unstable if the streaming exceeds a certain minimum value. The magnetic field reduces the growth rate of this instability, and also increases the value of the minimum streaming velocity, above which the system is unstable. The thermal motions in the plasma, however, tend to stabilize the system if the magnetic field is weak (i.e. , Ω being the electron cyclotron frequency, k the characteristic wave-number, and Vt the thermal velocity); but, in case of strong magnetic field (i.e. ), they increase the growth rate, provided (ωp being the electron plasma frequency).

The electron-energy distribution in a neon discharge is determined from the Boltzmann equation. Inelastic collisions with neutral atoms, as well as electron—electron Coulomb interactions, are included in the calculation. It is shown that, as predicted by Crescentini & Maroli (1968), the distribution is very close to the Druyvesteyn function when the electron density is very low (ne > 107 cm-3). The same conclusion, however, is not correct as the electron density increases to a higher value (ne > 1011 cm-3). In this case, the electron—electron Coulomb interactions play an important role in restoring the distribution toward a Maxwell jan function.

‘Effect of dissipation due to firehose instability on perturbation half-jet flow of a collisionless plasma’, by S. Mobioka and J. R. Spreitek. J. Plasma Physics, vol. 4, 1970, pp. 629–41

Equation (72) should be as follows: