H. H. Kuehl

Electromagnetic Radiation from an Electric Dipole in a Cold Anisotropic Plasma

The general solution to the problem of monochromatic radiation from an electric dipole in a magnetically biased, cold, tenuous plasma is presented. It is found that, generally, several waves exist in the radiation zone, traveling in different directions with different indices of refraction. For certain ranges of the plasma, gyro, and operating frequencies, the field becomes very large in certain directions compared with that in other directions, producing highly directive radiation characteristics. In general, the expression for the field is quite complicated although several special cases are treated which yield simple solutions. For high operating frequency it is found that the radiation pattern is identical to the isotropic case although a Faraday rotation takes place. Solutions are given for low and very low frequencies which place in evidence the guiding nature of the magnetostatic field. For the case of a large magnetostatic field it is shown that only two waves exist and that the time‐average power...

Interference structure near the resonance cone

The interference structure near the resonance cone of an oscillating point charge in a warm magnetized plasma is investigated theoretically, using the quasistatic approximation and neglecting ion motion. Depending on the frequency and plasma parameters, the interference structure appears inside, outside, or on both sides of the resonance cone. For frequencies less than both the plasma and cyclotron frequencies, the structure lies inside the resonance cone except for frequencies near the cyclotron frequency where the amplitude is small because of cyclotron damping. For frequencies between the upper‐hybrid frequency and the larger of the cyclotron and plasma frequencies, the structure lies outside the resonance cone provided the frequency and angle are sufficiently removed from the upper‐hybrid frequency and 90°, respectively. A simple expression for the angular interference spacing is derived.

Electric field and potential near the plasma resonance cone

The electric field and potential at and close to the resonance cone of an oscillating point charge and dipole in a warm magnetized plasma are investigated theoretically, neglecting ion motion. Approximate expressions are derived for both a drifting and a stationary Maxwellian plasma. The shift in angle of the maximum potential due to plasma drift is shown to be small and dependent on both drift and thermal velocities if the drift velocity is much less than the thermal velocity. For a stationary plasma, a comparison of the potential of a point charge with its electric field and with the potential and field of an arbitrarily‐oriented dipole shows that the potential of the point charge has the following distinguishing characteristics: The maximum lies closest to the cold‐plasma resonance cone; the angular location of this maximum is least dependent on damping mechanisms in the plasma; the interference structure is the largest. The approximate expression for potential yields results in good agreement with exi...

Reflection of an ion-acoustic soliton by plasma inhomogeneities

The coupled equations governing oppositely traveling, weakly nonlinear and weakly dispersive ion‐acoustic waves in a weakly inhomogeneous plasma are derived. From these equations, the reflected wave due to an ion‐acoustic soliton propagating in a weakly inhomogeneous plasma is obtained. It is shown that this reflected wave is small compared with both the trailing shelf and the soliton amplitude decrease due to energy transfer to the shelf.

Finite‐amplitude ion‐acoustic solitons in weakly inhomogeneous plasmas

The properties of an ion‐acoustic soliton in a weakly inhomogeneous plasma are studied. Unlike previous analyses, the soliton amplitude is not required to be small. The ion generation rate is assumed to be either proportional to the electron density or to be uniform. Assuming that the local soliton width is small compared with the scale length of the plasma inhomogeneity, a perturbation theory is developed which gives the local speed and amplitude of the soliton. For a small amplitude soliton, simple expressions for the local soliton speed, peak soliton potential, and peak soliton ion density are derived. It is shown that both the soliton velocity relative to the ion drift velocity and the peak soliton potential do not vary greatly as the soliton moves from the plasma center toward the sheath. The peak ion density, however, varies over a wider range. These results are shown to agree with those from direct numerical integration of the basic equations.

Cylindrical and spherical Korteweg–deVries solitary waves

Solitary wave solutions for the dimensionally modified Korteweg–deVries equation appropriate to symmetric ion acoustic waves in both cylindrical and spherical geometrics are presented. Expressions are given for the amplitude, velocity, width, and energy. The energy in the main body of the solitary wave continually decreases due to energy transfer to the trailing structure. The solutions are verified by comparison with a numerical integration of the differential equation.

Modified Korteweg–de Vries solitary wave in a slowly varying medium

A solitary wave solution of the modified Korteweg–de Vries equation with slowly varying coefficients is derived for a soliton initial condition. It is shown that a shelf is generated behind the main peak, and that an irreversible transfer of energy occurs from the main body of the solitary wave to the shelf.

Excitation of Waves in a Warm Plasma by a Current Source

The general expression for the electromagnetic field due to an arbitrary monochromatic current source in an unbounded, homogeneous, warm, collisionless plasma in the absence of a magnetostatic field is derived. A hydrodynamic description is used in which ion and electron motion is included. The general results are specialized to the case of an electric dipole source. It is found that the field is generally composed of three parts which, in the radiation region, correspond to the well‐known transverse, longitudinal electron, and longitudinal ion waves. The power flow in the radiation region is shown to be largest along the axis of the dipole for low frequencies whereas the maximum occurs perpendicular to the dipole at high frequencies.

Resonances and Wave Conversion below the Second Electron Cyclotron Harmonic

A theory is given describing the conversion of fast‐to‐slow waves and vice versa, propagating perpendicular to a static magnetic field in a planar geometry for frequencies near and below the second electron cyclotron harmonic. The half‐space and slab are treated with collisional effects included. It is shown that the power conversion between the two wave types is directly proportional to the scale length of the density gradient at the point in the plasma where the hybrid resonance condition is satisfied provided this scale length is small compared to a free‐space wavelength. In spite of the small coupling, appreciable interaction is shown to take place between a transverse wave incident on a plasma slab and the longitudinal wave when a resonance condition exists for the longitudinal wave. The linewidth of the resonances is found to depend on both the density gradient near the hybrid resonance points and collisional effects.

Reflection of an ion‐acoustic soliton from a planar boundary

The reflection of a planar ion‐acoustic soliton from an insulated or a biased metallic planar wall is studied. Numerical solutions of the cold‐ion fluid equations, the Boltzmann distribution for electrons, and Poisson’s equation show that the incident soliton is partially reflected and partially absorbed by the wall. The reflection is larger for wider solitons and for a more negatively biased wall. The numerical results are in reasonable agreement with the recent experiment of Nishida [Phys. Fluids 27, 2176 (1984)].