J. L. Hirshfield

INTERPRETATION OF SPATIALLY DECAYING ION-ACOUSTIC WAVES.

Detailed examination is given to circumstances surrounding the excitation and detection of spatially propagating ion‐acoustic disturbances in a plasma. For relatively weak damping, a theory is presented to show the major influence on spatial signal evolution engendered by source coupling details, by source geometry, and by three‐dimensional ion trajectories. In particular, near‐zone and far‐zone regions are identified for a disk source. Fresnel interference can dominate the near zone (within which many experiments are performed), so that serious questions can be raised as to the interpretation of observed decays. For relatively strong decays, the transition to the ballistic, three‐dimensional, free‐streaming solution is presented. Experiments are presented to illustrate some features of the theory, including measurements of Landau damping with 0.04 < ki/kr < 0.2 for 0.6 < ω/ωpi < 1.4. Observed Fresnel interference patterns are compared with theory.

SYMMETRY CONSIDERATIONS FOR GRID-LAUNCHED ION-ACOUSTIC WAVES.

Immersion of a fine‐mesh grid (or set of parallel grids) into a plasma is widely used to stimulate ion‐acoustic waves. The grid structure is usually biased so as to reflect electrons and transmit ions. The effect upon the ions due to applied rf fields in the grid region is to provide some combination of velocity and density modulation. The associated applied electric field perturbations will possess a combination of odd and even spatially symmetric parts, about the plane of symmetry of the grid system. The steady‐state solution of the governing differential equation in the ion‐acoustic limit is shown to depend critically upon this source symmetry, and to reduce to the usual solution only for the case of odd symmetry. Experiments designed to test these symmetry predictions have been carried out using an apparatus described previously, except that a four‐grid transmitter has been substituted for the three‐grid one. The outer two grids are grounded and the inner two grids can be driven either in phase (odd E...

Absorption of Electrostatic Waves by Plasma Electrons

Experimental observations with supporting theory are described of the energy exchange between a plasma column and an externally applied rf electric field that was nearly longitudinal. When electron collisions may be neglected and the wave‐particle interaction can be considered weak, the frequency‐dependent power absorption, as predicted by solution of the linearized Boltzmann equation, is a resonant process involving electrons having velocities near the phase velocity of the applied field. Similarities between absorption of rf energy in this experiment and collisionless absorption of electron plasma waves are evident, and the experimental results support the ideas of Landau damping. Application of “strong” rf fields to a drifting electron plasma produces a nonlinear deformation of the time‐averaged distribution. Measurements of this deformation compare favorably with a quasilinear calculation for weak nonlinear behavior.

Nonlinear harmonic generation of ion‐acoustic waves with dispersion

The observation of a dispersive effect on the nonlinear generation of ion‐acoustic wave harmonics is reported. This effect is a spatial beat modulation of the second harmonic with a beating length L given by the dispersion: L=2π/[K (2ω)−2K (ω)].

Nonlinear excitation of ion acoustic waves

The excitation of ion acoustic waves by nonlinear coupling of two transverse magnetic waves generated in a microwave cavity was investigated. Measurements of the wave amplitude showed good agreement with calculations based on the Vlasov equation.

Harmonic generation by Gould–Trivelpiece modes propagating into an axial density gradient

Prior experiments on the propagation of electrostatic waves on a plasma column (Gould–Trivelpiece modes) have shown linear wave reflections from an adjustable axial density gradient which scaled according to the predictions of WKB theory. For finite amplitude incident waves at radian frequency ω<ωpo, we have observed strong harmonic production at frequencies nω<ωpo where n in an integer and ωpo is the mean electron plasma frequency in the axially uniform part of the column. The harmonic production appeared to originate in the axially nonuniform plasma, and decreased markedly as the gradient was reduced experimentally. No threshold for harmonic production was observed, thus suggesting that parametric effects were not important. Second‐order perturbation theory based on the cold plasma equations is applied to an axially nonuniform plasma in a strong uniform axial magnetic field. The results show that nonlinear source terms enter into the governing differential equation for the second‐harmonic potential whic...

Phase effects in nonlinear wave-wave interactions

An attempt is made to clarify the differences in the nonlinear plasma interaction of two fixed-phase wavepackets from that of two random-phase packets, and present a simple interpretation which is in agreement with the available experimental results.

Ion‐acoustic disturbances stimulated by truncated source distributions

Plasma disturbances resulting from a modulated non‐Maxwellian ion distribution emanating into a half‐space plasma are discussed. The non‐Maxwellian ion distribution is formed experimentally by truncating the distribution entering an energy analyzer situated at one end of a plasma column. The lower energy ions are modulated and reflected back into the plasma. When all the ions are absorbed by the analyzer, no propagating ion disturbance is observed. On reflecting some low energy ions, an ion‐acoustic wave is detected. The wave amplitude initially increases when a larger segment of the ion distribution is reflected. However, when ions with velocities comparable to the phase velocity of the wave are reflected, the wave amplitude decreases. The signal velocity of the wave is also observed to increase as a greater number of ions are reflected. A modified fluid analysis to explain the observations is presented. In the analysis care is taken to include correct nonsymmetric velocity‐space source functions derived from a ballistic model.

ELECTROMAGNETIC INSTABILITY FOR COUNTERSTREAMING PLASMAS.

Growth rates for unstable ordinary polarization electromagnetic waves propagating at right angles to symmetric counterstreaming finite temperature plasmas are shown to be less than growth rates derived from a slightly modified dispersion relation for cold streams.

Coils and grids as ion‐wave launchers

Similarities between results of ion‐wave propagation on a single‐ended Q machine using either grid or coil excitation are shown to be not inconsistent with the notion that free‐streaming ion motions dominate both cases, contrary to recent claims of Sato et al.