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By means of a numerical simulation, nonlinear evolution of large amplitude dispersive Alfven waves is studied. An energy transfer from the parent wave to two daughter Alfven‐like waves and a soundlike wave is observed (a stimulated Brillouin scattering process). The observed growth rates and propagation characteristics of these daughter waves agree with the analytical results, which we obtain by extending the previous treatments by Goldstein, Derby, Sakai, and Sonnerup. Ions are first trapped by the electrostatic potential of the daughter soundlike waves. Along with the eventual decay (ion Landau damping) of the soundlike waves, ions are phase‐mixed and left heated in the parallel direction. The increased parallel energy of ions is transferred to the perpendicular thermal energy through the nonresonant scattering process in the colliding Alfven waves (parent and daughter waves). We further observe that the daughter Alfven waves, which still have a large amplitude, are also unstable for further decay, and that the wave energy is continuously transferred to the longer wavelength regime (inverse cascading process).

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[1] The shock front nonstationarity of perpendicular shocks in super-critical regime is analyzed by examining the coupling between ''incoming'' and ''reflected'' ion populations. For a given set of parameters including the upstream Mach number (M A ) and the fraction a of reflected to incoming ions, a self-consistent, time-stationary solution of the coupling between ion streams and the electromagnetic field is sought for. If such a solution is found, the shock is stationary; otherwise, the shock is nonstationary, leading to a self-reforming shock front often observed in full particle simulations of quasiperpendicular shocks. A parametric study of this numerical model allows us to define a critical a crit between stationary and nonstationary regimes. The shock can be nonstationary even for relatively low M A (2-5). For a moderate M A (5-10), the critical value a crit is about 15 to 20%. For very high M A (>10), a crit saturates around 20%. Moreover, present full simulations show that self-reformation of the shock front occurs for relatively low b i and disappears for high b i , where b i is the ratio of upstream ion plasma to magnetic field pressures. Results issued from the present theoretical model are found to be in good agreement with full particle simulations for low b i case; this agreement holds as long as the motion of reflected ions is coherent enough (narrow ion ring) to be described by a single population in the model. The present model reveals to be ''at variance'' with full particle simulations results for the high b i case. Present results are also compared with previous hybrid simulations.

The derivative nonlinear Schrödinger (DNLS) equation is derived by an efficient means that employs Lagrangian variables. An expression for the stationary wave solutions of the DNLS that contains vanishing and nonvanishing and modulated and nonmodulated boundary conditions as subcases is then obtained. The solitary wave solutions for elliptically polarized quasiparallel Alfvén waves in the magnetohydrodynamic limit (nonvanishing, unmodulated boundary conditions) are obtained. These converge to the Korteweg–de Vries and the modified Korteweg–de Vries solitons obtained previously for oblique propagation, but are more general. It is shown there are no envelope solitary waves if the point at infinity is unstable to the modulational instability. The periodic solutions of the DNLS are charcterized.

Large‐amplitude waves with typical frequencies of 0.01‐0.05 Hz are often observed in the foreshocks of earth and other planets. Large‐amplitude waves in the earth's foreshock are sometimes (but not always) observed in a highly time‐developed form, either as steepened pulses or as discrete oscillatory wave packets of finite length. This implies that nonlinearities are strong enough to modify their waveforms before the solar wind carries them out the foreshock. The instabilities and steepening of upstream waves in the earth's foreshock caused by backstreaming ions are discussed in the first part of the paper. For typical foreshock “diffuse” ion distributions, right and left‐hand polarized (RHP and LHP) waves propagating parallel to the local magnetic field are preferentially excited. Such noncompressional waves neither steepen nor grow fast enough to account for the amplitude polarizations and waveforms observed in the diffuse ion foreshock. Oblique waves develop a density compression and their magnetic field polarization is elliptical. Although these characteristics match the observations of the steepened waves in the diffuse ion zone, the growth rates of those waves oblique enough to steepen are too small to account for the observed amplitudes. On the other hand, the parallel propagating waves excited by the “reflected” ion distribution at the leading edge of the foreshock do grow fast enough, but do not steepen. We suggest that parallel propagating waves grow to finite amplitude in the “reflected” and “intermediate” ion zones of the earth's foreshock and refract as they are carried by the solar wind into the “diffuse” ion region, so that they become increasingly oblique and compressional. The more compressional they become, the more rapidly they steepen. Some steepen to the point where finite ion inertia dispersion wave creates a nonlinear wave train—a shocklet. Because wave refraction is less important in the very large foreshocks of interplanetary shocks, it is less likely that oblique, compressive, steepened waves will be generated in them, in agreement with observation. In the second part of this paper, we will simulate the time evolution of oblique low‐frequency compressive waves using a one‐dimensional hybrid code in which main ions are treated as superparticles, diffuse ions as a double‐adiabatic fluid, and electrons as an isothermal fluid. Unlike conventional hybrid codes, parallel and perpendicular pressures of fluids are treated independently. This is necessary in order to well describe the compressional properties of obliquely propagating right‐hand polarized waves in a high β plasma. We initialize the simulations with an oblique sinusoidal low‐frequency wave of finite amplitude. Nonlinear steepening, formation of discrete dispersive wave packets, and subsequent ion cyclotron damping of the wave packets are found to occur.

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We report on the development of unique, high-density helicon plasma sources and describe their applications. Characterization of one of the largest helicon plasma sources yet constructed is made. Scalings of the particle production efficiency are derived from various plasma production devices in open literature and our own data from long and short cylinder devices, i.e., high and low values of the aspect ratio A ͑the ratio of the axial length to the diameter͒, considering the power balance in the framework of a simple diffusion model. A high plasma production efficiency is demonstrated, and we clarify the structures of the excited waves in the low A region down to 0.075 ͑the large device diameter of 73.8 cm with the axial length as short as 5.5 cm͒. We describe the application to plasma propulsion using a new concept that employs no electrodes. A very small diameter ͑2.5 cm͒ helicon plasma with 10 13 cm −3 density is produced, and the preliminary results of electromagnetic plasma acceleration are briefly described.