Generation of electrostatic multiple harmonic Langmuir modes during beam-plasma interaction process has been observed in laboratory and spaceborne active experiments, as well as in computer simulation experiments. Despite earlier efforts, such a phenomenon has not been completely characterized both theoretically and in terms of numerical simulations. This paper is a first in a series of three papers in which analytic expressions for harmonic Langmuir mode dispersion relations are derived and compared against the numerical simulation result.
[1] We study formation process of electrostatic solitary waves (ESW) observed by recent spacecraft via one-and two-dimensional electrostatic particle simulations with open boundaries. The previous simulations have demonstrated that ESW correspond to Bernstein-Greene-Kruskal electron holes formed by electron beam instabilities. However, since the previous simulations were performed in uniform periodic systems, wave-particle interaction of an electron beam instability was taking place uniformly in the systems. In the present study, we inject a weak electron beam from an open boundary into the background plasma to study spatial and temporal development of a bump-on-tail instability from a localized source. In the open system, spatial structures of electron holes vary depending on the distance from the source of the electron beam. In an early phase of the simulation run, electron holes that are initially uniform in the direction perpendicular to the magnetic field become twisted through modulation by oblique electron beam modes. As the electron holes propagate along the magnetic field, they are aligned in the perpendicular direction through coalescence. Spatial structures of electron holes in a distant region from the source become one-dimensional. In a long-time evolution of the instability, ion dynamics becomes important in determining spatial structures of electron holes. A lower hybrid mode is excited locally in the region close to the source of the electron beam through coupling with electron holes at the same parallel phase velocity. The lower hybrid mode modulates electron holes excited in later phases, resulting in formation of modulated one-dimensional potentials. Since the perpendicular electric fields of electron holes are carried by the electron holes at the drift velocity of the electron holes, they can be observed even at a distant place from the source.
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An extreme case of electron shock drift acceleration in low Mach number collisionless shocks is investigated as a plausible mechanism of initial acceleration of relativistic electrons in large-scale shocks in galaxy clusters where upstream plasma temperature is of the order of 10 keV and a degree of magnetization is not too small. One-dimensional electromagnetic full particle simulations reveal that, even though a shock is rather moderate, a part of thermal incoming electrons are accelerated and reflected through relativistic shock drift acceleration and form a local nonthermal population just upstream of the shock. The accelerated electrons can self-generate local coherent waves and further be back-scattered -2toward the shock by those waves. This may be a scenario for the first stage of the electron shock acceleration occurring at the large-scale shocks in galaxy clusters such as CIZA J2242.8+5301 which has well defined radio relics.
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