The return current induced in a plasma by a relativisitc electron beam generates a new electron-ion two-stream instability (return current instability). Although the effect of these currents on the beam-plasma e-e instability is negligible, there exists a range of wave numbers which is unstable only to return current (RC) instability and not to e-e instability. The electromagnetic waves propagating along the direction of the external magnetic field, in which the plasma is immersed, are stabilized by these currents but the e.m. waves with frequencies,ω²≪Ω_e²≪ω_pe² (Ω_e andω_pe being cyclotron and plasma frequency for the electrons of the plasma respectively) propagating transverse to the magnetic field get destabilized. Heuristic estimates of plasma heating, due to RC instability and due to decay of ion-acoustic turbulence generated by the return current, are made. The fastest time scale on which the return current delivers energy to the plasma due to the scattering of ion-sound waves by the electrons can be ∼ω_pi⁻¹ (ω_pi being the plasma frequency for the ions).

The radiation, resulting from the nonlinear interaction of whistler solitons, which act as localized antennae, with the upperhybrid waves in the coronal loop, is shown to give rise to fine structures in solar radio bursts. All the observed features of microwave spikes in radio flares,e.g. their frequency, polarization and short duration can be explained by the presence of about 10⁶ solitons occupying a volume of ∼ 10⁸ m³, provided this interaction takes place at low altitudes. However, if this interaction takes place close to the top of the coronal loop, it gives rise to the isolated tadpole ‘eyes’ features in the dynamic spectra. About 10⁹ solitons are needed to account for the observed flux of these ‘eyes’.

A self consistent formulation of the Jeans instability of a dusty plasma with proper inclusion of charge dynamics is described. It is shown that charge fluctuations significantly affect the Jeans as well as the Buneman mode. For plasma particles (electrons and ions) in local thermal equilibrium, the Jeans lengthλ_J is given byλ_J≈λ_gF(R, ε, β/η), whereλ_g is the Debye length of the charged grains,R is the square of the ratio of the Jeans to the plasma frequency of the grains,ε is the square of the ratio of the Debye length of the grains and the plasma particles andβ/η is the ratio of the attachment to the decay frequency of the electronic charges to the grain surface. The functional form ofF is given in the text. Numerical investigation of the Jeans-Buneman mode for a two and three component plasma shows that the Jeans mode dominates atkλ_D≪1 (wherek is the wave number andλ_D is the Debye length of plasma particles), whereas atkλ_D≫1 only the Buneman mode operates. Charge fluctuations reduce the area of overlap of the two modes. Furthermore, in the absence of gravity, there exists a new, charge fluctuation induced unstable mode in a streaming dusty plasma. Astrophysical applications of the results are discussed.

Boundary layers are the sites where energy and momentum are exchanged between two distinct plasmas. Boundary layers occurring in space plasmas can support a wide spectrum of plasma waves spanning a frequency range of a few mHz to 100 kHz and beyond. The main characteristics of the broadband plasma waves (with frequencies >1 Hz) observed in the magnetopause, polar cap, and plasma sheet boundary layers are described. The rapid pitch angle scattering of energetic particles via cyclotron resonant interactions with the waves can provide sufficient precipitated energy flux to the ionosphere to create the diffused auroral oval. The broadband plasma waves may also play an important role in the processes of local heating/acceleration of the boundary layer plasma.

The nonlinear evolution of an electron acoustic wave is shown to obey the Davey-Stewartson I equation which admits so called dromion solutions. The importance of these two dimensional localized solutions for recent satellite observations of wave structures in the day side polar cap regions is discussed and the parameter regimes for their existence is delineated.

Electrostatic ion cyclotron instability pertaining to the higher harmonics of proton and helium cyclotron modes is investigated in three-component magnetised plasma consisting of beam electrons, protons and doubly charged helium ions. The effect of different plasma parameters, namely, angle of propagation, number density andtemperature of helium ions and electron beam speed, has been studied on the growth of proton and helium cyclotron harmonics. It is found that an increase in angle of propagation leads to the excitation of fewer harmonics of proton cyclotron waves with decreased growth rates and higher number of helium harmonics with decreased growth rates.Also, largely odd helium harmonics are excited, except for one particular case where the second harmonic also becomes unstable. The number density and temperature of ions have significant effect on the helium cyclotron instability compared to the proton cyclotron instability. Further, as the speed of electron beam is increased, the peak growth rate increases. Our results are relevant to laboratory and space plasmas where field-aligned currents exist.