In the present paper, it is argued that non-Maxwellian distribution functions are better suited to model space plasmas. A new model distribution function called the generalized (r,q) distribution function which is the generalized form of the generalized Lorentzian (kappa) distribution function has been employed to carry out theoretical investigation for parallel propagating waves in general and for Alfvén waves in particular. New plasma dispersion functions have been derived and their properties investigated. The new linear dispersion relation for Alfvén waves is investigated in detail.

Key Points:• Lion roar emission is explained by (r, q) distribution• Bi-Maxwellian model cannot always explain observation• The (r, q) model satisfactorily resolves observational uncertainties (2006) investigated the underlying cause of the lion roar generation. However, the analysis based upon the bi-Maxwellian distribution function did not adequately explain the observations qualitatively as well as quantitatively. This outstanding problem is revisited in the present paper, and a resolution is put forth in which, the flat-top non-Maxwellian distribution function with a velocity power law energetic tail, known as the (r, q) distribution, or the generalized kappa distribution is employed. Upon carrying out the linear stability analysis of the (r, q) distribution against the whistler wave perturbation, and upon comparison with the Cluster data, good qualitative and quantitative agreements are found between theory and data.

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Effect of trapping as a microscopic phenomenon in a degenerate plasma is investigated in the presence of a quantizing magnetic field. The plasma comprises degenerate electrons and non-degenerate ions. The presence of the quantizing magnetic field is discussed briefly and the effect of trapping is investigated by using the Fermi-Dirac distribution function. The linear dispersion relation for ion acoustic wave is derived in the presence of the quantizing magnetic field and its influence on the propagation characteristics of the linear ion acoustic wave is discussed. Subsequently, fully nonlinear equations for ion acoustic waves are used to obtain the Sagdeev potential and the investigation of solitary structures. The formation of solitary structures is studied both for fully and partially degenerate plasmas in the presence of a quantizing magnetic field. Both compressive and rarefactive solitons are obtained for different conditions of temperature and magnetic field.