Modelling energetic particles by a relativistic kappa-loss-cone distribution function in plasmas

Energetic particles found in planetary magnetospheres and other plasmas, where mirror geometries occur, often exhibit two typical characteristics: a pronounced high energy tail and an anisotropy. A relativistic kappa-loss-cone (KLC) distribution function f(kappa L) is initially developed which incorporates features of the well-known kappa type and loss-cone type, i.e. the anisotropy behaves as a loss-cone distribution; the energy satisfies proportional to [1/nu(2)]((kappa,1)) for a relatively large velocity nu as a kappa distribution f(kappa) does and spreads proportional to [1/p](kappa+1) at the relativistic energies (where kappa and p are the energy spectral index and the particle momentum, respectively). This indicates that the new distribution f(kappa L) obeys the power-law not only at the lower energies but also at the relativistic energies since the relativistic energy proportional to p. Numerical calculations are performed for a direct comparison between the new KLC distribution and the current kappa distribution, respectively. It is found that the regular kappa distribution generally decreases faster than the KLC distribution with the kinetic energy E-k especially when theta(2) increases (where theta(2) is the energy weight parameter), e-g. f(kappa)/f(kappa L) <= 10(-2) for E-k >= 2.0 MeV and theta(2) >= 0.25. However, no big difference occurs between both distributions through energies up to similar to 500 keV for theta(2) <= 0.025. Furthermore, the regular kappa distribution containing either the temperature anisotropy or both the loss cone and temperature anisotropy is quite different from the KLC distribution. The new KLC distribution may be applicable to the outer radiation belts of the Earth, the inner Jovian magnetosphere and other plasmas (including the laboratory machine) where relativistic particles are present.