Terms Of Plasma Dispersion Function Research Articles

Revisiting some analytical and numerical interpretations of Cairns and Kappa–Cairns distribution functions

In this tutorial, three-dimensional (3D) Cairns and Kappa-Cairns distribution functions are re-examined both analytically and numerically. The difference between one-dimensional (1D) and (3D) Cairns distribution functions (CDF) has been explained by deriving reduced 1D Cairns distribution function. It is noted that expressions of 1D and reduced 1D distributions such as Maxwellian and Kappa distributions are similar to each other, while the plots of 1D and reduced 1D CDF are significantly different from each other. The effect of non-thermality parameter on the 3D CDF is also studied by plotting it as a function of magnitude of the 3D velocity. It shows that the peak of the distribution function shifts toward higher speeds with an increase in the value of non-thermality parameter. The longitudinal dielectric response function is derived by using the 3D CDF for studying kinetic behavior of electrostatic waves in an unmagnetized isotropic plasma. The dielectric function is written in terms of plasma dispersion function and is then used to derive the dispersion relations and Landau damping increments for electron plasma waves, ion acoustic waves, and dust acoustic waves in a Cairns distributed plasma. The expressions of the dispersion relation and Landau damping rate of Cairns distributed plasma change into the corresponding expressions of the Maxwellian distributed plasma when the nonthermality parameter is taken equal to zero. Mathematical manipulations have been done for 3D Kappa-Cairns distribution function (KCDF) to find the correct normalization factor. An appropriate and valid range of values of the spectral index κ is obtained by calculating second moment of the velocity by integrating KCDF over 3D velocity space. The effect of non-thermality parameter and the spectral index κ on the 3D KCDF is studied by plotting it as a function of magnitude of the 3D velocity. It is also seen that the velocities where the tails of KCDF exists are much higher compared to the velocities where the tail of Kappa distribution occurs. For both 3D CDF and KCDF, it has been observed that the difference in the distribution functions becomes negligible when the value of the non-thermality parameter becomes more than 0.5.

Covariant kinetic dispersion theory of linear transverse waves parallel propagating in magnetized plasmas with thermal anisotropy

The properties of transverse waves parallel propagating in magnetized plasmas with arbitrary composition and thermally anisotropic, are investigated on the basis of relativistic Vlasov-Maxwell equations. The transverse dispersion relations for plasmas with arbitrary distribution functions are derived. These dispersion relations describe the linear response of the system to the initial perturbations and thus define all existing linear (transverse) plasma modes in the system. By analytic continuation the dispersion relations in the whole complex frequency plane are constructed. Further analysis is restricted to the important case of anisotropic bi-Maxwellian equilibrium plasma distribution functions. Explicit forms of the relativistically correct transverse dispersion relations are derived that hold for any values of the plasma temperatures and the temperature anisotropy. In the limit of nonrelativistic plasma temperatures the dispersion relations are expressed in terms of plasma dispersion function, however, the dependence on frequency and wave numbers is markedly different from the standard noncovariant nonrelativistic analysis. Only in the strictly unphysical formal limit of an infinitely large speed of light, c→∞, does the nonrelativistic dispersion relations reduce to the standard noncovariant dispersion relations.