Using Kappa Distributions to Identify the Potential Energy

Abstract

This paper reports on the properties of kappa distributions in the presence of a potential energy. The constructed phase space kappa distribution leads to a polytropic relationship between the local density and temperature. The kappa and polytropic indices are connected via a characteristic and universal relationship: their sum is a constant depending specifically on the potential features. Determining this constant comprises a method essential for revealing the functional form and understanding the nature of the particle potential energy. The method is applied to the solar wind proton plasma at 1 AU. It is shown that a satisfactory physical interpretation of the potential affecting solar wind protons can be given by the interplanetary radial electric field.

Energetic Ion Moments and Polytropic Index in Saturn's Magnetosphere using Cassini/MIMI Measurements: A Simple Model Based on κ‐Distribution Functions

“…Despite the above complications, we infer that the calculated polytropic indexes for Saturn's plasma sheet, together with the semiempirical description of the major thermodynamical parameters for both suprathermal H + and O + , can act as an invaluable input in recent models that aim to study the dynamics of Saturn's magnetosphere. In theory‐driven studies, our results can be used in the method provided recently by Livadiotis (), to estimate the dynamical degrees of freedom in a plasma application, through the connection between the κ ‐index and the polytropic index.…”

Kappa Distributions: Statistical Physics and Thermodynamics of Space and Astrophysical Plasmas

“…The kappa distributions have a tremendous number of applications in space and astrophysical plasmas, such as the inner heliosphere, including solar wind (e.g., [13,20,26,[38][39][40][41][42][43][44][45][46][47][48]), solar spectra (e.g., [49,50]), the solar corona (e.g., [51][52][53][54]), solar energetic particles (e.g., [55,56]), corotating interaction regions (e.g., [57]), and related solar flares (e.g., [21,33,58,59]); planetary magnetospheres, including the magnetosheath (e.g., [60,61]), magnetopause (e.g., [62]), magnetotail (e.g., [63]), ring current (e.g., [64]), plasma sheet (e.g., [65][66][67]), magnetospheric substorms (e.g., [68]), Aurora (e.g., [69]); magnetospheres of giant planets like the Jovian (e.g., [70][71][72]), Saturnian (e.g., [73][74][75][76]), Uranian (e.g., [77]), and Neptunian (e.g., <...>…”

“…Both the Maxwellian core and power-law tail can support useful techniques for finding the values of temperature and kappa. Some examples are the methods of exploiting the Maxwellian behavior of kappa distributions at the core [26,27,117] and the power-law behavior of kappa distributions at the tail [88][89][90]. Nevertheless, care must be shown when using power-laws in general.…”

“…There are various mechanisms capable of generating kappa distributions in space and astrophysical plasmas. Some examples are superstatistics [15][16][17][18], the effect of shock waves [19], weak turbulence [20], turbulence with a diffusion coefficient inversely proportional to velocity [21], the effect of pickup ions [22], pump acceleration mechanism [23], and polytropic behavior [24][25][26]; (see also [1], chapters 5, 6, 8, 10, 15, and 16). Also, common processes characteristic of space plasmas, such as the Debye shielding and magnetic coupling, have an important role in the generation of kappa distributions in plasmas [27].…”

Polytropes in plasmas described by kappa distributions – Application in atmospheric modelling

“…Surely, this is far from the characterization of space plasmas where 10 8 < <N D < <10 12 . [11] The kappa distributions have become increasingly widespread across the physics of space plasmas, describing particles in the heliosphere, from the solar wind and planetary magnetospheres to the heliosheath and beyond, the interstellar and intergalactic plasmas: inner heliosphere, including solar wind, [12][13][14][15][16][17][18][19][20][21][22][23][24][25][26] solar spectra, [27][28][29] solar corona, [30][31][32][33] solar energetic particles, [34,35] corotating interaction regions, [36] and solar flares related; [4,[37][38][39] planetary magnetospheres, including magnetosheath, [40,41] magnetopause, [42] magnetotail, [43] ring current, [44] plasma sheet, [45][46] magnetic reconnection, [47] magnetospheric substorms, [48] Aurora, [49] magnetospheres of giant planets, such as Jovian, [50][51][52]…”