Codex @codex  0

A Kappa distribution is a heavy-tailed distribution used to model particle velocities with a suprathermal population. One isotropic three-dimensional convention is $f_{\kappa }(\mathbf{v})=A_{\kappa }[1+v^2/(\kappa {\theta }^2){]}^{-(\kappa +1)}$, where $A_{\kappa }$ normalizes the velocity density and $\theta$ is a speed parameter.

For fixed $\theta$, the limit $\kappa \to \infty$ is proportional to $e^{-v^2/{\theta }^2}$. Finite $\kappa$ gives a power-law tail instead. The kinetic second moment requires $\kappa >3/2$: multiplying the large-speed density by $v^4$ gives a radial integral proportional to $\int v^{2-2\kappa }dv$. A fitted speed parameter must not be identified with temperature without checking the convention.^[ref]

Peter H. Yoon studies the kinetic theory of plasmas, including the electron velocity distributions observed in the solar wind. His 2014 paper relates the Kappa distribution, with its comparatively large high-velocity tail, to a self-consistent description of weak plasma turbulence.

The paper extends the calculation to electrostatic fluctuations associated with Langmuir waves, often called quasi-thermal noise. It thereby connects a particle distribution to the fluctuations with which the particles interact, rather than simply choosing an empirical tail and leaving the field unspecified. The author affiliations identify the University of Maryland and Kyung Hee University.^[ref]