Kappa Distributions: Theory and Applications

George Livadiotis, Senior Research Scientist, Southwest Research Institute

Statistical Mechanics is used to determine how a particle system behaves when it resides at thermal equilibrium – the concept that any flow of heat (thermal conduction, thermal radiation) is in balance. When a particle system is at thermal equilibrium (typical behavior of earthy gases, e.g., the air), the particles are distributed in a specific way: There are many particles with small velocities and very few with large velocities. It is possible to write a mathematical equation describing how many particles are found at each velocity; this mathematical expression is called a “Maxwellian distribution”, that is, a 3-dim Gaussian distribution with variable given by the particle velocity. However, exotic systems such as space plasmas have their particles distributed such that there are more high velocity particles than there should be if the space plasma were in equilibrium. The mathematical equation used to describe the space plasma is called a “kappa distribution”. Empirical kappa distributions have become increasingly widespread across space and plasma physics. Space plasmas from the solar wind to planetary magnetospheres and the outer heliosphere are systems out of thermal equilibrium, described by kappa distributions. A breakthrough in the field came with the connection of kappa distributions to non-extensive statistical mechanics. Understanding the statistical origin of kappa distributions was the cornerstone of further theoretical developments and applications.

Friday, April 28

FLN 4.01.20

4:00 – 5:00 PM