Understanding kappa distributions: A toolbox for space science and astrophysics

G. Livadiotis, D. J. McComas

Research output: Contribution to journalArticlepeer-review

293 Scopus citations


In this paper we examine the physical foundations and theoretical development of the kappa distribution, which arises naturally from non-extensive Statistical Mechanics. The kappa distribution provides a straightforward replacement for the Maxwell distribution when dealing with systems in stationary states out of thermal equilibrium, commonly found in space and astrophysical plasmas. Prior studies have used a variety of inconsistent, and sometimes incorrect, formulations, which have led to significant confusion about these distributions. Therefore, in this study, we start from the N-particle phase space distribution and develop seven formulations for kappa distributions that range from the most general to several specialized versions that can be directly used with common types of space data. Collectively, these formulations and their guidelines provide a "toolbox" of useful and statistically well-grounded equations for future space physics analyses that seek to apply kappa distributions in data analysis, simulations, modeling, theory, and other work.

Original languageEnglish (US)
Pages (from-to)183-214
Number of pages32
JournalSpace Science Reviews
Issue number1-4
StatePublished - Jun 2013
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Astronomy and Astrophysics
  • Space and Planetary Science


  • Heliosphere
  • Plasmas
  • Solar wind
  • Statistical mechanics
  • Thermodynamics


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