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The differential cosmic ray energy flux in the light of an ultrarelativistic generalized Lorentzian thermodynamics

  • R. A. Treumann
  • W. BaumjohannEmail author
Original Article

Abstract

The ultrarelativistic generalized Lorentzian quasi-equilibrium thermodynamic energy distribution is tentatively applied to the energy spectrum of galactic cosmic ray fluxes. It is found that the inferred power law slopes contain a component which evolves with cosmic ray energy in steps of thirds, resembling the sequence of structure functions in fully developed Kolmogorov turbulence. Within the generalized thermodynamics the chemical potential is estimated from the deviation of the fluxes at decreasing energy, presumably throwing light on the cosmic ray acceleration mechanism. A relation between involved turbulent volumina and structure functions is obtained. The conclusions drawn hold only within the realm of applicability of thermodynamics to cosmic ray spectra.

Keywords

Cosmic rays Energy spectra Generalized Lorentzian thermodynamics Ultrarelativistic Kappa-distribution 

Notes

Acknowledgements

This work was part of a Visiting Scientist Programme at the International Space Science Institute Bern. We acknowledge the interest of the ISSI Directorate and hospitality of the ISSI staff. We thank the ISSI system administrator S. Saliba for technical support and the librarians Andrea Fischer and Irmela Schweizer for access to the library and literature. Finally, we thank the reviewers for their friendly and constructive comments on the validity of the thermodynamic approach to the cosmic ray spectrum in view of the structure of the data and more recent measurements.

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Authors and Affiliations

  1. 1.International Space Science InstituteBernSwitzerland
  2. 2.GeophysicsMunich UniversityMunichGermany
  3. 3.Austrian Academy of SciencesSpace Research InstituteGrazAustria

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