alexa A Mathematical Model of the Maximum Rigidity Resulting from Diffusive Shock Acceleration
ISSN: 2329-6542

Journal of Astrophysics & Aerospace Technology
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Research Article

A Mathematical Model of the Maximum Rigidity Resulting from Diffusive Shock Acceleration

Keran O’Brien*

Department of Physics and Astronomy, Northern Arizona University, Flagstaff, AZ, USA

*Corresponding Author:
Keran O’Brien
Department of Physics and Astronomy
Northern Arizona University
Flagstaff, AZ, USA
Tel: 928-523-2661
E-mail: Keran.O'[email protected]

Received: March 09, 2016 Accepted: April 07, 2015 Published: April 14, 2016

Citation: O’Brien K (2016) A Mathematical Model of the Maximum Rigidity Resulting from Diffusive Shock Acceleration. J Astrophys Aerospace Technol 4:130. doi:10.4172/2329-6542.1000130

Copyright: © 2016 O’Brien K. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.



The primary cause of the high-energy particle acceleration of cosmic rays and solar-particle events is first-order Fermi diffusive shock acceleration. The importance of the maximum rigidity is that it governs the effective depth in the atmosphere that accelerated particles can reach. Because the rigidity is a function of the particle energy, a high rigidity implies a high energy and thus a more intense hadronic cascade and greater atmospheric penetration. Because of their high energies, cosmic rays can penetrate the Earth’s surface and be measured underground. However, whether solar-particle events will produce significant radiation exposure at aircraft altitudes depends on the maximum rigidity resulting from the shock. First-order shock acceleration is governed by the speed of the shock, the local magnetic field the length of time the shock continues and the strength of the shock. These factors are combined in a simple equation which provides a simple model for the maximum rigidity resulting from the shock. The equation derived from these considerations accounts reasonably well for cosmic-ray and solar-particle maximum rigidities.


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