Astrophysique et technologie aérospatiale

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

Abstract

Keran O’Brien

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.