Analytical solution of the space-dependent cosmic ray Fokker-Planck equation using Airy functions
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Bibliographic record
Abstract
Abstract The motion of energetic particles such as cosmic rays is complicated due to their interaction with turbulent magnetic fields. In particular, an analytical description of such interactions is difficult to achieve due to their stochastic and nonlinear nature. Therefore, transport equations are used to describe the motion of energetic particles. In phase-space, where the particle distribution function depends on position, time, and velocity, one uses a Fokker-Planck partial differential equation . While the general case of such a transport equation is too complicated to solve analytically, we consider the special case of a constant pitch-angle scattering coefficient. For this special case we explore analytical solutions of the Fokker-Planck equation by using Airy functions. We also develop an N -dimensional subspace method for this case corresponding to a semi-analytical approach. We compare the different methods, obtained results, and computational times needed with each other. We also determine different expectation values which are relevant for applications in particle transport theory.
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Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
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