Acceleration and Particle Field Interactions of Cosmic Rays: Formalism

The origin and acceleration theories of Ultrah High Energy Cosmic Rays (UHECRs) are still mesterious problem in modern physics and astrophysics. The acceleration of ultra high energy cosmic rays is conjectured to occur through interactions with electromagnetic fields in different astrophysical objects, like magnetic matter clumps, besides the well-known shock waves and elastic Fermi mechanisms. Based on this model, a considerable portion of the dynamics, that derives a charged particle parallel to a magnetic field B and under the influence of a force F, is assumed to be composed of acceleration by a non-magnetic force F_|| and a gyromotion along B direction plus drifts in the direction of F_⊥. The model and its formalism are introduced, section 2 and section 3. Various examples for drift motions and accelerating forces are suggested, section 4. The configuration of the cosmic electromagnetic in different astophysical plasma aspects could play intrinsic role in the acceleration process of UHECRs. In a forthcoming work, a quantitative estimation of the energy gained by charged cosmic rays in various astrophysical objects will be evaluated.