Acceleration and Particle Field Interactions of Cosmic Rays I: Formalism
  The acceleration of ultra high energy cosmic rays is conjectured to occur
through various interactions with the electromagnetic fields in different
astrophysical objects, like magnetic matter clumps, besides the well-known
shock and stochastic Fermi mechanisms. It is apparent that the latter are not
depending on the particle's charge, quantitatively. Based on this model, a
considerable portion of the dynamics, that derives a charged particle parallel
to a magnetic field $\mathbf{B}$ and under the influence of a force
$\mathbf{F}$, is assumed to be composed of an acceleration by a non-magnetic
force $\mathbf{F}_{\parallel}$ and a gyromotion along $\mathbf{B}$ direction,
plus drifts in the direction of $\mathbf{F}_{\perp}$. The model and its
formalism are introduced. Various examples for drift motions and accelerating
forces are suggested. The formalism is given in a non-relativistic version.
Obviously, the translation into the relativistic version is standard. In a
forthcoming work, a quantitative estimation of the energy gained by charged
cosmic rays in various astrophysical objects will be evaluated.
