44. Electromagnetic acceleration of particles to cosmic ray energies

It has been demonstrated that if a particle is accelerated in an electromagnetic field between two points designated by subscripts (1) and (2), the particle will gain energy in passing from (1) to (2) provided that the quantity J defined by is positive, where ds is an element of path, U s 1 and U s 2 are the initial and final values of the vector potential along the path, and t is the time. Moreover, if the particle is at rest at the point (1), its energy W 2 at the point (2) is such that here e is the charge on the particle.