Fundamental relativistic solution for the railgun

A fully relativistic analysis is made of the dynamics of a railgun based on three assumptions: (1) Ohm's law is valid in the rest frame of the plasma, (2) total electron momentum is transferred to the projectile, and (3) motion of the projectile is constrained to one direction. With these assumptions, a relativistic equation for the velocity of the projectile is obtained whose solution monotonically increases to one of two values depending on field strengths. For B>E, the maximum velocity is cE/B whereas for E>B it is c where c is the speed of light, and E and B are applied electric and magnetic fields, respectively.