Radial electric field in tokamaks as a relativistic effect

It is shown that near a straight current carrying filament of a plasma a relativistic radial electric field E = L r υ p 2 - υ e 2 c 2 may occur where υ → p and υ → e are the proton and electron fluid velocities with respect to the charged particle testing the field and L is the line charge density of electrons before the current rises. This electric field is extremely small in metallic conductors where the electric current is due to the very large density of conduction electrons and the drift velocity of each electron is relatively small ( υ e ≪ c), but becomes substantial in tokamaks where the electron density is much smaller and the drift velocities are very large. In the latter case, the above electric field in the cylindrical approximation is of the same order as the radial electric field measured due to ion pressure gradients and plasma rotation.