Calculation of the field and coherent radiation of relativistic bunches

The Lienard-Wiechert potentials are used to find the approximate formulas for the field strengths E(t) and H(t) near a point charge as functions of u(t), u(t), u(t) and r. where u is an arbitrary charge velocity and r is the radius vector between the charge and point of observation at time t. For u≤c the calculation is valid for arbitrary values of F, which, however, may satisfy the inequality F≥(1-u2/c2)2/2. When this inequality is observed the expression found is the same as the familiar asymptotic formula derived previously. It is indicated in which cases the result of the calculation may be applied to bounches moving in a plane undulator