New considerations concerning the high-frequency focusing of relativistic particles and Panofsky-Wenzel theorem

It is shown that the transverse momentum imparted to a relativistic particle, passing through an accelerating cavity near and parallel to its axis (z-axis), may be presented as a trajectory integral with an integrand being proportional to z-component of high-frequency magnetic field. The x- and y-component of this momentum are equal in value but opposite in sign. The obtained result is compared with Panofsky-Wenzel theorem. This result gives one more procedure to check the accuracy of high-frequency focusing simulation.