Synchrotron Radiation Wake in Free Space

In this paper, we derive the transverse radiation force of a bunch of ultrarelativistic charged particles coherently radiating in free space assuming that the bending radius is much larger than the beam dimensions. In contrast to a similar recent study, where the authors decompose the total transverse force and find only a part that is responsible for the distortion of the beam orbit, we derive a full expression for the force and leave the issues of the beam dynamics for a separate consideration. Another approach to the calculation of the transverse force has been previously developed. In many cases considered in this paper, the calculations are extremely cumbersome; they were systematically performed with the use of symbolic engine of the computer program MATHEMATICA.