Question about the Abraham-Lorentz force



The AL force is opposite to the particle speed (http://
en.wikipedia.org/wiki/Abraham-Lorentz_force). How do synchrotrons keep
particles on trajectory? How do they counter the AL force?
Any suggestions where I can find the solution for the equation of
motion in the presence of both the Lorentz and the Abraham-Lorentz
force?
.