Calculation of the noninertial space-charge force and the coherent synchrotron radiation force for short electron bunches in circular motion using the retarded Green’s function technique

The space-charge forces for short electron bunches in circular motion can be very different from the space-charge forces for short electron bunches undergoing straight-line motion. The two major effects introduced by the circular motion are an off-axis, so-called ‘‘noninertial space-charge’’ effect, in which there is essentially no net energy loss of the bunch, and a coherent synchrotron radiation effect, in which the bunch radiates coherent energy. The consequence of these effects is a potentially large growth in the electron bunch’s transverse emittance. We derive an expression for these forces from a Green’s function approach, starting with the definitions of the retarded scalar and vector potentials. In particular, we find an expression for the total electric field along the direction of motion from a short line of charge in circular motion. These expressions in turn can be used in numerical particle simulations to estimate the amount of emittance growth, including the effects of suppressing the coherent synchrotron radiation by reducing the beam pipe dimensions. © 1996 The American Physical Society.