Coherent transition radiation interferometric diagnostic for charged particle bunch self-modulation

We show that the amount of CTR energy emitted by an infinitely short bunch with parameters of the E209 experiment at SLAC depends on the bunch radius. Coherent transition radiation interferometry (CTRI) requires many events to build a trace. We also show that CTRI can be used to measure the period of a self-modulated charged particle bunch. This is true even though the self-modulation results from an instability growing from noise, which means its relative phase may be random from event to event. This further suggests that measurement of the SMI induced radial modulation using CTRI is possible.