Coherent Synchrotron Radiation for Laminar Flows

We investigate the effect of shear in the flow of charged particle equilibria that are unstable to the Coherent Synchrotron Radiation (CSR) instability. Shear may act to quench this instability because it acts to limit the size of the region with a fixed phase relation between emitters. The results are important for the understanding of astrophysical sources of coherent radiation where shear in the flow is likely.