Chromatic matching in a plasma undulator

The principle of chromatic matching, i.e., using two laser modes of different geometric mode numbers and different colors so that they copropagate at the same group velocity, is proposed in order to realize the plasma undulator concept. Chromatic matching allows one to overcome group velocity slippage, whereby lower-order modes outrun higher-order ones, allowing for extended interaction lengths. The dephasing limit can be mitigated by using a special tapering of the plasma channel such that the electron bunch propagates in phase with the laser mode in addition to maintaining a constant undulator frequency. Furthermore, controlled dephasing is proposed as a means to induce chirp in the generated X-ray spectrum.