Specific features of betatron oscillations and betatron emission in a hollow-channel plasma

Transverse betatron oscillations and the corresponding betatron emission are investigated for electrons in a strongly nonlinear wake wave excited by a high-power laser pulse in a hollowchannel plasma. The expressions for the oscillation period and critical frequency in the synchrotron regime of betatron emission are derived. A two-stage scheme is considered, in which an electron bunch formed in a plasma possessing a certain set of parameters generates betatron emission in a plasma possessing another set of parameters. The emission spectrum at the second stage is calculated in the absence of bunch acceleration.