Lie symmetry analysis of electron–electromagnetic wave interaction under condition of the anomalous Doppler effect

• We study electron–electromagnetic wave interaction under condition of anomalous Doppler effect.
• A four-parameter symmetry group is obtained, which determines point symmetries of the system.
• Solutions describing self-similar amplification and compression of short electromagnetic pulses are analyzed.
• Numerical simulation confirms that a small input pulse rapidly transforms into the self-similar solution.

Lie symmetry analysis is applied for a problem of interaction of electron cyclotron oscillators with a slow electromagnetic wave under condition of the anomalous Doppler effect. This analysis reveals scaling invariance of the system and existence of self-similar solutions which describe amplification of a short electromagnetic pulse with its subsequent compression. The results of theoretical analysis are confirmed by numerical simulations.