A quantum-like Landau Damping of an Electromagnetic Wavepacket

By using the Wigner transform, it is shown that the propagation of an electromagnetic (EM) wavepacket in a nonlinear medium, governed by nonlinear Schrödinger equation, can be described, in phase space, by a kinetic-like theory similar to the one based on the Vlasov equation which is used for describing the collective longitudinal dynamics of charged-particle bunches in accelerating machines. In this framework, the modulational instability of the wavepacket corresponds to the coherent instability of the particle bunch. Remarkably, a Landau damping of the EM wavepacket is predicted and put forward for a future investigation. Furthermore, the concept of coupling impedance associated with the EM wavepacket propagation is also introduced in analogy to the one of charged-particle bunches. This approach provides stability charts similar to the ones describing charged-particle beams in accelerating machines.