Interaction of Charged Particles with Strong Electromagnetic Wave in Dielectric Media. Induced Nonlinear Cherenkov Process

Abstract

What can we expect from particle–strong wave interaction in a medium essentially different from that of a vacuum? It is well known that in a medium with the refractive index \( n(\omega )>1\) (dielectric media) the Cherenkov effect takes place—charged particle moving with a velocity \(\mathbf {v}=\mathrm {const}\) radiates spontaneously transverse EM wave of frequency \(\omega \) at the angle \(\theta \) satisfying the condition of coherency \( \cos \theta \) \(=\) \(c/\mathrm {v}n(\omega )\). This means that in the presence of an external plane EM wave of the same frequency \(\omega \) propagating at this angle with respect to the particle motion the spontaneous Cherenkov radiation of the particle will acquire induced character and the inverse process of Cherenkov absorption from the incident wave by the particle is possible as well. This is the general character of arbitrary type spontaneous radiation process in corresponding induced one. However, in contrast to the noncoherent process (e.g., bremsstrahlung), if the spontaneous process is of coherent nature, such as the Cherenkov process, for the satisfaction of the condition of coherency the external wave should be weak enough to not change considerably the particle initial velocity \( \mathbf {v}\) and violate the mentioned condition of coherency of the spontaneous process. Consequently, this explanation of formation of induced process with the charged particles (induced free–free transitions in quantum terminology) corresponds to the linear theory. The behavior of induced Cherenkov process in the strong EM wave field is quite different from the mentioned one. The existence of the threshold value of the particle velocity for the spontaneous Cherenkov radiation (\(\mathrm {v }\) \(>c/n(\omega )\)) stipulates for the threshold value of the wave intensity essentially changing the character of the dynamics of the particle–wave interaction in a medium and, consequently, the character of electromagnetic processes in dielectriclike media , proceeding in the presence of strong radiation fields. As we will see later, the peculiarities that arise at the nonlinear interaction of charged particles with strong EM waves are the general features of coherent processes like the Cherenkov one. To reveal the nonlinear behavior and principal peculiarities of a particle–strong wave interaction in a medium, this chapter will present the nonlinear classical theory of induced Cherenkov process.