Visible radiation formed by channeled particles

Spontaneous and induced radiation by electrons/positrons in natural and photonic crystals. Volume free electron lasers (VFELs): From microwave and optical to X-ray range

“…The relativistic oscillator itself can be a relativistic atom or a relativistic charged particle channeled in the potential well of averaged crystallographic potential of axes (planes), or an oscillator formed by an external electromagnetic field (ultrasonic, laser). It was shown in [17,19,20,21,22] that the DRO spectrum is rather complex and is determined by the complex and anomalous Doppler effect (see Sections 1,…”

“…Under diffraction the index of refraction depends on the direction of particle motion and the frequency of radiated photon, therefore equation (1) determining the radiated photon spectrum is the equation with several solutions [11,19,20,21,22].…”

“…where eQ is the charge of the particle, v(t) and r(t) are the velocity and the trajectory of the particle at moment t. By introducing (21) into (20) we get…”