Diffraction phenomena in spontaneous and stimulated radiation by relativistic particles in crystals (Review)

Abstract

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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

“…If the diffracted radiation is observed at the angle θ = 0, we should compare it with the contribution from the parametric (quasi-Cherenkov) radiation. In this case the analogous ratio is estimated as [44,139]…”

“…It is well known [116] that the oscillation threshold can be determined from the condition that ∆ = 0, where ∆ is the determinant of the system (139).…”

“…It was shown that despite serious difficulties, the law of radiative instability of relativistic beams passing through the crystal, which was discovered in [49], enables achieving the generation threshold for induced X-ray radiation even at the beam current density j ∼ 10 8 A/cm 2 , while the current density required for X-ray laser generation in crystals by means of channeling X-ray radiation or radiation in a crystal undulator is j ∼ 10 12 ÷ 10 13 [139].…”

“…1 Diffraction phenomena accompanying spontaneous and stimulated radiation from relativistic particles in crystals ( [139])…”

Doppler effect in the oscillator radiation process in the medium

“…We will clear out when the effect is normal or anomalous and when we deal with complicated Doppler effect. The complicated Doppler effect takes place in the relativistic particle's radiation process when the medium has an eigenfrequency (for example in a resonant transition radiation [10] or in a crystal [11]) and when the particle has an eigenfrequency [12]. Under the given angle there are two emitted photons with different frequencies and the difference of these frequencies depends on the particle energy.…”