Parametric Beam Instability of Relativistic Charged Particles in a Crystal

Known schemes of coherent X-ray and gamma-ray sources are basically connected with the creation of the conditions, when resonant transitions of MSssbauer nuclei or the internal electron shell of heavy atoms have an inverse population. It was shown in refs. [1,2] that these conditions were realized for a relatively small threshold current (j ~ 10 2 A/cm2), when parametric X-rays [2,3] from the modulated electron beam were used. But in this scheme a solution of the very complicated problem of X-ray modulation of the ultrarelativistic particle beam is required. An essentially different mechanism of the coherent X-ray generation is considered in the present paper. It is shown that parametric X-rays lead to longitudinal self-modulation of the relativistic channelled particle beam and as a result the parametric beam instability arises. In this process the longitudinal energy of the particles efficiently transforms into the energy of the coherent monochromatic X-rays. The mechanism considered is in many aspects analogous to the processes which are used in the powerful generators of superhigh-frequency radiation and freeelectron lasers [ 4 7 ] . The interaction of the channelled particle beam with a radiation field and the crystal is described by the following self-consistent system of the Maxwell equations and the particle's equations of motion k 2 ~ ~(k, 60) k~(k. ~)