Parametric beam instability of the electron bunch in a crystal

Effect of the parametric beam instability (PBI) of the relativistic electron beam in a crystal was analyzed theoretically in1 (see also2). This effect is analogous to self-amplification of spontaneous emission (SASE) mechanism for X-ray Free Electron Laser (XFEL) with an undulator. However, in the case of PBI the transversal modulation of the beam is defined by channeling of the electron in a crystal and the longitudinal modulation arises because of the parametric X-ray radiation mechanism. It is shown in the present paper that the current density J in the electron bunch typical for FEL facility is enough for the beam self-modulation within the X-ray range if the crystal thickness is larger than the crystal absorption length L ≥ Labs. This process could be used for generation of the coherent X-ray pulses if the time τd of the crystal destruction affected by the electron bunch is less than its passing time τd < L=c. The value τd (J) is estimated for the case of the FLASH electron bunch propagating through a Si crystal.