Wake field of electron beam accelerated in a RF-gun of free electron laser “ELSA”

Time dependent formulation of the energy loss by an accelerated intense electron beam just emitted by the cathode of RF-FEL photoinjector

“…The beam's velocitybðz; tÞ and accelerationgðz; tÞ are shown to be parallel toẼ 0 and independent of time [14]:…”

“…These potentials were expressed as infinite series of the product of the pill-box cavity eigenmodes [14]:…”

“…It cannot be kept for the just emitted beam like those encountered in photoinjectors, where the photoemitted electrons experience an extremely quick acceleration from thermal to multipleMeV energy. Therefore, the density is far from being uniform [14][15][16][17]. A theoretical treatment of this situation, based on the normal mode analysis model in a pill-box cavity will be the aim of this paper.…”

“…We apply the method of Ref. [14] in order to obtain an explicit expression of the energy loss as a development on the complete base cavity normal modes. For practical interest, we shall adopt the photoinjector of the ''ELSA'' facility (CEA, Bruye´res leChaˆtel, France) shown in Fig.…”

“…We shall limit our modeling to a pill-box type cavity as was successfully justified by Ref. [14]. Experimental work tracing the longitudinal profile of an accelerated electron beam suggests that the beam has an approximately triangular profile [18,19].…”