Solution to the Initial Value Problem for a High-Gain FEL via Van Kampen¡'s Method

(WE-3-29)

Zhirong Huang and Kwang-Je Kim  

Argonne National Laboratory, Argonne, Illinois 60439, USA

Using Van Kampen¡¯s normal mode expansion [1], we solve the initial value problem for a high-gain free-electron laser (FEL) described by the three-dimensional Maxwell-Klimontovich equations. An expression of the radiation field is given for the process of coherent amplification and self-amplified spontaneous emission. It is noted that the effective start-up noise is larger for the case of nonvanishing beam energy spread [2] and emittance [3] than the case of vanishing energy spread and emittance. We discuss the physical interpretation of this phenomenon.

[1] N.G. Van Kampen, Physica 21, 949 (1955); K.M. Case, Ann. Phys. 7, 349 (1959).

[2] K.-J. Kim, Nucl. Instr. Meth. A 250, 396 (1986).

[3] M. Xie, presented at the American Physical Society April Meeting, Long Beach, 2000.