TY - JOUR
T1 - Ginzburg-Landau model for a free-electron laser
T2 - From single mode to spikes
AU - Ng, C. S.
AU - Bhattacharjee, A.
N1 - Funding Information:
This research is supported by the Air Force Office of Scientific Research Grant No. F49620-96-1-0068 and the Department of Energy Grant No. DE-FG02-91ER40669.
PY - 1998/4/21
Y1 - 1998/4/21
N2 - Single-mode operation of a free-electron laser is modeled by the Ginzburg-Landau equation. The linear stability of a single-mode solution is analyzed, and connections are established with known instabilities of the Ginzburg-Landau equation. It is found that there is no Benjamin-Feir instability and hence, the principal mode with the largest gain is always stable. However, the Eckhaus (or the phase) instability generally exists for a mode with frequency outside a range centered on the principal mode. This gives rise to two distinct possibilities: either there is spontaneous frequency shifting to the stable mode with the largest growth rate and a consequent tendency to approach single-mode operation, or there is a sudden chaotization and spikiness in the radiation field. Analytical criteria and scaling are given and tested by numerical simulations.
AB - Single-mode operation of a free-electron laser is modeled by the Ginzburg-Landau equation. The linear stability of a single-mode solution is analyzed, and connections are established with known instabilities of the Ginzburg-Landau equation. It is found that there is no Benjamin-Feir instability and hence, the principal mode with the largest gain is always stable. However, the Eckhaus (or the phase) instability generally exists for a mode with frequency outside a range centered on the principal mode. This gives rise to two distinct possibilities: either there is spontaneous frequency shifting to the stable mode with the largest growth rate and a consequent tendency to approach single-mode operation, or there is a sudden chaotization and spikiness in the radiation field. Analytical criteria and scaling are given and tested by numerical simulations.
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U2 - 10.1016/S0168-9002(97)01363-6
DO - 10.1016/S0168-9002(97)01363-6
M3 - Article
AN - SCOPUS:0032050836
VL - 407
SP - 34
EP - 39
JO - Nuclear Instruments and Methods in Physics Research, Section A: Accelerators, Spectrometers, Detectors and Associated Equipment
JF - Nuclear Instruments and Methods in Physics Research, Section A: Accelerators, Spectrometers, Detectors and Associated Equipment
SN - 0168-9002
IS - 1-3
ER -