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.

UR - http://www.scopus.com/inward/record.url?scp=0032050836&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0032050836&partnerID=8YFLogxK

U2 - 10.1016/S0168-9002(97)01363-6

DO - 10.1016/S0168-9002(97)01363-6

M3 - Article

AN - SCOPUS:0032050836

SN - 0168-9002

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

IS - 1-3

ER -