Analytic and numerical study of two-frequency undulator radiation

Effect of an axial magnetic field on electron betatron oscillations in undulator magnets

“…For higher values of beam energy, it is possible to reduce the beam wander as displayed for the two cases of x 1 ð0Þ ¼ 0:1 mm ( figure 3(a)) and x 1 ð0Þ ¼ 0:3 mm ( figure 3(b)). To appreciate the effects of beam wander we calculate the deviation as Áx ¼ ðÁx 2 Þ 1=2 ¼ ½ðx À x 0 Þ 2 1=2 , where x represents the betatron oscillation induced trajectory as solved for equation (7) and x 0 is the reference trajectory solved from equation (2). The results are plotted in figure 4 for a few values of x 1 ð0Þ ¼ 0:05, 0.1 and 0.3 mm.…”

“…The spectral features of the undulator radiation depends on a large number of beam and undulator field parameters. The effects of beam energy and emittance spread [1], non-relativistic and sextapolar field corrections [3], angular injection [4], undulator radiation in a parallel plate waveguide [5,6], new novel concepts in undulator fields such as two-frequency [7], two-harmonic [8] are well manifested and incorporated in the analysis of undulator radiation. There are two approaches where these effects are well analysed.…”

“…There are two approaches where these effects are well analysed. A common approach [1][2][3][4][5][6][7][8] to all these analyses is the ultra-relativistic approximation of the electron trajectories and analytical solution of the Lienard Wiechert potential in far-field approximation. In the second approach there exists interest in handling the problem with numerical computations.…”

Harmonic undulator free electron laser and betatron oscillations

“…Over the years, there are several suggestions for specific design of the undulator magnet to address specific problems of FEL Physics. The twofrequency and two-harmonic undulator [15][16][17][18][19][20][21] and the optical klystron undulator [22][23][24][25] are some examples which have attracted wide interest in this context.…”

Two-color free-electron laser with two orthogonal undulators

“…Experiments on dual frequency production have been recently carried out on them with different methods [11][12][13][14][15][16][17][18] in various regimes of radiation frequency. Some of the initially proposed designs [19][20][21] were based on the use of staggered undulator magnets with different values of deflecting parameters to achieve lasing at two distinct wavelengths [22][23][24][25][26][27], an idea recently revisited and demonstrated in the x rays' range at the FEL Linac Coherent Light Source (LCLS) [8,11]. Another option, recently demonstrated at the FERMI soft x-ray seeded FEL [10], involves the use of either a chirped or a two-color seed laser [13,14].…”