Higher harmonic inverse free-electron laser interaction

We expand the theory of the inverse free electron laser (IFEL) interaction to include the possibility of energy exchange that takes place when relativistic particles traversing an undulator interact with an electromagnetic wave of a frequency that is a harmonic of the fundamental wiggler resonant frequency. We derive the coupling coefficients as a function of the IFEL parameters for all harmonics, both odd and even. The theory is supported by simulation results obtained with a three-dimensional Lorentz equation solver code. Comparisons are made between the results of theory and simulations, and the recent UCLA IFEL experimental results where higher harmonic IFEL interaction was observed.

Figure 1

(Color online) Coupling coefficients $\mathsf{J}{\mathsf{J}}_n$ for $n=1,3,5$ vs $K$.

Figure 2

(Color online) (a) Maximum energy gain (in units of $m{c}^2$) for an electron beam interacting with electromagnetic waves at the first three IFEL resonant frequencies, followed through two wiggler periods. (b) Maximum energy gain (in units of $m{c}^2$) for two coupling schemes with non-negligible second harmonic IFEL interaction. (c) Electron beam trajectory inside the wiggler.

Figure 3

(Color online) Maximum energy gain (in units of $m{c}^2$) for second harmonic IFEL interaction vs input angle.

Figure 4

(Color online) Coupling coefficient for second harmonic IFEL interaction vs $\theta$.

Figure 5

(Color online) Maximum energy gain (in units of $m{c}^2$) for second harmonic IFEL interaction vs spot size of ${\mathrm{TEM}}_{10}$ mode.

Figure 6

(Color online) Maximum energy gain (in units of $m{c}^2$) of particles injected in a IFEL accelerator at different energies. The vertical arrows indicate the higher harmonic IFEL resonant energies ${\gamma }_{r,n}$ with $n=1,2,3$.

Figure 7

(Color online) Coupling strength $K$ $\mathrm{J}{\mathrm{J}}_n\left(K\right)$ vs harmonic number $n$.

Figure 8

Longitudinal phase space and bunching factor improvements for a multicolor-driven IFEL.

Figure 9

(Color online) Resonant energies for the first three harmonic IFEL interactions along the Neptune IFEL undulator, and evolution of the simulated electron beam maximum energy for two different laser focus positions.

Figure 10

(Color online) Measured and simulated output energy spectrums for the Neptune IFEL accelerator experiment for two different laser focus positions. The simulated spectra have been normalized to the same area as the measured ones.