Beam conditioning for free electron lasers: Consequences and methods

The consequences of beam conditioning in four example cases [VISA, a soft x-ray free-electron laser (FEL), LCLS, and a “Greenfield” FEL] are examined. It is shown that in emittance limited cases, proper conditioning reduces sensitivity to the transverse emittance and, furthermore, allows for stronger focusing in the undulator. Simulations show higher saturation power, with gain lengths reduced by a factor of 2 or more. The beam dynamics in a general conditioning system are studied, with “matching conditions” derived for achieving conditioning without growth in the effective emittance. Various conditioning lattices are considered, and expressions derived for the amount of conditioning provided in each case when the matching conditions are satisfied. These results show that there is no fundamental obstacle to producing beam conditioning, and that the problem can be reduced to one of proper lattice design. Nevertheless, beam conditioning will not be easy to implement in practice.

Figure 1

Radiation power as a function of undulator length in the VISA FEL. Conditioned and unconditioned beams at different emittances are compared.

Figure 2

Radiation power as a function of undulator length in the soft x-ray FEL. Conditioned and unconditioned beams at different emittances are compared.

Figure 3

Radiation power as a function of undulator length for LCLS, with different beta functions, and with conditioned and unconditioned beams.

Figure 4

Radiation power as a function of undulator length for LCLS, with different values of beam emittance, beta function, and for conditioned and unconditioned beams. Note that a conditioned beam with 4 times larger emittance (black line) achieves the same performance as the nominal case (red diamonds).

Figure 5

Radiation power as a function of undulator length for a “Greenfield” FEL at 12 GeV. Different beta functions and emittances are shown, with conditioned and unconditioned beams.

Figure 6

Radiation power as a function of undulator length for a Greenfield FEL at 28 GeV. Different beta functions and emittances are shown, with conditioned and unconditioned beams.

Figure 7

Lattice parameters for a simple chromatic, conditioning beam line. The left-hand plots show the “matched” case, and the right-hand plots the “mismatched” case. Black lines correspond to the horizontal plane, red lines to the vertical plane. Top: Beta functions. Bottom: Variation of the above beta functions with energy, expressed in terms of the $W$ function.

Figure 8

Phase space ellipses in the horizontal plane after ten cells of the mismatched conditioning lattice, at three distinct longitudinal beam coordinates: $z=0$ (stars), $z=2\mathrm{mm}$ (squares) and $z=-2\mathrm{mm}$ (diamonds). For the matched case, all curves coincide.

Figure 9

Results of simulation of ${\mathrm{TM}}_{210}$ cavity conditioner. Correlation between energy and horizontal action after conditioning. The emittance growth is negligible.

Figure 10

Results of GENESIS simulations using LCLS parameters. FEL performance of $4.8\mu \mathrm{m}$ emittance ($4\times$ nominal) conditioned beam from ${\mathrm{TM}}_{210}$ cavity lattice (blue line with squares) is compared with performance of a similar, ideally conditioned beam (black dashed line) and of the nominal, unconditioned case (red diamonds); see Fig. 4.