Transverse-to-longitudinal emittance exchange to improve performance of high-gain free-electron lasers

The ability to generate small transverse emittance is perhaps the main limiting factor for the performance of high-gain x-ray free-electron lasers (FELs). Noting that beams from an rf photocathode gun can have energy spread much smaller than required for efficient FEL interaction, we present a method to produce normalized transverse emittance at or below about $0.1\mu \mathrm{m}$, which will lead to a significantly shorter length undulator as well as a lower electron beam energy for an x-ray FEL project. The beam manipulation consists of producing an unequal partition of the initially equal emittances into two dissimilar emittances by a flat-beam technique and exchanging the larger transverse emittance with a smaller longitudinal emittance. We study various issues involved in the manipulation. In particular, a new emittance exchange optics we found enables an exact emittance exchange necessary for this scheme.

Figure 1

Power gain length $L_G$ of an x-ray FEL at $0.4\AA$ versus the undulator parameter $K$ for (a) a beam with a normalized transverse emittance of $1\mu \mathrm{m}$ and a peak current of 3.5 kA, and (b) a beam with a normalized transverse emittance of $0.1\mu \mathrm{m}$ and a peak current of 1.0 kA. The electron beam energy in both cases is adjusted according to the FEL resonant condition, with the relative rms energy spread at $1\times {10}^{-4}$.

Figure 2

Schematic diagram for exact longitudinal-to-transverse emittance exchange, consisting of two identical doglegs (${\mathbf{M}}_D$) and a transverse cavity (${\mathbf{M}}_C$). The matrix for ${\mathbf{M}}_D$ and ${\mathbf{M}}_C$ are given by Eqs. (19, 20), respectively.

Figure 3

Evolution of the transverse horizontal (red), vertical (green), and longitudinal (blue) emittances along the photoinjector beam line. The purple and cyan boxes at the bottom indicate the locations of the rf gun and the skew quadrupoles, respectively, while the blue lines indicate the accelerating cavity contour.

Figure 4

Transverse phase space (left two plots) and longitudinal phase space (right two plots) before (top row) and after (bottom row) the emittance exchange as simulated with ELEGANT, using particles from the injector simulation, but not including CSR.

Figure 5

The rms bunch length and energy spread in the emittance exchange system where the effective bunch length is quite long during most of the transport, due to the large initial bend-plane beta function and emittance.