Arbitrary emittance partitioning between any two dimensions for electron beams

The flat-beam transform (FBT) for round symmetric beams can be extended using the concept of eigenemittances. By tailoring the initial beam conditions at the cathode, including adding arbitrary correlations between any two dimensions, this extension can be used to provide greater freedom in controlling the beam’s final emittances. In principle, this technique can be used to generate extraordinarily transversely bright electron beams. Examples are provided where an equivalent FBT is established between the horizontal and the longitudinal beam dimensions.

Figure 1

Rough scaling of photons per pulse versus photon energy for conventional technology (black) and from using eigenemittance partitioning (red). The scaling for conventional technology is dashed beyond 10 keV, due to uncertainty in the CSR model’s validity for ultrashort bunches in the compressors.

Figure 2

Numerical modeling of the final emittance ratio for a variety of beam-matrix elements: (a) varying $d$ while setting $b=1$, $e=-1$; (b) varying $d$ while setting $b=1$, $e=1$; (c) final emittance ratio for a nonsymmetric FBT, varying the initial emittance ratio.

Figure 3

Conventional $x\mathrm{\text{−}}y$ FBT configuration—initial beam correlations are established at the cathode with an applied axial magnetic field, altering the beam’s eigenemittances, and these new eigenemittances are recovered through three skew quadrupoles.

Figure 4

The correspondence of the photon positions between the normal and tilted incident laser pulses.

Figure 5

(a) Table of acceptable correlations coupling all three dimensions that lead to two tiny eigenemittances and one large eigenemittance. Acceptable pairs of correlations are one from each of the two groups of the same color, with the black areas as excluded, where the row index is a function of the column index. (b) Eigenemittance evolution as a function of $x\mathrm{\text{−}}y$ and $x^{\prime }\mathrm{\text{−}}z$ correlations [using the yellow sections from part (a)]. When both correlations vanish, the eigenemittances are the initial uncorrelated emittances of $1/1/1\mu \mathrm{m}$.