Emittance and phase space exchange for advanced beam manipulation and diagnostics

Alternative chicane-type beam lines are proposed for exact emittance exchange between transverse phase space $(x,x^{\prime })$ and longitudinal phase space $(z,\delta )$, where $x$ is the transverse position, $x^{\prime }$ is the transverse divergence, and $z$ and $\delta$ are relative longitudinal position and energy deviation with respect to the reference particle. Methods to achieve exact phase space exchanges, i.e., mapping $x$ to $z$, $x^{\prime }$ to $\delta$, $z$ to $x$, and $\delta$ to $x^{\prime }$, are suggested. Schemes to mitigate and completely compensate for the thick-lens effect of the transverse cavity on emittance exchange are studied. Some applications of the phase space exchange for advanced beam manipulation and diagnostics are discussed.

Figure 1

Emittance exchange beam line based on a chicane and two doglegs.

Figure 2

A chicane-type exact EEX beam line. Two quadrupoles (green diamonds) are put upstream of the transverse cavity to reverse the dispersion.

Figure 3

Exact EEX beam line with $|\eta k|<1$.

Figure 4

Transverse phase space distribution (left plots) and longitudinal phase space distribution (right plots) before (top row) and after (bottom row) the chicane-type EEX beam line.

Figure 5

Schematic of a beam line to generate optical microbunch based on PSEX.

Figure 6

(a) Initial transverse phase space after the mask. (b) Final longitudinal phase space after PSEX. (c) Ratio of $z_f$ to $x_i$. (d) Ratio of ${\delta }_f$ to $x_i^{\prime }$.

Figure 7

(a) Initial $z-y$ correlation. (b) Final $x-y$ correlation after PSEX.