Current-horn suppression for reduced coherent-synchrotron-radiation-induced emittance growth in strong bunch compression

Control of coherent synchrotron radiation (CSR)-induced emittance growth is essential in linear accelerators designed to deliver very high brightness electron beams. Extreme current values at the head and tail of the electron bunch, resulting from strong bunch compression, are responsible for large CSR production leading to significant transverse projected emittance growth. The Linac Coherent Light Source (LCLS) truncates the head and tail current spikes which greatly improves free electron laser (FEL) performance. Here we consider the underlying dynamics that lead to formation of current spikes (also referred to as current horns), which has been identified as caustics forming in electron trajectories. We present a method to analytically determine conditions required to avoid the caustic formation and therefore prevent the current spikes from forming. These required conditions can be easily met, without increasing the transverse slice emittance, through inclusion of an octupole magnet in the middle of a bunch compressor.

Figure 1

Baseline design layout of an FEL linac utilizing a two-stage bunch compression scheme, based on the designs presented in [38, 39].

Figure 2

Electron trajectories showing individual particles’ longitudinal position, $z_f$, evolving with distance along a bunch compressor chicane, $s$. The vertical gray line at $s=8.9\mathrm{m}$ represents the end of the chicane. The caustic equation, Eq. (7), is shown by the bold red line. Left inset: close up of trajectories near the end of the chicane. Right inset: double-horned current profile at chicane end.

Figure 3

Correlation between the final longitudinal position of a particle leaving a bunch compressor for a given initial longitudinal position for a particle entering a bunch compressor.

Figure 4

Boundaries between regions of one and two caustic current horns, and zero and one caustic current horn. The analytical expression for these boundaries is Eq. (12). Here they are shown for an arbitrary $R_{56}$ value of $-11.8\mathrm{mm}$, and first-, second-, and third-order longitudinal chirp values of $h_1=81.0563{\mathrm{m}}^{-1}$, $h_2=5929.08{\mathrm{m}}^{-2}$, and $h_3=1.30211\times 10^7{\mathrm{m}}^{-3}$ respectively. [Chirp values $h_1$, $h_2$, and $h_3$ are defined in Eq. (1).]

Figure 5

Regions of $h_2$, $h_3$ space where single, multiple, or zero caustics are expected to be found. Position (1) indicates the working point of a standard chicane with $R_{56}=-11.8\mathrm{mm}$, and with the same initial distribution parameters used in Fig. 4. Through addition of an octupole to BC1, the working point can be moved from position (1) to position (2) which lies in a noncaustic region.

Figure 6

Layouts of the FEL linac using an S-band injector and X-band linac. Section 6 compares simulation results of these two configurations with the baseline design shown in Fig. 1.

Figure 7

Optics through BC1, showing ${\beta }_x$ (green), ${\beta }_y$ (blue), ${\eta }_x$ (red), and ${\eta }_{xp}$ (orange).

Figure 8

Regions indicated where caustics are expected to be found and where they are absent. The boundaries between these regions are given by Eq. (12). The addition of a weak sextupole to BC2 changes the $T_{566}$, $U_{5666}$ coordinate of the working point, moving it closer to the upper boundary, and consequently shifting some of the current from the tail to the head of the bunch.

Figure 9

Optics through BC2, showing ${\beta }_x$ (green), ${\beta }_y$ (blue), ${\eta }_x$ (red), and ${\eta }_{xp}$ (orange).

Figure 10

Beta functions along the linac, with ${\beta }_x$ (blue) and ${\beta }_y$ (green).

Figure 11

Longitudinal phase space distribution and current profiles at the end of the linac for the three layouts described in Figs. 1, 6, and 6. (a) baseline layout which does not include any multipoles. (b) Layout 1 which includes an octupole magnet in BC1. (c) Layout 2 which includes the same octupole in BC1 as well as a weak sextupole magnet in BC2. Note the head of the bunch corresponds to negative values of longitudinal position.

Figure 12

Longitudinal phase space distribution and current profiles at the end of the linac for the three layouts described in Figs. 1, 6, and 6, without CSR or laser heating included in the simulation. (a) baseline layout which does not include any multipoles. (b) Layout 1 which includes an octupole magnet in BC1. (c) Layout 2 which includes the same octupole in BC1 as well as a weak sextupole magnet in BC2. Note the head of the bunch corresponds to negative values of longitudinal position.

Figure 13

Projected horizontal (blue square) and vertical (orange $+$) emittances produced with the Layout 2 design [Fig. 6] with various octupole field strengths.

Figure 14

Slice properties of the bunch at the end of the linac for the X-band Baseline design (blue circle), Layout 1 (orange $+$), and Layout 2 (green asterisk). The $x$ centroid offset and the variation in $x^{\prime }$ along the length of the bunch cause increased projected emittance growth of the baseline design.

Figure 15

Longitudinal phase space distribution and current profiles at the end of the S-band linac with CSR and laser heating included for (a) without any octupole magnets and (b) with an octupole included in BC2. Note the head of the bunch corresponds to negative values of longitudinal position.

Figure 16

Longitudinal phase space distribution and current profiles at the end of the S-band linac without CSR or laser heating included in the simulation for (a) without any multipole magnets and (b) with an octupole included in BC2. Note the head of the bunch corresponds to negative values of longitudinal position.

Figure 17

Slice properties of the bunch at the end of the S-band linac for without an octupole (blue circle), and with an octupole (green asterisk). The $x$ centroid offset and the variation in $x^{\prime }$ along the length of the bunch cause increased projected emittance growth of the baseline design.