Microbunch rotation in an x-ray free-electron laser using a first-order achromatic bend

Electrons in an x-ray free electron laser (XFEL) develop periodic density fluctuations, known as microbunches, which enable the exponential gain of x-ray power in an XFEL. When an electron beam microbunched at a hard x-ray wavelength is kicked, microbunches are often washed out due to the dispersion and $R_{56}$ of the bend. An achromatic (dispersion-free) bend with a small $R_{56}$, however, can preserve microbunches, which rotate to follow the new trajectory of the electron bunch. Rotated microbunches can subsequently interact in a repointed undulator to produce a new beam of off-axis x rays. In this work, we demonstrate hard x-ray multiplexing in the Linac Coherent Light Source hard x-ray undulator line using microbunch rotation through a $10\mathrm{\mu }\mathrm{rad}$ first-order-achromatic bend created by transversely offsetting quadrupole magnets in the FODO lattice. Quadrupole offsets are determined analytically from beam-matrix theory. We also discuss the application of microbunch rotation to out-coupling a cavity-based XFEL.

Figure 1

Offset quadrupole triplet for microbunch rotation.

Figure 2

Key matrix parameters for a $10\mathrm{\mu }\mathrm{rad}$ rotation with the parameters given in Table 1, experiment I.

Figure 3

Bunching factor through a microbunch rotation triplet, using the parameters in Table 1, experiment I, $10\mathrm{\mu }\mathrm{rad}$. The bunching factor is compared for the analytical model with thick quadrupoles, elegant with first- or second-order matrices, and genesis.

Figure 4

Microbunch recovery as a function of (a) photon energy, (b) electron beam energy spread, (c) electron beam energy, (d) quadrupole strength, and (e) the drift distance between quadrupoles. Parameters in Table 1, experiment I, were used.

Figure 5

Side view of experimental setup in LCLS-II hard x-ray undulator hall.

Figure 6

Averaged images showing the on axis (top) and rotated (bottom) spots. (a) Experiment I, $10\mathrm{\mu }\mathrm{rad}$, (b) experiment I, $20\mathrm{\mu }\mathrm{rad}$, and (c) experiment II, $10\mathrm{\mu }\mathrm{rad}$. Approximate spot pulse energies are given next to each spot.

Figure 7

Scans of the $K$ in the repointed undulator line for (a) experiment I, $10\mathrm{\mu }\mathrm{rad}$, linear taper; (b) experiment I, $10\mathrm{\mu }\mathrm{rad}$, quadratic taper; (c) experiment I, $20\mathrm{\mu }\mathrm{rad}$, quadratic taper; and (d) experiment II, $10\mathrm{\mu }\mathrm{rad}$, linear taper. Overlaid text gives the Gaussian-fitted $K$ detune as a percentage of nominal $K$. Error bars give the standard error of the mean. Errors in fit centers give the error on the Gaussian fit.

Figure 8

Gain in rotated undulator section for the $10\mathrm{\mu }\mathrm{rad}$, experiment I, quadratic taper case. In this run, the power in the on-axis spot was $120\mathrm{\mu }\mathrm{J}$. Error bars give the standard error of the mean.

Figure 9

Phaseshifter scan demonstration for experiment I, $10\mathrm{\mu }\mathrm{rad}$ case. With all 32 undulators aligned on axis, a phaseshifter was scanned (blue circles). With the microbunch rotation triplet and repointed undulator line installed, the phaseshifter just upstream of the microbunch rotation triplet was scanned (orange squares). Error bars give the standard error of the mean.

Figure 10

Microbunch rotation as an outcoupling scheme for a cavity-based XFEL.

Figure 11

Comparison of the optimal microbunch recovery angle determined using thick quad with instantaneous kick matrices, integrated function magnet matrices, elegant, and genesis.

Figure 12

Optimized undulator tapers for the four $K$ scans shown in Fig. 7.

Figure 13

Gain curve plotting the x-ray pulse energy in the last eight undulators with 32 LCLS HXU undulators lasing. Error bars give the standard error of the mean.

Figure 14

Angular separation between the on-axis and rotated beams in Fig. 8. Error bars give the standard error of the mean, plus the error in screen calibration.

Figure 15

Analytical calculation of the impact of errors in (a) electron beam energy, (b) alternating quadrupole offsets ($o_1+\mathrm{err}$, $o_2-\mathrm{err}$, $o_3+\mathrm{err}$), and (c) uniform quadrupole offsets ($o_1+\mathrm{err}$, $o_2+\mathrm{err}$, $o_3+\mathrm{err}$) for experiment 1 parameters.

Figure 16

XTCAV measurements at the end of LCLS-HXU. (a) Experiment I, no undulators inserted; (b) experiment II, lasing at half power; (c) experiment I, full power 32 on-axis undulator lasing; and (d) experiment II, full power 32 on-axis undulator lasing. (e)–(g) give the slice current, energy, and energy spread for the measurements in (a)–(d). Sign convention is head on left and tail on right.

Figure 17

Simulated beam from elegant, as inserted into genesis at the beginning of the undulator line. (a) $\gamma -t$ phase space for experiment I, (b) $\gamma -t$ phase space for experiment II, (c) $x-t$ phase space for experiment I, and (d) $x-t$ phase space for experiment II. (e)–(g) give the slice current, energy, and energy spread for each simulation. Sign convention is head on left, tail on right.

Figure 18

Longitudinal profiles of simulations in Fig. 7. (a) Transverse position of beam at beginning of undulator line, (b) slice emittance at the beginning of the undulator line, (c) power after nine repointed undulators at optimal $K$, (d) bunching factor at the beginning of nine repointed undulators at optimal $K$, (e) electron energy loss comparing the beginning of the undulator line to the beginning of the repointed undulator line, and (f) predicted $K$ detune based on energy loss, after subtracting a linear taper of 0.000185/undulator. Dashed lines give the $K$ detunes found from the associated $K$ scans. Sign convention is head on left and tail on right.

Figure 19

Simulated demonstration of increased negative $K$ detune on beam tail. The electron beam is divided into 100 bins, then simulations matching the 50th (red), 60th (green), and 70th (blue) bins are compared. (a) $K$ scans with Gaussian fits, (b) transverse position of beam at beginning of undulator line, (c) power after nine repointed undulators at optimal $K$, (d) bunching factor at beginning of nine repointed undulators at optimal $K$, (e) electron energy loss comparing the beginning of the undulator line to the beginning of the repointed undulator line, and (f) predicted $K$ detune based on energy loss, after subtracting a linear taper of 0.000185/undulator. Dashed lines give the $K$ detunes found from the associated $K$ scans. Sign convention is head on left and tail on right. Errors in fit centers give the error of the Gaussian fit.

Figure 20

A CBXFEL outcoupling scheme where the electron beam is sent around the cavity mirror, and microbunches are lased in an afterburner undulator section outside of the cavity.

Figure 21

A sample electron beam trajectory, calculated analytically using the parameters in Table 1, experiment I, $10\mathrm{\mu }\mathrm{rad}$ rotation.