Robustness of a plasma acceleration based free electron laser

Laser plasma accelerators (LPA) can sustain $\mathrm{GeV}/\mathrm{m}$ accelerating fields offering outstanding new possibilities for compact applications. The LPA beam brightness can now be comparable to radio-frequency accelerators’ (RFA), thanks essentially to the beams short duration ($<3\mathrm{fs}$) and low emittance (as small as 0.1 micron). Still, the mrad level divergence and few percent level energy spread, remain limiting parameters in the cases of demanding applications such as free electron lasers (FELs). Several concepts of transfer line were proposed to mitigate those intrinsic properties targeting undulator radiation applications. We study here the robustness of the chromatic matching strategy for FEL amplification at 200 nm in a dedicated transport line, and analyze its sensitivity to several parameters. We consider not only the possible LPA source jitters, but also various realistic defaults of the equipment such as magnetic elements misalignments or focussing strength errors, imperfect undulator fields, etc.

Figure 1

COXINEL schematic view. LPA: laser plasma accelerator, PMQ: Permanent magnet quadrupole, EMQ: electromagnetic quadrupole, cBPM: cavity beam position monitor [44, 45] for orbit correction, Seed: coherent source at 200 nm generated by frequency mixing using the same IR laser as for electron beam generation. Undulator: center located at 6.796 m from the LPA source point.

Figure 2

(Left) Horizontal and (right) vertical phase-spaces at the undulator center. (Up) Density color map, ranging from red for higher to blue for lower densities. (Down) Energy color map, ranging from red for higher to blue for lower energies. Beam transport simulation in the nonlinear case with BETA and sympletic 6D tracking using the S2I-CM optics with $r_{11}=r_{33}=10$ and $r_{56}=0.4\mathrm{mm}$.

Figure 3

Beam size envelopes and normalized emittances in the (red) horizontal and (blue) vertical plane, and rms bunch length ${\sigma }_s$ along the COXINEL line. Beam transport simulation in the nonlinear case with (line) BETA and sympletic 6D tracking and (dashed line) OCELOT, both using the S2I-CM optics with $r_{11}=r_{33}=10$ and $r_{56}=0.4\mathrm{mm}$.

Figure 4

Electron beam longitudinal phase-space and corresponding slice parameters at the undulator center. Simulation in the nonlinear case: without chicane for (a) and blue curves in (g–k), with chicane for (d) and blue curves in (l–p). Simulation including space-charge forces: without chicane for (b) and red curves in (g–k), with chicane for (e) and red curves in (l–p). Simulation including space-charge forces and CSR effects: without chicane for (c) and black curves of (g–k) and with chicane for (f) and black curves of (l–p). Simulation with BETA and sympletic 6D tracking using the S2I-CM optics with $r_{11}=r_{33}=10$ and $r_{56}=0.4\mathrm{mm}$ for cases with chicane.

Figure 5

(a) FEL power along the undulator simulated with (line) BETA, sympletic 6D tracking and GENESIS, (dashed line) OCELOT and CHIMERA. (b) FEL peak power longitudinal profile, (c) FEL spectrum at the undulator exit, (d) FEL radiation size and (e) FEL divergence along the undulator, simulated with GENESIS. (a–e) Beam transport simulation in the nonlinear case without collective effects and using the S2I-CM optics with $r_{11}=r_{33}=10$ and $r_{56}=0.4\mathrm{mm}$.

Figure 6

FEL peak power at 200 nm versus chicane strength. (a) Simulation without collective effects and with magnifications $r_{11}=r_{33}$ of (black circle) 10, (red square) 12 and (blue square) 15. (b) Simulation with $r_{11}=r_{33}=10$ and (black) without collective effects, (blue) with the space charge and (red) with the space charge and the CSR. Beam transport simulation in the nonlinear case with BETA and sympletic 6D tracking using the S2I-CM optics. FEL simulation with GENESIS.

Figure 7

FEL peak power at 200 nm along the undulator with a (black) 1 pC and (red) 5 pC per % of energy bandwidth. Beam transport simulation with GENESIS without collective effects using the S2I-CM optics with $r_{11}=r_{33}=10$ and $r_{56}=0.4\mathrm{mm}$. Normalized emittance: 0.2 mm mrad, divergence: 1 mrad. FEL simulation with GENESIS.

Figure 8

Normalized FEL peak power at 200 nm versus electron beam charge and divergence. Beam transport simulation with OCELOT without collective effects using the S2I-CM optics with $r_{11}=r_{33}=10$ and $r_{56}=0.4\mathrm{mm}$. Normalized emittance preserved at 1 mm mrad. FEL simulation with CHIMERA.

Figure 9

Effect of random source jitters ($5\mu \mathrm{m}\mathrm{rms}$ in transverse position, 1 mrad rms in divergence and 1% rms in energy spread) on the LPA beam quality. (a) Rms orbits in the (red) horizontal and (blue) vertical plane. (b) Dispersion functions in the (red) horizontal plane, (blue) vertical plane and (black) horizontal plane without jitter. (c–d) Statistical emittance distribution (500 tries) without the energy spread jitter, but with transverse position and divergence jitters ($5\mu \mathrm{m}\mathrm{rms}$ in transverse position, 1 mrad rms in divergence) and including orbit corrections. Simulation in the nonlinear case with BETA and sympletic 6D tracking without collective effects using the S2I-CM optics with $r_{11}=r_{33}=10$ and $r_{56}=0.4\mathrm{mm}$.

Figure 10

Normalized FEL peak power at the undulator exit versus initial LPA beam (a) transverse position and (b) pointing (angle) in the (red circle) horizontal and (blue square) vertical plane. Beam transport simulation in the nonlinear case with BETA and sympletic 6D tracking without collective effects using the S2I-CM optics with $r_{11}=r_{33}=10$ and $r_{56}=0.4\mathrm{mm}$. FEL simulation with GENESIS.

Figure 11

(Left) horizontal and (Right) vertical acceptance of the transport line. Beam energy at 180 MeV using S2I-CM optics with $r_{11}=r_{33}=10$ and $r_{56}=0.4\mathrm{mm}$. Beam transport simulation in the nonlinear case with BETA and sympletic 6D tracking.

Figure 12

Beam losses along COXINEL line assuming an energy spread of (blue) 1% rms, (red) 10% rms and (black) 20% rms together with a divergence of 1 mrad rms. Beam transport simulation in the nonlinear case with BETA and sympletic 6D tracking without collective effects using the S2I-CM optics with $r_{11}=r_{33}=10$ and $r_{56}=0.4\mathrm{mm}$.

Figure 13

Effect of random magnet misalignments/defaults on the electron beam (a) rms orbits and (b) rms dispersion functions, in the (red) horizontal and (blue) vertical plane, (line) without and (dashed line) with orbit correction. (c–d) Effect on the statistical normalized emittance distribution in the horizontal and vertical plane (500 tries) with orbit correction. Initial undisturbed emittances are about $2\pi \mathrm{mm}\mathrm{mrad}$ in both planes. (a–b) Random displacement of all the quadrupoles magnetic center by up to $100\mu \mathrm{m}$, together with a random tilt of the dipoles of up to 1 mrad and a random error on their possible relative strength of up to 0.1%. (c–d) Random displacement of all the quadrupoles only. Beam transport simulation in the nonlinear case with BETA and sympletic 6D tracking without collective effects using the S2I-CM optics with $r_{11}=r_{33}=10$ and $r_{56}=0.4\mathrm{mm}$.

Figure 14

FEL peak power at 200 nm at the undulator exit versus second PMQ radial offset (blue) with and (red) without orbit correction. Beam transport simulation in the nonlinear case with BETA and sympletic 6D tracking without collective effects using S2I-CM optics with $r_{11}=r_{33}=10$ and $r_{56}=0.4\mathrm{mm}$. FEL simulation with GENESIS.

Figure 15

FEL peak power at the undulator exit versus chicane strength for various quadrupole strength shifts: (blue) ideal, (dark green) $+8\%$ on PMQ 1, (red) $+1\%$ on PMQ 2, (light blue) $+1\%$ on PMQ 3, (purple) $+8\%$ on EMQ 1, (light green) $+4\%$ on EMQ 2, (black) $+20\%$ on EMQ 3. Beam transport simulation in the nonlinear case with BETA and sympletic 6D tracking without collective effects using the S2I-CM optics with $r_{11}=r_{33}=10$. FEL simulation with GENESIS.

Figure 16

(a) Electron beam trajectory in the horizontal plane using measured undulator magnetic field and (b) FEL power along the undulator using (line) measured and (dashed line) purely sinusoidal undulator magnetic field. Beam transport in the nonlinear case with OCELOT using the S2I-CM optics with $r_{11}=r_{33}=10$ and $r_{56}=0.4\mathrm{mm}$. FEL simulation with CHIMERA.

Figure 17

FEL peak power versus undulator tapering using (dotted line) real and (dash squared line) ideal undulator magnetic field. Beam transport in the nonlinear case with OCELOT using the S2I-CM optics with $r_{11}=r_{33}=10$ and $r_{56}=0.4\mathrm{mm}$. FEL simulation with CHIMERA.

Figure 18

FEL peak power at 40 nm at the undulator exit versus chicane strength using a magnification of (black circle) 15 and (blue square) 20. Beam transport simulation in the nonlinear case with BETA and sympletic 6D tracking without collective effects using the S2I-CM optics with a 400 MeV beam. FEL simulation with GENESIS.

Figure 19

FEL (a) peak power longitudinal profile and (b) spectrum at the undulator exit. FEL (c) transverse size and (d) divergence along the undulator. FEL radiation at 40 nm in optimum case of Fig. 18 ($r_{11}=r_{33}=15$ and $r_{56}=0.25\mathrm{mm}$). Beam transport simulation in the nonlinear case with BETA and sympletic 6D tracking without collective effects using the S2I-CM optics. FEL simulation with GENESIS.