Formation of temporally shaped electron bunches for beam-driven collinear wakefield accelerators

Beam-driven collinear wakefield accelerators (CWAs) that operate by using slow-wave structures or plasmas hold great promise toward reducing the size of contemporary accelerators. Sustainable acceleration of charged particles to high energies in the CWA relies on using field-generating relativistic electron bunches with a highly asymmetric current profile and a large energy chirp. A new approach to obtaining such bunches has been proposed and illustrated with the accelerator design supported by particle tracking simulations. It has been shown that the required particle distribution in the longitudinal phase space can be obtained without collimators, giving CWAs an opportunity for employment in applications requiring a high repetition rate of operation.

Figure 1

Doorstep distributions described by Eq. (6) (shaded areas) with associated wakefields (traces) calculated for a bunch length $L=\lambda$, with $\chi =0$ (green trace) and $\chi =-\frac{1}{10\lambda }$ (red trace), where transformer ratios are 5.8 and 5.6 respectively. The wakefields are computed for a bunch charge of 10 nC and use a single-mode Green’s function [Eq. (2)] with $f=180\mathrm{GHz}$ and ${\kappa }_{\parallel }=14.3\mathrm{kV}/\mathrm{pC}/\mathrm{m}$ calculated using echo [44].

Figure 2

A target drive bunch peak current (a) and longitudinal phase space (b) distributions at the end of the drive bunch accelerator.

Figure 3

Block diagram of the drive bunch accelerator.

Figure 4

Current (a) and (c) and LPS (b) and (d) distributions obtained from the backward-tracking optimization (a) and (b) and forward-tracked up BC2 end (c,) and (d) to confirm the agreement with the targeted distribution shown in Fig. 2.

Figure 5

Programmed macroparticle distributions at the photocathode surface: for an optimized laser pulse (blue trace), taking into account the photocathode response (orange trace), and both the cathode response and finite bandwidth (BW) of the laser pulse (green trace). The laser bandwidth is taken to be $\delta f=2\mathrm{THz}$.

Figure 6

Current profile (a) with associated LPS (b), and horizontal (c) and vertical (d) phase-space distributions simulated with astra at the end of the photoinjector (11.67 m from the photocathode). In plot (b), the red trace represents the slice rms energy spread ${\sigma }_E$.

Figure 7

Axial electric ${\mathcal{E}}_z$ (red trace) and magnetic $B_z$ (blue trace) fields experienced by the reference particle as it propagates along the optimized photoinjector (a) with corresponding kinetic energy (b), transverse (blue) and longitudinal (red) beam emittances (c), and sizes (d) evolving along the injector.

Figure 8

Updated accelerator design, with the addition of the injector beam line and a laser heater section.

Figure 9

Layout of bunch compressor BC1 (top diagram) with evolution of associated betatron function (a) and pertinent linear (b), second-order (c), and third-order (d) transfer-map elements along the beam line (with $s=0$ corresponding to the beginning of BC1). In plots (b)–(d) the left and right axes refer to the horizontal chromatic functions ${\eta }_{i,x}$ and accumulated longitudinal transfer-map elements from 0 to location $s$ along BC1. In the top diagram the red, blue, green, and purple rectangles correspond, respectively, to quadrupole, dipole, sextupole, and octupole magnets.

Figure 10

Layout of bunch compressor BC2 (top diagram) with evolution of associated betatron function (a) and pertinent linear (b), second-order (c), and third-order (d) transfer-map elements along the beam line (with $s=0$ corresponding to the beginning of BC2). In plots (b)–(d) the left and right axes refer to the horizontal chromatic functions ${\eta }_{i,x}$ and accumulated longitudinal transfer-map elements from 0 to location $s$ along BC2. The top diagram follows the same conventions as in Fig. 9.

Figure 11

The geometry of the bunch compressors BC1 (a) and BC2 (b), where red, blue, green, and purple rectangles are quadrupoles, dipoles, sextupoles, and octupoles magnets, respectively.

Figure 12

Evolution of the betatron (left axis) and horizontal dispersion (right axis) functions along the proposed linac. The vertical dispersion is zero throughout the linac. The magnetic-lattice color coding for the element follows Fig. 9 with the accelerating cavities shown as gold rectangles.

Figure 13

Current profile (a) and associated LPS (b) distributions simulated with astra at the end of the photoinjector (see Fig. 6) with added uncorrelated fraction energy spread following a Gaussian distribution with rms spread ${\sigma }_E/E=1.5\times {10}^{-3}$. In plot (b) the red trace represents the slice rms energy spread ${\sigma }_E$.

Figure 14

Current (a) with associated LPS (b), and transverse horizontal (c) and vertical (d) phase-space distributions simulated with elegant at the end of BC2 using the optimized linac and bunch-compressor settings summarized in Table 4 and the injector distributions from Fig. 13. In plot (b) the red trace represents the slice rms energy spread ${\sigma }_E$.

Figure 15

Comparison of the Pareto front with the analytical trade-off curve between the peak field and transformer ratio described by Eq. (30) of Ref. [10]. Each blue dot represents a numerically simulated configuration with the red star representing the configuration with parameters listed in Table 4.

Figure 16

Target (from Fig. 2) and optimized final current distributions (respectively shown as green- and red-shaded curves) with associated wakefields (respectively displayed as green and red traces). The transformer ratio for the simulated distribution is $\mathcal{R}=5.0$.

Figure 17

Final $(z,x)$ (a) and $(z,y)$ (c) beam distributions corresponding to the data shown in Fig. 14, and slice analysis for positions $⟨x⟩$ and $⟨y⟩$ (b) and rms beam size and emittances (d).

Figure 18

Wakefields obtained from 100 simulations with jitter in linacs L1, L2, and L39. All cavities are taken to have relative jitter in accelerating voltage of 0.01% and phase jitter 0.01°. The red line shows the average wakefield while the blue shaded region represents the fluctuation of wakefields due to jitter over 100 random realizations of the linac settings. The average transformer ratio is $5.00\pm 0.05$. The reconstructed current profile (green-shaded curve) is obtained numerically using Eq. (4).

Figure 19

Wakefields obtained from 100 simulations with factional magnetic field jitter $\mathrm{\Delta }B/B={10}^{-4}$ on all the magnets. The red line shows the average wakefield while the blue shaded region represents the fluctuation of wakefields due to jitter over 100 random realizations. The reconstructed current profile (green-shaded curve) is obtained numerically using Eq. (4).

Figure 20

Current distribution (shaded curves, right axis) and associated wakefields (traces) for the nominal charge and $\pm 2\%$ relative change in charge (9.8 and 10.2 nC).

Figure 21

Treatment of collective effects as energy kicks downstream of beam line elements. In forward (respectively backward) tracking, transformations of beam line elements (respectively energy kicks) were applied, followed by energy kicks (respectively beam line elements).