Design and operation of transfer lines for plasma wakefield accelerators using numerical optimizers

The Advanced Wakefield (AWAKE) Experiment is a proof-of-principle experiment demonstrating the acceleration of electron beams via proton-driven plasma wakefield acceleration. AWAKE Run 2 aims to build on the results of Run 1 by achieving higher energies with an improved beam quality. As part of the upgrade to Run 2, the existing proton and electron beamlines will be adapted and a second plasma cell and new 150-MeV electron beamline will be added. The specification for this new 150-MeV beamline will be challenging as it will be required to inject electron bunches with micron-level beam size and stability into the second plasma cell while being subject to tight spatial constraints. In this paper, we describe the techniques used (e.g., numerical optimizers and genetic algorithms) to produce the design of this electron line. We present a comparison of the methods used in this paper with other optimization algorithms commonly used within accelerator physics. Operational techniques are also studied including steering and alignment methods utilizing numerical optimizers and beam measurement techniques employing neural networks. We compare the performance of algorithms for online optimization and beam-based alignment in terms of their efficiency and effectiveness.

Figure 1

Schematic of the configuration of the two-electron beamlines, plasma cells, and a section of the proton transfer line. Dipoles are shown in cyan, the quadrupoles in red, the sextupoles in yellow, and the octupoles in white.

Figure 2

Mean (data points) and range (shaded region) of the objective function evaluations from a population of solutions used by a genetic algorithm for the optimization of quadrupole strengths and positions.

Figure 3

2D projections of the distribution of a bunch tracked through the transfer line to the plasma injection point. The color of the data points denotes the $\mathrm{\Delta }E/pc$ value.

Figure 4

Points on the Pareto front at the final evaluation (red) and the population from the first evaluation (gray) of the multiobjective optimization of quadrupole strengths and positions; the axes are the two objective functions constructed from the horizontal and vertical components of Eq. (7). The inset shows an expanded view of the final Pareto front. Only viable solutions with no magnet overlap are included.

Figure 5

(a) The minimum objective function [$f(x)$] values from the optimization of quadrupole strengths and positions using GAs, the Nelder-Mead algorithm and Powell’s method. The Nelder-Mead algorithm and Powell’s method were started 20 times with random starting values. The minimum and maximum values for each are indicated. (b) The number of function evaluations to reach the minimum $f(x)$ for each of the 20 optimization attempts.

Figure 6

mad-x simulation of the transfer line design after the optimization of the sextupole and octupole positions and strengths. Twiss parameters ${\beta }_x$ (black), ${\beta }_y$ (red), and dispersion $D_x$ (green) and $D_y$ (blue) are shown below, with a synoptic overview of the transfer line above, with dipoles (green), quadrupoles (black), sextupoles (blue), and octupoles (red).

Figure 7

Horizontal and vertical beam sizes averaged over 50 seeds with quadrupole misalignments sampled randomly from a Gaussian distribution with standard deviation given by the $x$ axis.

Figure 8

Schematic showing the locations of BPMs (cyan), a BTV (yellow), and correctors (purple). Magnet positions are shown as outlines. The beam goes from left to right.

Figure 9

(a) The minimum objective function [$f(x)$] values from the minimization of the injection-point beam size by optimizing sextupole and octupole transverse offsets using (left) Py-BOBYQA (objfun_has_noise = True), (center) RCDS, and (right) Py-BOBYQA (objfun_has_noise=False). (b) The number of function evaluations to reach the minimum $f(x)$. The algorithms were tested on 20 error seeds; the minimum and maximum values for each are indicated.

Figure 10

Distributions of (a) beam sizes and (b) relative proton-electron transverse bunch offsets at the injection-point for 100 seeds with errors as defined in Table 4 after beam-based alignment. The orange lines denote the experimental specifications.

Figure 11

Schematic of the proton beamline (blue), electron beamline (red), and common line (green). The relevant BPMs are shown as rectangles and the electron line dipoles as triangles; quadrupoles are not shown in this diagram. The beams propagate from left to right. The iris marker highlights the start of the plasma.

Figure 12

A comparison of the optics model beam trajectory prediction (orange) and the PGNN prediction (green) with the measured high-charge BPM data (blue), shown for the horizontal (a) and vertical (b) planes. The start of the common line is denoted by a vertical black line.

Figure 13

The data points show the horizontal and vertical rms values for beam jitter and position predictions at BPM 51; the error bars give 95% confidence interval. The resolution scaling from the low charge is given as a dashed line under the assumption that the low-charge results were resolution limited. The NN error denotes the error from a neural network without including predictions from the beamline model.