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Model-based, derivative-free, trust-region algorithms are increasingly popular for optimizing computationally expensive numerical simulations. A strength of such methods is their efficient use of function evaluations. In this paper, we use one such algorithm to optimize the beam dynamics in two cases of interest at the Argonne Wakefield Accelerator (AWA) facility. First, we minimize the emittance of a 1 nC electron bunch produced by the AWA rf photocathode gun by adjusting three parameters: rf gun phase, solenoid strength, and laser radius. The algorithm converges to a set of parameters that yield an emittance of 1.08 μm. Second, we expand the number of optimization parameters to model the complete AWA rf photoinjector (the gun and six accelerating cavities) at 40 nC. The optimization algorithm is used in a Pareto study that compares the trade-off between emittance and bunch length for the AWA 70MeV photoinjector. THE AWA FACILITY The 70MeV rf photoinjector at the Argonne Wakefield Accelerator (AWA) facility [1] consists of an rf gun followed by six rf accelerating cavities, hereafter referred to as the linac. See Fig. 1 for the beam line layout. The 1.5 cell rf gun operates at 1.3GHz with three solenoids and a Cs2Te photocathode excited by a 248 nm UV laser. Solenoid 1 (S1) is used to buck the field at the cathode, while the other two solenoids (S2 and S3) are used for emittance compensation. The accelerating cavities, also operated at 1.3GHz, are 7 cell standing-wave cavities [2] each with independently controllable phase. The cavities are labeled L1-L6 in Fig. 1. OPTIMIZATION ALGORITHM Model-based, derivative-free algorithms are frequently used to optimize computationally expensive simulations due to their judicious use of function evaluations. In cases specific to accelerator physics, beam properties at different operational parameters are observed; these methods then build models of the unknown function and minimize these models to identify candidate parameters to evaluate. BOBYQA [3] is one such method that is available via the NLopt [4] package and was used in this study. Given a candidate set of optimal parameters v , BOBYQA constructs a quadratic model using function values of points near v . This model is minimized in a neighborhood of v in order to produce a ∗ nneveu@hawk.iit.edu point v̂. If v̂ has a smaller objective function value than v , the estimate of the optimum is updated to v̂, and a newmodel is constructed. If v̂ is not a sufficient improvement over v , the model around v is improved. For more information about derivative-free optimization, see [5]. The parameters v are generated and supplied to the open source particle-in-cell code OPAL-t [6]. This code was chosen in part because it models the 3D space charge necessary to accurately simulate the linac. The optimization package NLopt and OPAL-t were used in combination with Python code written at Argonne National Laboratory to perform simulation evaluations and optimization. All the files needed to replicate the results in this paper are available at www.mcs.anl.gov/~jlarson/AWA. Interested parties are welcome to adapt the code to their needs and suggest improvements. OPTIMIZATION PARAMETERS When optimizing the gun, three parameters were varied: solenoid strength (S3), gun phase (φg), and laser radius (R) of a uniform pulse. The minimized objective was emittance ( x). (The phase is defined as 0◦ at maximum energy gain.) When optimizing the entire linac, seven additional parameters were varied: the longitudinal laser full width at half maximum (T) and accelerating cavity phases (φL). The optimization parameters and bounds are given in Table 1; we denote the set of ten optimization parameters as v = [S3, φg, R,T, φL], where φL = [φL1, . . . , φL6 ] represents the phase of each linac cavity L1-L6. Table 1: Parameter Bounds for Gun and Linac Optimization Variable Range Unit Solenoid Strength 0 ≤ S3 ≤ 440 amps Phase of Gun −60 ≤ φg ≤ 60 degrees Laser Radius 0.1 ≤ R ≤ 30 mm Laser FWHM1 2 ≤ T ≤10 ps Cavity Phase1,2 −20 ≤ φL ≤ 20 degrees 1 not varied during gun optimization 2 φL = [φL1, . . . , φL6 ] GUN OPTIMIZATION Much work has been done to optimize 1.5 cell rf guns at 1 nC [7]. This known solution was used as a baseline THPAB155 Proceedings of IPAC2017, Copenhagen, Denmark ISBN 978-3-95450-182-3 4100 Co py rig ht © 20 17 CC -B Y3. 0 an d by th er es pe ct iv ea ut ho rs 05 Beam Dynamics and Electromagnetic Fields D11 Code Developments and Simulation Techniques

Photoinjector optimization using a derivative-free, model-based trust-region algorithm for the Argonne Wakefield Accelerator