The linac-based test facility FLUTE (Ferninfrarot Linac Und Test Experiment) at KIT will be used to study novel accelerator technology and provide intense THz pulses. In this paper, we present start-to-end simulation studies of FLUTE with different bunch charges. We employ a parallel Bayesian optimization algorithm for different bunch charges of FLUTE to find optimized accelerator settings for the generation of intense THz radiation

Bründermann, E.

Garcia, A. Santamaria

Müller, A-S.

Schwarz, M.

Schäfer, J.

Xu, C.

English

Santamaria Garcia, Andrea

KITopen

OPTIMIZATION STUDIES OF SIMULATED THz RADIATION AT FLUTEC. Xu∗, E. Bründermann, A. Santamaria Garcia, J. Schäfer, M. Schwarz,  A.-S. Müller Karlsruhe Institute of Technology (KIT),  Karlsruhe, GermanyAbstractThe linac-based test facility FLUTE (Ferninfrarot LinacUnd Test Experiment) at KIT will be used to study novel ac-celerator technology and provide intense THz pulses. Inthis paper, we present start-to-end simulation studies ofFLUTE with different bunch charges. We employ a par-allel Bayesian optimization algorithm for different bunchcharges of FLUTE to find optimized accelerator settings forthe generation of intense THz radiation.INTRODUCTIONThe accelerator test facility FLUTE [1] at KIT will beused to generate broadband THz radiation for various exper-iments. It will operate with a wide range of bunch chargesfrom pC to nC, for which the radiation needs to be opti-mized. The electron bunch at FLUTE is first created at anRF photoinjector and accelerated up to 7 MeV. It then trav-els through a linac, which further accelerates the bunch up to50 MeV. At the end, the bunch is compressed longitudinallyvia a bunch compressor with 4 dipole magnets down to thefs range, allowing the generation of intense THz pulses withcoherent synchrotron radiation (CSR).Spatial light modulators are being integrated into the pho-tocathode laser system to have 3D control of the laser pulseand provide a tailored initial electron distribution for intenseTHz pulse generation [2, 3]. In previous studies, a geneticalgorithm (GA) was employed in the parameter optimiza-tion to minimize the bunch length at 1 pC bunch charge [4].Nevertheless, it is known that GA is prone to local optimaand often requires more computation resources or multiplerestarts to mitigate this problem [5]. In this paper, we imple-ment a parallel variant of the Bayesian optimization (BO) [6],which is as efficient as GA and can globally optimize thegiven physical objective functions even with a large param-eter space. We present the first optimization results usingparallel Bayesian optimization (PBO) for minimum electronbunch length and maximum peak THz pulse E-field, bothfor low and high charge cases.PARALLEL BAYESIAN OPTIMIZATIONBuild GP modelf ∼ GP(µ, k)Acquisition functionEINext sample pointsxi = (x1i , . . . , xpi )Run simulationsASTRA, OCELOTObjective functionyi = σz,−→E , . . .Augment data(Xj−1, Yj−1).append(xi, yi)µ, σ αxi∈{1,...,N} . . .6D particledistributionyi(Xj, Yj)Initial(X0, Y0)Figure 1: Workflow of the parallel Bayesian optimizationalgorithm. The boxes are calculations and the arrows are theinput and output variables.∗ chenran.xu@kit.eduBayesian optimization is widely used for global optimiza-tion of an unknown objective function 𝑓 (𝑥). Figure 1 showsthe BO algorithm workflow used in this paper. In each step,BO builds a statistical model, where the most widely used isa Gaussian process (GP), of the objective 𝑓. The GP model𝒢𝒫(𝜇, 𝑘) predicts the mean 𝜇(𝑥) and uncertainty 𝜎(𝑥) ofthe objective function value 𝑦 = 𝑓 (𝑥) at an unknown point𝑥 = (𝑥1, … , 𝑥𝑝), where 𝑝 is the number of input parameters.The kernel function 𝑘(𝑥, 𝑥′) describes the expected similaritybetween two data points. In this study, we choose the radialbasis function (RBF) as kernel. Based on the GP model,an acquisition function 𝛼 can be calculated to efficientlyguide the optimization and choose the next point to sample𝑥𝑖. Here we use the expected improvement (EI) [7] acquisi-tion, which calculates the expected value of improvement ofa point 𝑥 over the best observed value so far 𝑓best.In the non-parallel version of BO, the next sample pointis selected at the maximum of the acquisition 𝛼EI(𝑥). Sincethe objective is calculated through physics simulations, wecan further increase the performance of BO by evaluating𝑁 multiple parameter settings in parallel, with 𝑁 being theparallel capacity of available computing resources. For theparallel Bayesian optimization (PBO) implementation in thispaper, we use a local penalization function to select batchsample points [6]. The 𝑖-th sample point 𝑥𝑖 is chosen bymaximizing the product of acquisition 𝛼 and penalizationfunction 𝜑=𝜑1 ∗ ⋯ ∗ 𝜑𝑖−1, where 𝜑𝑖−1 ∈ (0, 1] effectivelypenalizes the acquisition value of a point locally around aprevious sample point in the parallel batch 𝑥𝑖−1. This allowsan efficient sampling of the parameter space in a singleoptimization step 𝑗.IMPLEMENTATION OF CSROPTIMIZATIONBased on the knowledge of FLUTE, we choose the fol-lowing 6 parameter as input for the PBO algorithm: phaseand gradient of the photoinjector gun and linac RF field,solenoid magnetic field and the bunch compressor bendingangle.The total spectral intensity of the synchrotron radiationemitted by an electron bunch isd2𝐼d𝜔dΩ = [𝑁e + 𝑁e(𝑁e − 1)𝐹(𝜔)]d2𝐼0d𝜔dΩ , (1)where 𝑁e denotes the number of electrons in the bunch, 𝐹(𝜔)is the form factor, and d2𝐼0/d𝜔dΩ is the single particlespectral density. The first part is the incoherent radiation,scaling linearly with the electron number 𝑁e. The secondpart is the coherent synchrotron radiation (CSR), whichscales quadratically. Due to the large number of electrons ina bunch, the coherent radiation, where the form factor 𝐹 is13th Int. Particle Acc. Conf. IPAC2022, Bangkok, Thailand JACoW PublishingISBN: 978-3-95450-227-1 ISSN: 2673-5490 doi:10.18429/JACoW-IPAC2022-WEPOMS023WEPOMS023ContentfromthisworkmaybeusedunderthetermsoftheCCBY4.0licence(©2022).Anydistributionofthisworkmustmaintainattributiontotheauthor(s),titleofthework,publisher,andDOI2292MC5: Beam Dynamics and EM FieldsD11: Code Developments and Simulation Techniquesclose to 1, is enhanced by many orders of magnitude. Forfrequencies corresponding to wavelengths shorter than thebunch length, the form factor 𝐹 and thus the CSR intensitydrop rapidly. We choose the rms bunch length 𝜎𝑧 as anobjective function, because minimizing 𝜎𝑧 will extend theform factor 𝐹(𝜔) to higher frequencies and increase theoverall CSR intensity.Alternatively, we use the peak electric field of the THzpulse as an objective function, which leads to a more directoptimization of the THz pulse despite requiring more pro-cessing steps of the output particle distribution. Based onthe semi-analytic approach introduced in [8, 9], we are ableto calculate the CSR E-field emitted by an arbitrarily shapedbunch𝐸(𝑡) = 𝑁e ∫∞−∞𝐸0(𝜏)𝜚(𝑡 − 𝜏) d𝜏= 𝑁e1𝜋ℜ ∫∞0̃𝐸0(𝜔) ̃𝜚(𝜔) ei𝜔𝑡 d𝜔 ,(2)where 𝑁e is the number of electrons, 𝐸0 is the single electronE-field, and 𝜚 is the normalized charge density of the electronbunch. The Fourier-transformed charge density ̃𝜚(𝜔) is thenobtained analytically via a step-wise linear interpolation of 𝜚and the E-field of the bunch emitted CSR in the time-domain,which is numerically integrated for all frequencies.The complete structure of FLUTE is implemented as asimulation model using the tracking codes ASTRA [10] andOCELOT [11]. The electron bunch is first created by AS-TRA and tracked from the cathode to the entrance of thebunch compressor, including the space charge (SC) effectalong the track. The ASTRA output particle distribution isthen fed into an OCELOT model, which tracks the bunchfurther until the end of the magnet chicane and, in addition,includes the CSR effects. The final distribution is used tocalculate the respective objective function 𝑓. For the simu-lation presented in this paper, 10,000 macro particles weregenerated and tracked in ASTRA and OCELOT, where eachsimulation took about 10 min. The parallel Bayesian opti-mization algorithm was run on a computing cluster with20 parallel evaluations and a maximum of 50 optimizationsteps. The optimization took in total about 6 hours, wherethe majority of time was spent on the time-consuming sim-ulations. For each optimization, we choose the same 20random sample points to initialize the GP model. The GPhyperparameters, such as the variance and the kernel lengthscales, are fitted dynamically during the optimizations. Al-ternatively, these hyperparameters can be estimated fromprior knowledge of the physics model or dedicated parameterscan results. Although the later option will require moretime, it could further increase the convergence speed of theBayesian optimization.RESULTSWe first consider the 1 pC bunch charge case, where theinitial distribution is generated by a laser pulse with a trans-verse size of 0.25 mm and a pulse length of 700 fs. Fig-ure 2(a) shows the longitudinal phase space of the electron40.541.041.542.042.5E[MeV]µE : 41.5 MeVσE : 0.3% stdσz: 6.1 fs(a) Before optimization1 pC40.541.041.542.042.5E[MeV]µE : 41.5 MeVσE : 0.5% stdσz: 3.9 fs(b) Bunch length−20 0 20t [fs]40.541.041.542.042.5E[MeV]µE : 41.4 MeVσE : 0.4% stdσz: 4.6 fs(c) Peak E-field1 10 1003638404244 µE : 41.1 MeVσE : 1.0% stdσz: 54.6 fs(d) Before optimization100 pC3638404244 µE : 40.9 MeVσE : 1.8% stdσz: 11.6 fs(e) Bunch length−100 0 100t [fs]3638404244 µE : 40.2 MeVσE : 1.8% stdσz: 14.0 fs(f) Peak E-fieldFigure 2: Longitudinal phase space of the compressed elec-tron bunches with (a-c) 1 pC charge and (d-f) 100 pC charge.(a,d) previous settings in design stage, (b,e) optimized set-tings to minimize bunch length, and (c,f) optimized settingsto maximize the peak electric field of THz pulse.bunch using design stage parameter settings obtained froma parameter scan method. The optimization results withbunch length 𝜎𝑧 and peak E-field of the THz pulse 𝐸maxas objective are shown in Figs. 2(b) and (c) respectively.The projection onto the time axis corresponds to the currentdensity profile. The bunch length optimization further com-presses it down to 𝜎𝑧 = 3.9 fs. On the other side, the peakE-field optimization manages to keep more electrons in thecore of the bunch and reaches a higher peak current, eventhough with a larger rms bunch length of 4.6 fs.For the high bunch charge case with 100 pC, the initial dis-tribution is generated from a laser pulse with a transverse sizeof 0.25 mm and a pulse length of 2 ps. Figures 2(d-f) showthat the optimizations with both objective functions obtainvery similar results and longitudinal phase space distribu-tions. The minimum bunch length 𝜎𝑧 = 11.6 fs is smallerthan the design stage value of 54.6 fs by a factor of ∼ 4.7.Both bunches from BO optimizations have an higher energyspread, which is a side effect of moving away from the nom-inal linac phase for a more linear accelerating gradient andthus a better compression.The total emitted SR spectrum for different settings areshown in Figs. 3(a,c). It is visible that all the spectra decreaserapidly above the critical frequency 𝜔𝑐 ∼ 1.4 × 1014 s−1(corresponding to ca. 22 THz). For the 1 pC case, the spec-trum of the 𝐸max-optimization extends to higher frequenciesand has a smooth curve, while the spectra for other settings13th Int. Particle Acc. Conf. IPAC2022, Bangkok, Thailand JACoW PublishingISBN: 978-3-95450-227-1 ISSN: 2673-5490 doi:10.18429/JACoW-IPAC2022-WEPOMS023MC5: Beam Dynamics and EM FieldsD11: Code Developments and Simulation TechniquesWEPOMS0232293ContentfromthisworkmaybeusedunderthetermsoftheCCBY4.0licence(©2022).Anydistributionofthisworkmustmaintainattributiontotheauthor(s),titleofthework,publisher,andDOI1013 1014 1015ω [1/s]10−2410−2310−2210−2110−20SRintensity[Js](a) Total SR spectrum−20 −10 0 10 20t [fs]0.00.20.40.6E[MV/m](b) E-field of THz pulse1013 1014 1015ω [1/s]10−2010−1910−1810−1710−16(c) Total SR spectrum−50 0 50t [fs]010203040(d) E-field of THz pulse1 pC 100 pCBefore opt. Peak E-field Bunch lengthFigure 3: Bunch SR spectrum and THz pulse electric fieldfor (a,b) 1 pC and (c,d) 100 pC bunch charge.show side bumps in the high-frequency region due to het-erogeneous charge densities in the bunch. For each particledistribution, the electric field of the THz pulse is calculatedat distance 𝑅 = 1 m and phase 𝜙 = 0, as shown in Fig. 3(b,d).For 1 pC bunch charge, the peak E-field of 𝐸max-optimizationreaches 600 kV/m, which is higher than for the bunch lengthoptimization with 400 kV/m and is higher than the designsettings of 350 kV/m by a factor of ∼ 1.7. For the designsettings, the THz pulse shape follows roughly the shapeof the bunch current profile. Decreasing the bunch lengthfurther, smoothes the bunch structure. Then, the resultingTHz pulse approaches a Gaussian shape with a FWHM ofabout 1/𝜔𝑐. Whereas for the 100 pC case, the final bunchesare still longer than 1/𝜔𝑐. Therefore reducing the bunchlength efficiently, extends the form factor 𝐹 to higher fre-quencies and increases the THz pulse E-field. As shown inFigs. 3(c,d), both settings have a clearly more intense SR. Apeak E-field of 43 MV/m is reached, which is higher thanthe previous design value at 8.4 MV/m by a factor of 5. Dueto the inevitably larger bunch length, the THz pulse peakE-field of the 100 pC increases by a factor of ∼ 70 comparedto the 1 pC case, despite having a 100 times higher bunchcharge.180 185 190 195 200 205Gun phase [deg]150155160165170175Linacphase[deg]0.00.10.20.30.40.5THzpeakE-field[MV/m]Figure 4: Example of GP predicted parameter space.The minimal rms bunch length obtained by BO at 1 pC isslightly longer than the previous GA result with 𝜎𝑧 = 3.2 fs,obtained from a different initial bunch setting. The final THzpulses and optimized accelerator parameters are compara-ble. This is due to the large parameter space for explorationand a small number of allowed steps. To mitigate this, onecan consider running a follow-up BO or a GA optimizationwith a smaller parameter range around the optimal points.Additionally, BO builds a probabilistic model along the op-timization, while GA only keeps a set of best settings inmemory. After optimizations, the resulting GP posterior canalso be used as a surrogate of the parameter space. For exam-ple, Fig. 4 shows the 2D GP posterior subspace of gun andlinac RF phases, where a positive linear correlation betweenthe phase settings of gun and linac is clearly visible. This isfully consistent with the physics expectation, as the gun andlinac are placed with a fixed distance, which correspondsto a fixed phase advance. Large deviation from it resultsin unmatched phase and consequently a lower THz pulseintensity.CONCLUSION AND OUTLOOKWe implemented a parallel version of the Bayesian opti-mization algorithm, which can be run on a cluster to speedup the parameter optimization. The accelerator settings forFLUTE were optimized for bunch charges of 1 pC as well as100 pC and for two objectives: minimizing the bunch lengthand maximizing the CSR THz pulse electric field. The peakE-field proves to be a more suitable objective as it encodesmore information about the bunch and leads to a more directoptimization. With the small number of parameters and twoindividual objectives in this study, the constructed GP modelis relatively simple and provides optimized results fast andwith good statistics. However, the outcome is more or lesspredictable. In contrast, in more complex systems, the GPmodel could help unveiling unknown trends and correlationsbetween machine parameters. BO is a useful tool to quicklyoptimize the parameter settings during the design phase of anew accelerator or for new operation modes, but one has tocarefully design the objective function. It can also help tounderstand the correlation between the physical parameterswith the GP posterior prediction. We plan to implementmore coherent synchrotron radiation types as optimizationobjectives, for example transition radiation and edge radia-tion. Additionally, parallel BO can be further extended toallow Pareto-front optimization for different objectives, e.g.finding the minimal bunch lengths for electron bunches withhighest possible energy.ACKNOWLEDGEMENTSThis work is in part funded by the Initiative and Network-ing Fund by the Helmholtz Association (Autonomous Ac-celerator, ZT-I-PF-5-6). C. Xu and J. Schäfer acknowledgethe support by the DFG- funded Doctoral School “KarlsruheSchool of Elementary and Astroparticle Physics: Scienceand Technology”.13th Int. Particle Acc. Conf. IPAC2022, Bangkok, Thailand JACoW PublishingISBN: 978-3-95450-227-1 ISSN: 2673-5490 doi:10.18429/JACoW-IPAC2022-WEPOMS023WEPOMS023ContentfromthisworkmaybeusedunderthetermsoftheCCBY4.0licence(©2022).Anydistributionofthisworkmustmaintainattributiontotheauthor(s),titleofthework,publisher,andDOI2294MC5: Beam Dynamics and EM FieldsD11: Code Developments and Simulation TechniquesREFERENCES[1] M. J. Nasse et al., “FLUTE: A versatile linac-based THzsource,” Review of Scientific Instruments, vol. 84, no. 2,p. 022 705, 2013, doi:10.1063/1.4790431[2] C. Xu et al., “Machine Learning Based Spatial Light Modu-lator Control for the Photoinjector Laser at FLUTE,” in Proc.IPAC’21, Campinas, Brazil, May 2021, pp. 3332–3335, doi:10.18429/JACoW-IPAC2021-WEPAB289[3] M. Nabinger et al., “Transverse and Longitudinal Modulationof Photoinjection Pulses at FLUTE,” presented at IPAC’22,Bangkok, Thailand, Jun. 2022, paper TUPOPT068, this con-ference.[4] M. Yan et al., “Optimization of THz Radiation Pulses atFLUTE,” in Proc. of International Particle Accelerator Con-ference (IPAC’16), Busan, Korea, May 8-13, 2016, Busan,Korea, 2016, pp. 3067–3069, doi:doi:10.18429/JACoW-IPAC2016-WEPOY037[5] O. Kramer, Genetic Algorithm Essentials, 1st. Springer Pub-lishing Company, Incorporated, 2017.[6] J. 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Meth.A, vol. 768, pp. 151–156, 2014, doi:10.1016/j.nima.2014.09.05713th Int. Particle Acc. Conf. IPAC2022, Bangkok, Thailand JACoW PublishingISBN: 978-3-95450-227-1 ISSN: 2673-5490 doi:10.18429/JACoW-IPAC2022-WEPOMS023MC5: Beam Dynamics and EM FieldsD11: Code Developments and Simulation TechniquesWEPOMS0232295ContentfromthisworkmaybeusedunderthetermsoftheCCBY4.0licence(©2022).Anydistributionofthisworkmustmaintainattributiontotheauthor(s),titleofthework,publisher,andDOI

Optimization Studies of Simulated THz Radiation at FLUTE

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Optimization Studies of Simulated THz Radiation at FLUTE

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