Accurate and confident prediction of electron beam longitudinal properties using spectral virtual diagnostics
A. Hanuka, C. Emma, T. Maxwell, A. Fisher, B. Jacobson, M. J. Hogan, Z. Huang
AAccurate and confident prediction of electron beam longitudinal properties usingspectral virtual diagnostics
A. Hanuka, ∗ C. Emma, T. Maxwell, A. Fisher, B. Jacobson, M. J. Hogan, and Z. Huang
SLAC National Accelerator Laboratory, Menlo Park, CA 94025, USA (Dated: September 29, 2020)Longitudinal phase space (LPS) provides a critical information about electron beam dynamicsfor various scientific applications. For example, it can give insight into the high-brightness X-rayradiation from a free electron laser. Existing diagnostics are invasive, and often times cannot operateat the required resolution. In this work we present a machine learning-based Virtual Diagnostic(VD) tool to accurately predict the LPS for every shot using spectral information collected non-destructively from the radiation of relativistic electron beam. We demonstrate the tool’s accuracyfor three different case studies with experimental or simulated data. For each case, we introduce amethod to increase the confidence in the VD tool. We anticipate that spectral VD would improvethe setup and understanding of experimental configurations at DOE’s user facilities as well as datasorting and analysis. The spectral VD can provide confident knowledge of the longitudinal bunchproperties at the next generation of high-repetition rate linear accelerators while reducing the loadon data storage, readout and streaming requirements.
Measurement and control of the Longitudinal PhaseSpace (LPS) of electron beams is critical for the per-formance of high brightness linear accelerators (linacs)in scientific applications ranging from linear colliders[1, 2], Ultra-Fast Electron Diffraction (UED) [3], laserand THz beam manipulation [4, 5] and Free ElectronLasers (FELs) [6, 7]. For example, the properties ofFEL photon beams are strongly dependent on the qual-ity and stability of the high brightness electron beamswhich drive them, making electron beam diagnostics acritical component for the success of these light sources.In particular, measurement of the electron beam LPSgives key insight into the FEL process, and is necessaryto determine and mitigate deleterious effects which hin-der the FEL gain mechanism. Such effects include theMicrobunching Instability (MBI) [8] and its associatedspectral pedestal [9] which limits the spectral purity ofseeded Xray-FELs.Using LPS images we can determine not only the longi-tudinal emittance and longitudinal bunch shape, but alsothe slice energy spread, a critical parameter for FELs, aswell as the energy chirp, which can give insight into beamdynamics with respect to accelerator parameters such ascharge, gun phase, and laser spot size on the photocath-ode. LPS is typically measured using X-band transversedeflecting cavity (XTCAV) [10], which unfortunately of-ten times intercepts the beam during measurement, mak-ing it impossible to simultaneously measure and deliverthe beam to experiments - see Fig. 1. Furthermore, theresolution of XTCAV measurements is limited to > µ mand repetition rate of 120 Hz at LCLS. These limitationswould be further enhanced for higher repetition rates,which are critical for the operation of accelerator test fa-cilities such as FACET-II [11] and LCLS-II [12]. There-fore, there is a need to develop diagnostics tools for futurehigh-repetition rate accelerator and collider operationsthat are capable predicting the LPS continuously and ona single-shot basis. Machine Learning (ML) tools have been recently at-tracting growing interest for optimization performance,control, and prediction tasks of particle accelerators [13–18]. ML models are generalizable non-linear interpolat-ing functions, that can quickly map millions of inputsto similarly numerous outputs. This makes them logicalcandidates for reconstructing complicated 2D LPS distri-butions. Virtual Diagnostics (VD) using ML models arepromising computational tools intended to provide highaccuracy predictions of beam measurements in a particleaccelerator that are usually unavailable for users for var-ious reasons. For example, the diagnostic may interceptthe beam, or it may not provide measurements at a highenough repetition rate or high enough resolution.Recent work [19, 20] trained a neural network to pre-dict the LPS using nondestructive linac controls and elec-tron beam XTCAV images as inputs; we refer to thismethod as scalar VD . However, as illustrated in Ref. [19],this method is susceptible to prediction errors if there is afailure in one of the read-back linac controls. As a result,the scalar VD has limited prediction accuracy of the LPS,which may be exacerbated in more complicated acceler-ator operation modes such as two-bunch configurations[21]. In addition, for a given linac controls there are in-herent pulse-length temporal and beam density shot-to-shot fluctuations in the beam due e.g. to MBI [22–24],which are not captured by scalar (integrated) diagnosticsignals. As a result the scalar VD will be insensitive tosuch variations. In order to transition such VD tools frominitial proof-of-concept demonstrations to single-shot di-agnostics used in regular operation, it is therefore essen-tial to increase the robustness, accuracy and confidenceof their diagnostic predictions.In this paper we present a solution that improves theconfidence and accuracy of VD predictions by using adirect measurement of the electron beam radiation spec-trum to recover LPS on a single shot basis. We trainthe virtual diagnostic model using spectral information a r X i v : . [ phy s i c s . acc - ph ] S e p FIG. 1: Simplified schematic of start-to-end typical experimental configuration, from the photoinjector to theXTCAV diagnostic and beam delivery to to experiments (not to scale). (1) An example of XTCAV’s longitudinalphase-space measurement and the corresponding electron beam current profile. (2) Matching non-destructivespectral measurement from diffraction or bend radiation.which can be obtained non-destructively from a diffrac-tion or bend radiation, and may be measured by a mid-IR [25] or Thz spectrometer [26]. To demonstrate ourmethod we use three separate facilities as case stud-ies: the Linac Coherent Light Source (LCLS) normal-conducting accelerator [6], the superconducting LCLS-II linac [12] and the FACET-II accelerator [21]. Theseexamples illustrate different advantages of the spectraltechnique, namely its additional accuracy, its ability toconfidently resolve shot-to-shot features that scalar VDis unable to (e.g. MBI which is important for LCLS-II),and its use in improving confidence in prediction beyondthe ground truth measurement (e.g. high current shotsin FACET-II). The ML methods presented here, includ-ing quantifying uncertainty and increasing prediction’sconfidence, are useful for other applications as well.
Methods
Typically, longitudinal 2D phase space (LPS) is mea-sured at the XTCAV, and the longitudinal 1D beam pro-file, or current, are derived from the LPS. An IR spec-trometer can be used to measure electron beam radiationbefore the electron beam is manipulated for various ap-plications - see Fig. 1 Given the electron beam radiationspectrum, numerical analysis techniques, such as con-strained deconvolution [27, 28], iterative phase retrieval[26, 29, 30], or analytic phase computation by Kramers-Kronig dispersion relation [31] could be applied to calcu-late the 1D longitudinal beam profile [25, 32, 33]. How-ever, the reconstructed signal using those techniques isnot unique [26, 30, 34]. In addition, the full 2D longi-tudinal phase space cannot be reconstructed from thesetechniques. Therefore, we propose to train a neural net-work to predict the LPS or current profile from a non-destructive spectral measurement; we refer to as spectralVD . In what follows, we trained a feed-forward neural net-work (NN) using the spectrum and longitudinal currentprofiles as inputs. When applicable, we compared theresults to the scalar VD with the same NN architecture.Next, we repeat this training process for full LPS imagesof the electron beam. We first discuss the accuracy andadvantages of the spectral VD method based on LCLSexperimental data. We further extend our method topredict current profiles from the LCLS-II and FACET-IIfacilities. This illustrates the versatility of the methodas applied to a high repetition-rate machine (LCLS-II)or a high-current, ultra-short bunch facility (FACET-II).For each case study, we present a different method toincrease the confidence in the prediction, since the VDwill be available instead of the XTCAV measurement.Such method would indicate for example when the VDhas moved outside of its range of reliability and the pre-dictions should not be trusted.
1. LCLS - Improved accuracy over scalar VD withexperimental data
For this case study, we use experimental data fromLCLS to demonstrate the improved accuracy of the spec-tral VD prediction over the scalar VD for 1D current pro-files as well as 2D LPS images. By comparing the pre-dictions of both VDs we are able to flag low-confidencepredictions.Training data for a feed-forward neural network hasbeen acquired from thousands of measurements ( ∼ ∼ . µ m and0.92 MeV/pixel [10]) at the accelerator exit. We adoptthe same pre-processing as in Ref. [19] where the imageswere cropped and centered before the NN was trained.The input for the spectral VD included the spectrumof each current profile. The spectral information canbe collected for example using coherent transition radi-ation (CTR) or non-destructively using coherent diffrac-tion radiation (CDR). Here, since we didn’t have accessto simultaneous spectrometer measurements at the time,we calculated the spectrum by applying Fourier trans-form to the current profile up to 60 THz, down-sampledit to 0.6 THz resolution, and added 10% random noiseto match the current state-of-the-art IR spectrometers[26, 35]. The input for the scalars VD included five accel-erator controls read-back: amplitude and phase of linac01, amplitude of L1x (the X-band linearizer upstreamof the first bunch compressor), and non-destructive cur-rent measurements (using coherent radiation monitors[36, 37]) before and after linac 02. All datasets wererandomly shuffled and partitioned into 80% for training(from which 10% for validation) and 20% for testing.The NN architecture we used is a fully connected feed-forward NN composed of three hidden layers (200, 100,50) with rectified linear unit activation function, andrandom initialization of the weights. For training weused batch size of 64, 500 epochs and Adam optimizerwith fixed learning rate of 0.001 in our experiments.For all the examples presented we use the open sourceKeras and Tensor-flow libraries to build the NN mod-ule [38, 39]. The results are averaged over 20 trials withrandom weights initialization. As a quantitative relativemeasure of the error between the prediction ˆ y and themeasurement (or simulation) y , we used mean squarederror MSE( y, ˆ y ) = (cid:80) N − i =0 ( y i − ˆ y i ) and normalized MSENMSE( y, ˆ y ) = MSE / (cid:80) N − i =0 y i . As a quantitative mea-sure of the 2D LPS prediction’s accuracy, we computethe mean structural similarity index measure (SSIM) be-tween two images [40].The prediction of the current profile for four test shots(i.e. not used in the NN training) is shown in Fig. 2(a)-(d). There is an excellent agreement (total NMSE forthe entire test set of 0.28% ± . ∼ . > .
2. LCLS-II - Shot-to-shot prediction ofmicrobunching via ensembling
For this case study, we use simulated data of the LCLS-II superconducting soft X-ray linac to show an examplewhere prediction on a shot-basis is only available usingthe spectral VD. LCLS-II has a 1km bypass line betweenthe linac and the undulator, so that MBI is especiallypronounced. We train an ensemble of neural networksto produce a confidence interval that is then used as athreshold to veto bad predictions, thus increasing theconfidence in the diagnostic.There are cases in which a neural network trained us-ing scalar inputs is insensitive to certain features of theLPS. One such example is trying to use a neural networkto resolve details of the microbunching structure of anelectron beam. The MBI in linac-driven FELs resultsfrom the amplification of microscopic density modula-tions during the transport of an electron beam from theelectron source to the undulator. During the transportshot-to-shot amplitude fluctuations starting from noisecan lead to macroscopic fluctuations of the LPS, cur-rent profile and electron beam bunching factor b ( λ ) = N (cid:80) Nn =1 exp( i πct n /λ ). Here λ is the wavelength, and t is time. These in turn can seed the growth of unwantedradiation modes in the FEL and/or reduce the FEL peakpower. Suppressing the MBI has been the subject of ex-tensive research (see e.g. [41] and references therein).As an example, the LCLS-II super-conducting linacwill drive a soft X-ray FEL for which the MBI is being studied carefully in its relation to FEL performance [9,23, 24]. The LPS may change on a shot-to-shot-basis dueto the MBI despite the accelerator set-points remainingun-changed. Thus, we need a diagnostic which is able topredict the amplitude of microbunching fluctuations on asingle-shot basis to aid in interpretation of experimentalresults. In this case we can only use spectral informationto train the neural network to make these predictions asthe coherent radiation spectrum is directly sensitive tosingle-shot fluctuations of the current profile, contrary tointegrated scalar diagnostics.We generated thousands of simulated examples using ELEGANT [42]. While the simulation’s controls remainedun-changed, we varied the noise’s random seed, so eachsimulation results in a different LPS (shown in Figure4(a)). We sampled down the LPS to match the resolutionof the XTCAV, and calculated the current profile. Wecalculated the spectrum up to 60 THz in a resolution of0.6 THz, which matches the CRISP spectrometer [26].The spectrum and current profile of the electron beamwere then used to train a neural network-based virtualdiagnostic as above. In this case we used a wider neu-ral network to capture the rich structure in the MBIdata. The overall predicted current error for test shotswas NMSE=1 . ± ± , ∼ ∼ µm is shown in colorbar. Notably, accurate predic-tion of the current translates to accurate prediction ofthe bunching factor.
3. FACET-II - Flagging high peak current shotsbeyond diagnostic resolution
For this case study, we use simulated data of theFACET-II two bunch mode with high peak current toshow an example where accurate prediction is limitedto the XTCAV current resolution of
I < I max ∼
35 kAFIG. 4: LCLS-II Super-conducting soft X-ray microbunching simulations in
ELEGANT . (a) Two different LPS resultedfrom shot noise in the electron beam. (b1) and (c1) Two test shots of current profile with bad and good spectral VDpredictions respectively shown in magenta. The transparent magenta area corresponds to the predicted std. (b2)and (c2) Corresponding bunching factor calculated from the simulated and predicted current profiles. (d) Maximumpredicted standard deviation vs the averaged MSE in current prediction. Dashed line is set as the std threshold forclassifying shots as good. The error of the predicted bunching factor averaged over the wavelength’s range from 0 to10 µm is shown in colorbar.[43]. By using the spectral information not only for thenetwork prediction, but also for correlating an integratedspectral intensity with the predicted peak current, we areable to flag suspect shots with peak current I > I max be-yond the XTCAV resolution. This approach is crucial forbuilding confidence in the virtual diagnostic predictionwhich may be used online to facilitate the interpretationof experimental data and tuning of the machine settings.Reliability the virtual diagnostics tool is critical for op-erations. As shown for the LCLS case study, one way toincrease the confidence in the prediction would come fromthe redundancy of two separate NN trained on differentinput, and flagging suspect shots for which there is signif-icant discrepancy between the two NN predictions. How-ever, there are cases where the scalar VD isn’t applicableas in LCLS2 case study, in those cases the confidence inprediction could come from ensemble methods, e.g. aver-aging randomly initialized NNs. Nevertheless, those pre-dictions would be limited to the XTCAV ground truth.Thus, there is a need to develop a method to increase theconfidence in the prediction by resolving features that arebeyond the XTCAV limited resolution, such as high peakshots ( I peak > I max ) or short bunches ( ≤ . µm ).Spectral VD is able to resolve the discrepancies be-tween predicted current profiles and actual current atthe interaction point (IP), beyond the limited resolutionof XTCAV. For example, FACET-II accelerator oper-ating with two-bunch configuration, will generate veryshort bunches ( µ m rms size) with high peak current( I peak > I max ). The XTCAV will underestimate buncheswith I peak , IP > I max - see Figure 5(a). Such measure-ment would be smeared out on the XTCAV (referredas ’bad’ shot), and would look similar to a ’good’ shotwith I peak , IP (cid:39) I max - shown in Fig. 5(b). Thereforethe XTCAV alone cannot distinguish between ’bad’ and’good’ shots, and the scalar VD wouldn’t allow us to dis- FIG. 5: Facet-II two-bunch mode simulations in LUCRETIA . (a)+(b) Current profile at the interactionpoint (IP) (blue) is smeared on the XTCAV (red) forhigh and low peak current shots respectively. (c) Thespectrum of the electron beam for the two shots isdifferent; the high peak current shot has higherfrequencies content. (d) Maximum XTCAV current ofthe simulated and predicted current profiles with thecorresponding MSE as a colorbar. (e) Maximumpredicted XTCAV current vs spectral intensityintegrated on the interval [5,200] THz with thematching maximum IP current as the colorbar. Shotswith spectral intensity smaller than the cutoff (shown inblack line) are with I peak < I max .tinguish those shots either. However, very short buncheswith high peak current will radiate strong coherent radi-ation at high frequencies (THz range), thus the spectrumof the shots would be different - see 5(c).Accordingly, we train spectral VD with NN architec-ture similar to LCLS-II on ∼ LUCRETIA [44] simu-lations, quantifying the expected jitter of the FACET-II linac based on the parameters from [45]. The inputwas the bunch spectrum up to 60 THz, and the out-put was the corresponding XTCAV current profile. Fig-ure 5(d) shows the simulated and predicted maximumcurrent with the prediction MSE as a colorbar. There isgood agreement of the simulated and predicted profiles(total NMAE=3 . ± . I peak , IP < I max .Shots that are not in this region would be flagged as ’bad’shots. Determining if shot’s spectral intensity is in thegood region on a shot-to-shot basis will be complemen-tary to the spectral VD, and will provide assurance thatthe predicted current profiles from the XTCAV map tothe IP current profiles.Figure 5(e) shows the maximum predicted current onthe XTCAV, and the corresponding spectral intensity in-tegrated on the interval [5,200] THz. The maximum IPcurrent is shown as the colorbar. All shots with spectralintensity smaller than the cutoff (shown in black line) arewith IP current smaller than 35 kA. This means that allpredictions in this high confidence region can be trusted(46% of the shots). Shot in the gray region are flagged as’bad’, since the IP current was much higher to be resolvedby the XTCAV.Lastly, we would like to note two additional points: (1)the VDs would require re-training to account for long-term phenomenon such as drift. (2) In addition to theirutilization as predictive tools, VDs can be combined withoptimization algorithms to tailor electron beam proper-ties to match desired characteristics. Knowledge of theLPS and the ability to generate desired LPS distributionswill increase the physics understanding of experiments atFACET-II and LCLS-II. Conclusions and outlook
We present a virtual diagnostic tool to predict the 2Dlongitudinal phase space (LPS) and the 1D current profilefrom a non-invasive spectral measurement of the electronbeam’s diffraction or bend radiation. We demonstratedour method on three separate facilities as case stud-ies: the Linac Coherent Light Source (LCLS) normal-conducting accelerator, the superconducting LCLS-IIlinac and the FACET-II accelerator. Each example il-lustrates different advantage of the spectral VD.For the LCLS case, the spectral VD provided moreaccurate predictions than the previously demonstratedscalar VD, which predicts the LPS from non-invasive ac- celerator control scalars. The confidence in the predic-tion would come from flagging shots for which there issignificant discrepancy between the two neural network(NN) predictions. For the LCLS-II case, the spectral VDwas able to resolve shot-to-shot features relevant to mi-crobunching, wherein the scalar VD isn’t applicable atall. The confidence in prediction would come from en-sembling, namely averaging several randomly initializedNNs.For the FACET-II case, the scalar VD is used not toonly to accurately predict the current profile, but alsoto distinguish between ∼
35 kA peak current shots andhigher peak current shots that would appear similar tothe former due to the XTCAV limited resolution. Theconfidence in prediction for high current shots wouldcome from correlating the std of the current predictionwith its integrated spectral intensity, as high peak cur-rent shots would have more spectral information in higherfrequencies.Increasing the reliability and robustness of the virtualdiagnostics tools are critical for deployment and opera-tions, even beyond the limited resolution of the routinelyused XTCAV. We are able to extract robust and mean-ingful information from complex LPS measurements bycombining the spectral VD’s accurate prediction withvarious methods to increase the confidence in the predic-tion. The Spectral VD has the potential to maximize thescientific output of accelerators, and bring the concept ofautonomous control of accelerators one step further.
Acknowledgments
The authors would like to acknowledge Zhen Zhangand Daniel Ratner for discussions about the bunchingfactor, and to Glen White for help setting up Facet-IIsimulations. The authors are grateful to Greg Stewart forhis help in creating Figure 1. This work was supported bythe Department of Energy, Laboratory Directed Researchand Development program at SLAC National AcceleratorLaboratory, under contract DE-AC02-76SF00515. ∗ [email protected][1] ILC, SLAC-R-857 , Tech. Rep. (Stanford, 2007)arXiv:0709.1893 .[2] “The compact linear collider (clic) - 2018 summary re-port,” (2018), arXiv:1812.06018 [physics.acc-ph] .[3] M. Z. Mo, X. Shen, Z. Chen, R. K. Li, M. Dun-ning, K. Sokolowski-Tinten, Q. Zheng, S. P. Weathersby,A. H. Reid, R. Coffee, I. Makasyuk, S. Edstrom, D. Mc-Cormick, K. Jobe, C. Hast, S. H. Glenzer, and X. Wang,Review of Scientific Instruments , 11D810 (2016).[4] E. Hemsing, G. Stupakov, D. Xiang, and A. Zholents,Rev. Mod. Phys. , 897 (2014).[5] E. C. Snively, M. A. K. Othman, M. 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