Virtual-diagnostic-based time stamping for ultrafast electron diffraction

In this work, nondestructive virtual diagnostics are applied to retrieve the electron beam time of arrival and energy in a relativistic ultrafast electron diffraction (UED) beamline using independently measured machine parameters. This technique has the potential to improve the temporal resolution of pump and probe UED scans. Fluctuations in time of arrival have multiple components, including a shot-to-shot jitter and a long-term drift which can be separately addressed by closed loop feedback systems. A linear-regression-based model is used to fit the beam energy and time of arrival and is shown to be able to predict accurate behavior for both long- and short-time scales. More advanced time-series analysis based on machine learning techniques can be applied to improve this prediction further.

Figure 1

The HiRES beamline. The UED beamline starts at D1 and goes through the dogleg to DD, while the diagnostic beamline goes straight from D1 to VS3. Adapted with permission from [9].

Figure 2

(a) Synchronization scheme: rf amplifier run at 50% duty cycle with a 2-ms period. Up to ten laser shots arrive at $4\mathrm{\mu }\mathrm{s}$ intervals for a short period toward the end of each rf pulse, where the rf is generally most stable. (b) Correlation plots of rf gun amplitude and relative energy deviation (measured at the dipole spectrometer) for synchronized and temporally misaligned acquisition schemes.

Figure 3

Synchronous measurements of beam TOA at TCAV: correlations of TOA with electron gun amplitude (without the use of the rf bunching cavity, similar to data in Fig. 2). Left: TCAV rf jitters are not taken into account in postprocessing. Right: fluctuations in TCAV rf amplitude and phase are used to correct beam time-of-arrival measurements. In (a), long-term drifts are uncompensated. In (b), a moving average is subtracted to show only short timescale jitters. Note the much smaller $y$ scale in the bottom plots.

Figure 4

Standard deviation of transverse beam centroid calibrated to TOA relative to the reference beam as a function of the width of the acquisition time window. Inset shows a short timescale.

Figure 5

Time-of-arrival fluctuation measured using the TCAV screen while the PID-type feedback was engaged. Residual drifts not corrected by the feedback are present. The linear regression is also shown. The uncertainty due to long-term drifts is reduced to the 200 fs level similar to the shot-to-shot, short-term jitter shown in Fig. 4.

Figure 6

Top 10 model predictors and the associated TOA movement with 1 STD movement in the validation set. Details of the predictors can be found in Table 1 in Appendix pp1.

Figure 7

Linear regression predictions with and without traditional PID-type feedback (FB) engaged. (a) The variation from the mean of the training data is shown, after conversion to relative energy deviation. (b) the validation errors are shown. Note that the FB off case shows greater improvement than the FB on case on both an absolute and a relative scale.

Figure 8

Measured current fluctuations extrapolated to perceived relative energy fluctuations for a 750-keV electron beam, as in the experiment.

Figure 9

TFT TOA median and interquartile range (shaded) predictions in the validation set. Predictions are compared with linear regression (LR) predictions and the ground truth.

Figure 10

Left: error histogram comparing the absolute value of the residuals from the linear regression and TFT models. Note that the error is bunched closer to zero for the TFT. Right: residual correlation for linear regression and TFT models. Note that the use of a TFT predictor reduces the correlation in the residuals between time steps.