Vector-based feedback of continuous wave radiofrequency compression cavity for ultrafast electron diffraction

Abstract

The temporal resolution of ultrafast electron diffraction at weakly relativistic beam energies ($\lesssim$100 keV) suffers from space-charge induced electron pulse broadening. We describe the implementation of a radio frequency (RF) cavity operating in the continuous wave regime to compress high repetition rate electron bunches from a 40.4 kV DC photoinjector for ultrafast electron diffraction applications. Active stabilization of the RF amplitude and phase through a feedback loop based on the demodulated in-phase and quadrature components of the RF signal is demonstrated. This scheme yields 144 ± 19 fs RMS temporal resolution in pump-probe studies.

FIG. 1.

(a) Map of the electric field of the 40.4 kV DC electron gun (From DrX Works^TM) along the central axis. (b) CAD model of the GARUDA beamline. Beam steering optics are omitted from this drawing. (c) Map of the peak electric field along the central axis of the RF cavity. The final figures (d) and (e) show the simulated electron bunch transverse and longitudinal RMS size, respectively, against the average bunch position. Note that the 100 μm pinhole is not present in this simulation.

FIG. 2.

Simulated temporal RMS width (σ_t) of the electron pulse at the sample plane as a function of RF phase and RF power. The compression reaches ${\sigma }_t\approx 140$ fs. The simulations were performed with 40.4 keV beam energy, 1.0 fC bunch charge, and 0.25 eV thermal emittance.

FIG. 3.

(a) Cavity temperature simulation under 50 W continuous-wave RF power operating with one cooling channel. The maximum and minimum temperature differ by about 5 °C (image courtesy of Radiabeam Technologies). (b) S21 measurements for the cavity conducted in vacuum. The resonance occurs at 2.856 GHz frequency with a bandwidth of 1.4 MHz FWHM.

FIG. 4.

Relative size of an electron diffraction pattern from a thin-film gold crystal as a function of the RF phase in the cavity at 2.3 W input power. This is given by the circular data points and red fit curve, and was directly measured from the distances between several Bragg peaks on the detector. The triangular data points and blue fit curve give the electron bunch velocity inferred from the variation in diffraction pattern scale.

FIG. 5.

Schematic diagram of the RF compression circuit. This illustrates how the 2.856 GHz RF wave out of the DRO is used to simultaneously synchronize the RF cavity and the laser oscillator. The arrows represent the signal direction.

FIG. 6.

RMS integrated timing jitter of the master dielectric resonator oscillator (2.856 GHz) and the laser oscillator (79.333 MHz).

FIG. 7.

Map between the voltages applied to the modulation IQ mixer and the voltages measured on the demodulation IQ mixer. The demodulation IQ mixer voltages are expressed in terms of an amplitude and phase. In the ideal case, A₂ and ${\varphi }_2$ would relate to I₁ and Q₁ through Eqs. (10) and (11), respectively. This empirical mapping corrects for deviations from the ideal.

FIG. 8.

RF phase (left) and amplitude (right) stability with PID feedback on (green) and off (red). The top panels show the raw readings over a 12 h period. The middle panels give histograms of these readings demonstrating the superior stability attained with feedback. The bottom panels give the averages of standard deviations of the raw data binned over different time scales.

FIG. 9.

Electron diffraction patterns from 1T-TaS₂ in the (a) nearly commensurate charge density wave (NCCDW) state and (b) incommensurate charge density wave (ICCDW) state. (c) and (d) Intensity cuts along the dashed lines drawn in (a) and (b). The average Bragg peak width (RMS) is measured to be ${\sigma }_q=$ 0.104 Å⁻¹. (e) A UED time trace of the NCCDW peak intensity during a photo-induced transition to the ICCDW state. The data are fit to F(t) [defined in Eq. (13)] which is plotted as the solid green curve. The dashed blue curve is the intrinsic sample response given by $\chi (t)$ [defined in Eq. (12)]. The dotted blue curve is the instrument response function which fits to an RMS width of 144 ± 19 fs. These data were collected with a pump fluence of 2.7 mJ/cm², 180 fs FWHM laser pulse width, 500 Hz repetition rate, and a bunch charge of 3.3 fC. RF power jitter was below 3 mW RMS.

FIG. 10.

(a) Electron bunch relative arrival time (t_a) as a function of RF phase. The slope of t_a vs phase at the zero-crossing is 1.54 ps/°. (b) Instrument response time (τ_i) as a function of RF phase. The data in both (a) and (b) were collected for an RF power of 34.5 dBm. (c) Instrument response time as a function of RF cavity power at zero phase. The green solid lines are from the GPT model. Each data point in these plots is extracted from a UED time-trace with pump fluence of 4 mJ/cm², 180 fs FWHM laser pulse width, 500 Hz repetition rate, and bunch charge of 1 fC. Note that these data were collected before optimized RF amplitude stability was achieved; here the power jitter was at the level of 200 mW RMS.