Monochromation of pulsed electron beams with terahertz radiation at a planar mirror

TL;DR

The paper tackles the challenge of reducing the intrinsic energy spread of pulsed electron beams from femtosecond photoemission. It introduces a THz-mirror monochromator that leverages the natural parabolic energy-space correlations, applying a tunable parabolic energy change $\Delta E = -a r^2 - b t^2$ via laser-derived THz fields to counteract both longitudinal and transverse energy spread, with a single or dual THz pulse. An analytic framework models the beam–THz interaction, deriving expressions for the ideal energy relation $E_{ideal}(r,t)$ and the THz-induced momentum kicks, and is validated against General Particle Tracer (GPT) simulations across a range of THz frequencies, beam sizes, and pulse durations. The work also analyzes practical considerations, including jitter stability and a transmission-friendly mesh reflector, showing that current-carrying efficiency and tolerance to amplitude/phase noise remain favorable, with potential rms energy spreads reduced to tens of meV. Overall, the proposed THz monochromator offers a low-loss, synchrony-locked approach to ultrafast monochromation that can outperform prism-based methods while preserving beam current.

Abstract

Exquisite control of electron beam energy is required for many electron spectroscopy and imaging applications. For both continuous and pulsed beams, the beam energy spread is fundamentally limited by the electron source, and is typically a sizable fraction of an electron-volt. In this paper, we present a means to reduce electron beam energy spread after emission to the level of a few 10s of meV rms using femtosecond photoemission and an interaction with laser-derived single- to few-cycle terahertz (THz) radiation. We show analytically and in particle tracking simulations that this interaction can remove energy spread stored in both the transverse and longitudinal degrees of freedom. We analytically formulate the limit of energy spread that this technique can achieve, and map the non-ideal affects arising at high frequencies. The interaction is mediated by the beam's passage through a mirror which is reflective to terahertz radiation but allows transmission of the majority of the electron beam (e.g. a wire mesh). This method then only requires beam current losses of a few tens of percent, far smaller than what is achieved in prism and slit-based electron monochromators.

Figures (12)

• Figure 1: Schematics of the THz monochromator and beamline. $\boldsymbol{a)}$ Electrons are emitted from a flat photocathode and accelerated by a 60 kV dc gun with a peak field of 6 MV/m and an anode diameter of 3 mm. The beam is collimated in a solenoid before passing through the THz mirror monochromator. $\boldsymbol{b)}$ The THz pulse shape used for this set of simulations, where $t$ is the time of arrival and $T$ is the period of one cycle. $\boldsymbol{c)}$ The two THz pulses reflect off of a mirror at angle $\theta_T$ to the normal. The pulses are P-polarized, with $\vec{E}$ in the $x$-$z$ plane and $\vec{B}$ along $\hat{y}$. An electron with zero transverse momentum passes through the mirror at angle $\theta_B$.
• Figure 2: GPT particle distributions before and after the THz monochromator with two pulses at 0.3 THz. For the simulation shown here $\sigma_{x0} = 1$$\mu$m and $\sigma_{t0} = 8.6$ fs. $\boldsymbol{a)}$ Real space radius vs time of arrival colored by energy deviation (from the mean) before the mirror, showing the correlations that develop during transport. $\boldsymbol{b)}$ Real space energy deviation after monochromation. $\boldsymbol{c)}$ Particle energy vs time of arrival colored by radius. The blue-colored distribution is taken from before the mirror monochromator and the red-colored is from after. $\boldsymbol{d)}$ Particle energy vs radius colored by time of arrival.
• Figure 3: Energy change from 1 pulse (red) and two pulses (blue) for cross sections in time offset and radius for central frequencies at $\boldsymbol{a,b)}$ 0.3 THz, $\boldsymbol{c,d)}$ 0.5 THz, and $\boldsymbol{e,f)}$ 0.7 THz. The gray dots show the distribution from GPT simulations, with the negative energy plotted for better comparison to the energy change parabola. The cross sections in time are taken at $(x,y)=0$, and the cross sections in $x$ are taken at $(y,t)=0$. For every simulation shown here $\sigma_{x0} = 1$$\mu$m and $\sigma_{t0} = 8.6$ fs. Here time of arrival is measured relative to a particle emitted from the cathode with zero longitudinal momentum, hence the sharp cutoff at t=0.
• Figure 4: Final energy spread after the THz interaction as a function of THz frequency. The solid lines are found by minimizing $\sigma_E$ with respect to the parameters $E_0$ and $w_0$ in Eqn. \ref{['dpz']}. The points correspond to the result of a GPT simulation using the optimal parameters from the analytic optimization at that frequency. For every simulation shown here $\sigma_{x0} = 1$$\mu$m and $\sigma_{t0} = 8.6$ fs, and the distribution just before the mirror is shown in Fig. \ref{['fig:dists']}. THz pulse parameters for each point are described in Appendix \ref{['Appendix_parameters']}.
• Figure 5: Energy spread after fluctuations in $\boldsymbol{a)}$ gun voltage and $\boldsymbol{b)}$ terahertz pulse energy for two pulses at 0.3, 0.5, and 0.7 THz.