Analytical and Numerical Studies of Dark Current in Radiofrequency Structures for Short-Pulse High-Gradient Acceleration

TL;DR

This work tackles RF breakdown in high-gradient, normal-conducting structures by analyzing dark current dynamics under short RF pulses ($\mathcal{O}(1\ \text{ns})$) using analytical and CST PIC-based simulations for X-band photogun cavities. It presents an analytic multipacting theory in crossed RF fields, identifies resonance bands and converged phase-locked trajectories, and couples these with time-domain simulations to track field emission, multipacting, and plasma effects. The results show that rapid RF ramping and a brief flat-top suppress dark current growth by limiting emission, quenching sustained multipacting, and reducing plasma formation, aligning with low dark current observations in AWA experiments. These findings support the potential of short-pulse operation to enable higher gradients in compact accelerators and point to future work on self-consistent plasma dynamics under fast-varying fields with first-principles simulations.

Abstract

High-gradient acceleration is a key research area that could enable compact linear accelerators for future colliders, light sources, and other applications. In the pursuit of high-gradient operation, RF breakdown limits the attainable accelerating gradient in normal-conducting RF structures. Recent experiments at the Argonne Wakefield Accelerator suggest a promising approach: using short RF pulses with durations of a few nanoseconds. Experimental studies show that these O(1 ns) RF pulses can mitigate breakdown limitations, resulting in higher gradients. For example, an electric field of nearly 400 MV/m was achieved in an X-band photoemission gun driven by 6-ns-long RF pulses, with rapid RF conditioning and low dark current observed. Despite these promising results, the short-pulse regime remains an under-explored parameter space, and RF breakdown physics under nanosecond-long pulses requires further investigation. In this paper, we present analytical and numerical simulations of dark current dynamics in accelerating cavities operating in the short-pulse regime. We study breakdown-associated processes spanning different time scales, including field emission, multipacting, and plasma formation, using simulations of the X-band photogun cavities. The results reveal the advantages of using short RF pulses to reduce dark current and mitigate RF breakdown, offering a path toward a new class of compact accelerators with enhanced performance and reduced susceptibility to breakdown.

Figures (19)

• Figure 1: Model and RF design of the $X$-band photogun cavities driven by short RF pulses. (a) Cross-sectional view of the copper cavities along the central plane. (b) Normalized electric field magnitude distribution at 11.7 GHz. (c) Electric field on the photocathode surface for an input RF pulse with 200 MW peak power; the inset shows the time profile of the input RF signal, with a 3 ns rise, 3 ns flat top and 3 ns fall.
• Figure 2: RF conditioning of the $X$-band photogun cavities. (a) Conditioning history of the peak electric field $E_0$ at the photocathode surface (blue), and the ratio of the measured to simulated peak reflected RF signal $R$ (orange). (b-d) Comparison of measured (dashed red) reflected RF signals with simulated signals (solid green, assuming no RF breakdown) at the corresponding stages denoted by the vertical lines in Panel (a). This figure is reprinted with permission from Tan et al., Phys. Rev. Accel. Beams 25, 083402 (2022) under the terms of the Creative Commons Attribution 4.0 International license.
• Figure 3: Schematic representation of the multipactor analysis setup. (a) Simulation geometry used for electron trajectory evaluation. (b) Crossed RF field configuration showing an electron trajectory under combined $E_r$, $E_z$, and $B_\theta$ fields. The parameters $v_0$ (initial velocity) and $\alpha$ (emission angle) are defined at emission. $r$ and $z$ denote the radial and longitudinal coordinates, respectively, while $a$ and $L$ are the cavity radius and length, respectively.
• Figure 4: Comparison of RF field amplitudes from cst simulations and analytical approximations for the full-cell cavity with radius $a = 9.49$ mm and length $L = 6.50$ mm. The field amplitudes, $B_\theta$ in (a), $E_r$ in (b), and $E_z$ in (c), are all scaled to an axial field amplitude of $E_{z0} = 100$ MV/m at the cavity center. Solid red curves represent cst simulation data, and black dashed lines indicate the analytical field amplitudes used in the model. The shaded region in (c) indicates the radial range near the sidewall where the analytical field approximation is applied.
• Figure 5: Single-trip SEY ($\delta$) map for the full cell of the $X$-band photogun cavities for different combinations of initial axial emission position $z_0$ and RF field amplitudes, characterized by the axial electric field at the cavity center $E_{z0}$. The color scale indicates the magnitude of $\delta$.