Solid-state or crystal acceleration has for long been regarded as an attractive frontier in advanced particle acceleration. However, experimental investigations of solid-state acceleration mechanisms which offer [Formula: see text] acceleration gradients have been hampered by several technological constraints. The primary constraint has been the unavailability of attosecond particle or photon sources suitable for excitation of collective modes in bulk crystals. Secondly, there are significant difficulties with direct high-intensity irradiation of bulk solids, such as beam instabilities due to crystal imperfections and collisions etc. Recent advances in ultrafast technology with the advent of submicron long electron bunches and thin-film compressed attosecond x-ray pulses have now made accessible ultrafast sources that are nearly the same order of magnitude in dimensions and energy density as the scales of collective electron oscillations in crystals. Moreover, nanotechnology enabled growth of crystal tube structures not only mitigates the direct high-intensity irradiation of materials, with the most intense part of the ultrafast source propagating within the tube but also enables a high degree of control over the crystal properties. In this work, we model an experimentally practicable solid-state acceleration mechanism using collective electron oscillations in crystals that sustain propagating surface waves. These surface waves are driven in the wake of a submicron long particle beam, ideally also of submicron transverse dimensions, in tube shaped nanostructured crystals with tube wall densities, [Formula: see text]. Particle-In-Cell (PIC) simulations carried out under experimental constraints demonstrate the possibility of accessing average acceleration gradients of several [Formula: see text] using the solid-state tube wakefield acceleration regime. Furthermore, our modeling demonstrates the possibility that as the surface oscillations and resultantly the surface wave transitions into a nonlinear or “crunch-in” regime under [Formula: see text], not only does the average gradient increase but strong transverse focusing fields extend down to the tube axis. This work thus demonstrates the near-term experimental realizability of Solid-State Tube Wakefield Accelerator (SOTWA). The ongoing progress in nanoengineering and attosecond source technology thereby now offers the potential to experimentally realize the promise of solid-state or crystal acceleration, opening up unprecedented pathways in miniaturization of accelerators.
Some applications of particle-in-cell codes to problems of high intensity beams
