Fundamental limits on fiber-based electron acceleration—and how to overcome them

To accelerate ultrarelativistic charged particles, such as electrons, using an electromagnetic pulse along a hollow-core waveguide, the pulse needs to have a longitudinal electric field component and a phase velocity of c , the speed of light in vacuum. We derive an approximate closed-form expression for the wavelength at which the phase velocity of the TM 01 mode in a metal-clad hollow-core fiber with a dielectric layer is c . The expression is then used to derive conditions for material dispersion required of the dielectric in order to simultaneously have c phase and group velocity. It is shown that the dispersion would need to be so heavily anomalous that the losses in the anomalously dispersive regime would render such a particle accelerator useless. We then propose the utilization of gain in the form of two spectral peaks in the dielectric to circumvent the otherwise fundamental limits and allow for TM 01 pulses with c phase and group velocity, and thus arbitrary length scaling of fiber-based electron accelerators. In theory, the group velocity dispersion could also be made zero with further gain-assisted dispersion engineering, allowing for the copropagation of dispersionless electromagnetic pulses with relativistic particles.