Relativistic Harmonic Generation with Flat Spectrum: Boosted Coherent Synchrotron Emission from Continuously Accelerated Electron Nanobunches

We demonstrate analytically and numerically that relativistic harmonics with a flat spectrum as I_n/I₀=n^-2/3 can be achieved when an electron nanobunch obtains considerable acceleration during the photon emission process.  Here I_n is the intensity of the nth harmonic. Different from the γ-spike distribution in relativistically oscillating mirror and coherent synchrotron emission (CSE), in this mechanism, the electron relativistic factor γ is rising significantly even during the stationary phase point, leading to boosted radiation bursts.  Using two-dimensional particle-in-cell simulations, we find an approach to produce harmonics with such a flat spectrum, where an intense femtosecond laser pulse is incident on the front edge of a thick target. The excited strong surface plasma wave field supports the continuous longitudinal acceleration for electrons. The obtained spectrum is much flatter than the -4/3-power law of the conventional CSE mechanism. This paves the way to unprecedentedly large energy attosecond pulses.