Temporal profile of betatron radiation from laser-driven electron accelerators

Abstract

Temporal profile of X-ray betatron radiation was theoretically studied for the parameters available with current laser systems. Characteristics of the betatron radiation were investigated for three different configurations of laser wakefield acceleration: typical self-injection regime and optical injection regime with perpendicularly crossed injection and drive beams, both achievable with 100 TW class laser, and ionization injection regime with sub-10 TW laser system that was experimentally verified. Constructed spectrograms demonstrate that X-ray pulse durations are in order of few tens of femtoseconds and the optical injection case reveals the possibility of generating X-ray pulses as short as 2.6 fs. X-ray pulse duration depends mainly on the length of the trapped electron bunch as the emitted photons copropagate with the bunch with nearly the same velocity. These spectrograms were calculated using novel simplified method based on the theory of Liénard-Wiechert potentials. It takes advantage of the fact that the electron oscillates transversally in the accelerating plasma wave in the wiggler regime and, thus, emits radiation almost exclusively in the turning points of its sine-like trajectory. Therefore there are only few very narrow time intervals, which contribute significantly to the emission of radiation, while the rest can be neglected. These narrow time intervals are determined from the electron trajectories calculated using particle-in-cell simulations and the power spectrum at given point in far field is computed for each electron using the Fourier transform. Spectrograms of the emitted radiation are constructed by summing contributions of individual particles, since the incoherent nature of the electron bunch is assumed.

Attosecond betatron radiation pulse train

“…The temporal profile of betatron radiation was calculated using the method based on the Fourier transform of the emitted signal which can be determined by using trajectories of the trapped electrons 54 . It takes advantage of the fact that each electron performs betatron motion in the wiggler regime and the emitted signal is composed of a series of sharp peaks radiated at the turning points of the electron trajectories separated by relatively long intervals of silence.…”

Attosecond betatron radiation pulse train

“…The temporal profile of betatron radiation was calculated using the method based on the Fourier transform of the emitted signal which can be determined by using trajectories of the trapped electrons [51]. It takes advantage of the fact that each electron performs betatron motion in the wiggler regime and the emitted signal is composed of a series of sharp peaks radiated at the turning points of the electron trajectories separated by relatively long intervals of silence.…”

Generation of attosecond electron bunches and x-ray pulses from few-cycle femtosecond laser pulses

“…This value is in line with an electron beam of average energy around 50 MeV and divergence ∼10 mrad in which each individual electron emits in a cone of 1/γ in their direction of motion. The duration of the betatron radiation is usually inferred from the duration of the electron bunch, but here we compute the spectrogram [39], showing d 3 I/dEdΩdt on axis in figure 4(b) and its integration over the frequency to get the temporal profile of the radiation on axis. Most of the radiation is received at early times, with a tail at lower energies arriving at later times, following the structure of the beam.…”