Non-linear QED approach for betatron radiation in a laser wakefield accelerator

Laser plasma-based accelerators provide an excellent source of collimated, bright, and adequately coherent betatron-type x-ray pulses with potential applications in science and industry. So far the laser plasma-based betatron radiation has been described within the concept of classical Liénard–Wiechert potentials incorporated in particle-in-cell simulations, a computing power-demanding approach, especially for the case of multi-petawatt lasers. In this work, we describe the laser plasma-based generation of betatron radiation at the most fundamental level of quantum mechanics. In our approach, photon emission from the relativistic electrons in the plasma bubble is described within a nonlinear quantum electrodynamics (QED) framework. The reported QED-based betatron radiation results are in excellent agreement with similar results using Liénard–Wiechert potentials, as well as in very good agreement with betatron radiation measurements, obtained with multi-10-TW lasers interacting with He and multielectron N \(_2\) ${}_2$ gas targets. Furthermore, our QED approach results in a dramatic reduction of the computational runtime demands, making it a favorable tool for designing betatron radiation experiments, especially in multi-petawatt laser facilities.