Two-stage acceleration of electrons by intense laser-cluster interaction in strong magnetic environment

Collisionless laser absorption occurs via anharmonic resonance (AHR) in the over-dense (cluster) plasma potential during the few-cycle laser-cluster interaction for intensity > 10¹⁶ W/cm² and wavelength > 780 nm. The ponderomotive energy (U_p) of electrons in the collisionless case often serves as a benchmark for the average absorbed energy per cluster-electron (E_A) as demonstrated by numerous experiments, theories, and simulations. In this study, we report substantially enhanced E_A ≈ 30 − 70U_p, a 15 − 30 times energy increase with an external (crossed) magnetic field close to the electron-cyclotron resonance (ECR) using a simple rigid sphere model (RSM) and a comprehensive three-dimensional particle-in-cell (PIC) simulation. With the relativistic mass increase during the interaction, electrons swiftly depart from the conventional (non-relativistic) ECR, but time-dependent relativistic ECR (RECR) occurs which enhances E_A further. Here, AHR (first stage) and ECR/RECR (second stage) work together for laser coupling to electrons. After meeting the requisite phase matching condition ∆ψ ≈ π (∆ψ is the phase-difference between the driving electric field and corresponding velocity component), prompt generation of electron via AHR occurs only for a short duration and then deviates. The auxiliary magnetic field, on the other hand, changes the AHR scenario inside the cluster and aids in sustaining the appropriate phase matching criterion for the released cluster-electron for an extended duration of the laser pulse accompanied by frequency matching for ECR/RECR. This work may be important to understand how electrons are energized/accelerated by drawing electro-magnetic field energy in the strong magnetic field environment in astrophysical plasma conditions.