Laser cluster interaction in ambient magnetic fields for accelerating electrons in two stages without external injection

In the few-cycle pulse regime of laser-cluster interaction (intensity [Formula: see text] , wavelength [Formula: see text] nm), laser absorption is mostly collisionless and may happen via anharmonic resonance (AHR) process in the overdense (cluster) plasma potential. Many experiments, theory and simulation show average absorbed energy per cluster-electron ([Formula: see text] ) close to the electron’s ponderomotive energy ([Formula: see text] ) in the collisionless regime. In this work, by simple rigid sphere model (RSM) and detailed particle-in-cell (PIC) simulation, we show enhanced [Formula: see text] 30–70[Formula: see text] —a 15–30 fold increase—with an external (crossed) magnetic field near the electron-cyclotron resonance (ECR). Due to relativistic mass increase, electrons quickly deviate from the standard (non-relativistic) ECR, but time-dependent relativistic-ECR (RECR) happens which also contributes to enhanced [Formula: see text] . Here laser is coupled to electrons in two stages, i.e, AHR and ECR/RECR. To probe further we retrieve the phase-difference [Formula: see text] between the driving electric field and corresponding velocity component for each electron (in PIC and RSM). We find absorption by electron via AHR happens in a very short interval [Formula: see text] for less than half a laser period where [Formula: see text] remains close to [Formula: see text] (necessary condition for maximum laser absorption) and then [Formula: see text] drops to its initial [Formula: see text] (meaning no absorption) after such short-lived AHR. On the contrary, auxiliary magnetic field near the ECR modifies AHR scenario inside the cluster and also helps maintaining the required phase [Formula: see text] for the liberated cluster-electron accompanied by frequency matching for ECR/RECR for a prolonged [Formula: see text] (which covers 50–60% of the laser pulse through pulse maxima) even after AHR—leading to jump in [Formula: see text] 30–70[Formula: see text] . We note that to realize the second stage of enhanced energy coupling via ECR/RECR, the first stage via AHR is necessary.