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

Abstract

In the few-cycle pulse regime of laser-cluster interaction (intensity $$>10^{16}\,\text{ W/cm}^{2}$$ > 10 16 W/cm 2 , wavelength $$> 780$$ > 780 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 ($${\mathcal {E}_A}$$ E A ) close to the electron’s ponderomotive energy ($$U_\mathrm {p}$$ U p ) in the collisionless regime. In this work, by simple rigid sphere model (RSM) and detailed particle-in-cell (PIC) simulation, we show enhanced $${\mathcal {E}_A}\approx$$ E A ≈ 30–70$$U_\mathrm {p}$$ U p —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 $${\mathcal {E}_A}$$ E A . Here laser is coupled to electrons in two stages, i.e, AHR and ECR/RECR. To probe further we retrieve the phase-difference $$\Delta \psi$$ Δ ψ 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 $$\Delta \tau$$ Δ τ for less than half a laser period where $$\Delta \psi$$ Δ ψ remains close to $$\pi$$ π (necessary condition for maximum laser absorption) and then $$\Delta \psi$$ Δ ψ drops to its initial $$\pi /2$$ π / 2 (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 $$\Delta \psi \approx \pi$$ Δ ψ ≈ π for the liberated cluster-electron accompanied by frequency matching for ECR/RECR for a prolonged $$\Delta \tau$$ Δ τ (which covers 50–60% of the laser pulse through pulse maxima) even after AHR—leading to jump in $${\mathcal {E}_A}\approx$$ E A ≈ 30–70$$U_\mathrm {p}$$ U p . We note that to realize the second stage of enhanced energy coupling via ECR/RECR, the first stage via AHR is necessary.