Laser cluster interaction in external magnetic field: emergence of nearly mono-energetic weakly relativistic electron beam

Recent studies [Sci Rep 12, 11256 (2022)] on laser interaction (wavelength 800~nm, intensity $>{10}^{16}\text{Wcmcm}$) with deuterium nano-cluster in an ambient magnetic field ($B_0$) demonstrate that collisionless absorption of laser occurs in two stages via anharmonic resonance (AHR) and electron-cyclotron resonance (ECR) or relativistic ECR (RECR) processes. Auxiliary $B_0$ enhances coupling of laser to cluster-electrons via improved frequency-matching for ECR/RECR as well as phase-matching for prolonged duration of the 5-fs (fwhm) broadband pulse and the average absorbed energy per electron ${\bar{\mathcal{E}}}_A$ significantly jumps up $\approx 36-70$ times of its ponderomotive energy ($\text{Up}$). In this paper, we report energy dispersion of these energetic electrons and their angular distribution in position and momentum space by performing hybrid-PIC simulations. By simulating bigger clusters (radius $R_0\approx 3-4$~nm) at high intensities $\approx {10}^{16}-{10}^{18}\text{Wcmcm}$, we find ${\bar{\mathcal{E}}}_A\approx 36-70\text{Up}$ similar to a small cluster ($R_0\approx 2$~nm), but total energy absorption increases almost linearly with increasing cluster size due to more number of available energy carriers.