Heated Plasma Expansion

We derive a new family of self-similar solutions for externally heated collisionless plasmas modelled by the electron-ion two-fluid system coupled through the self-consistent electrostatic field. The length scales of charge separation(Debye length λ_D) and of ion dynamics(λ_s=C_sτ_s) relative to the length scale of the heated self-similar domain serve as two independent free parameters governing the expansion dynamics. The parametric variation of the solutions demonstrate a continuous transition among vastly different regimes of plasma dynamics from Coulomb explosion to quasi-neutral expansion, and from subsonic expansion to ion flows with supersonic exit. The inclusion of charge separation effects resolves local density modulation features including collisionless, hydrodynamic shock-like structures. Furthermore, the solutions admit a range of different electron temperature closures that are more general than the typically used polytropic description, through a third free parameter. For 1-dimensional planar expansion, we identify five distinct regimes depending on the heating and initial conditions and propose analytic scaling relations for the length scales and energies of the expanding plasma. This new family of solutions is applied to laser–plasma interactions, offering insights into the expansion behavior based on the laser-plasma parameters, scaling relations for optimizing laser-plasma schemes and thus guidance for experimental designs.