Ponderomotive acceleration of hot electrons in tenuous plasmas

The oscillation-center Hamiltonian is derived for a relativistic electron injected with an arbitrary momentum in a linearly polarized laser pulse propagating in tenuous plasma, assuming that the pulse length is smaller than the plasma wavelength. For hot electrons generated by collisions with ions under an intense laser drive, multiple regimes of ponderomotive acceleration are identified, and the laser dispersion is shown to affect the process at plasma densities down to 10¹⁷ cm⁻³. We consider the regime when the cold plasma is not accelerated, requiring a/γ_g⪡1, where a is the laser parameter, proportional to the field amplitude, and γ_g is the group-velocity Lorentz factor. In this case, the Lorentz factor γ of hot electrons does not exceed Γ≡aγ_g after acceleration, assuming its initial value also satisfies γ₀≲Γ. Yet γ∼Γ is attained within a wide range of initial conditions; hence, a cutoff in the hot-electron distribution is predicted.