Spectroscopic determination of electron energies in a discharge of atomic H produced by a monoenergetic electron beam

We construct a collisional-radiative model for atomic H produced in H2 gas at units and tens of mTorr pressures by a monoenergetic electron beam at units of keV energies. Unlike similar work in regimes of higher pressure and lower electron energies, we calculate the electron energy dependence of the two strongest Balmer lines (Hα and Hβ). A key result is that the intensity ratios do not uniquely specify the electron energy, and so we propose a new method for measurement of the spatial energy profile using the absolute and relative intensities in tandem. The model shows qualitative agreement with semi-empirical distributions of absolute and relative intensities versus electron energy for beams emerging from a biconical hollow cathode