Absolute densities of energetic hydrogen ion species in an abnormal hollow cathode discharge

We develop an optical measurement for densities of fast (units to tens of keV) hydrogen ions in an abnormal hollow cathode discharge in units to tens of mTorr pressure range. This method combines results from previous collisional-radiative models, comparing the intensity of Balmer H_α due to dissociative excitation of H₂ by fast electrons to Doppler-shifted emission arising from charge exchange of energetic ions. The method requires only two inputs: the current density due to fast electrons and a single H_α spectrum of the characteristic emission channel at the anode. We model in particular the cylindrical interelectrode discharge of an inertial electrostatic confinement device. Experimentally, we find that the density of fast ions emerging from the cathode (bias -50.3em0exkV at 200.3em0exmTorr) is in the order 10¹⁴0.3em0exm^-3, increasing approximately linearly with current in the 10--300.3em0exmA range. Calculated densities agree with values obtained in similar apparatus using Langmuir probes and analysis of dust particle motion.