Absolute densities of energetic hydrogen ion species in an abnormal hollow cathode discharge
J. Kipritidis · J. Khachan · M. Fitzgerald · O. Shrier
Abstract and summary · read the original at the source · APS default licence, not a Creative Commons licence
In one page
An inertial electrostatic confinement device is the simplest fusion machine anyone can build: a wire cage held at tens of kilovolts inside a vacuum chamber, pulling ions inward to collide at the centre. The hard part is knowing what is actually in there. Kipritidis, Khachan, Fitzgerald and Shrier at the University of Sydney show that the light the discharge already emits carries the answer. Hydrogen glows red at the Balmer alpha line, and that line arrives in two forms: an unshifted central peak from slow atoms knocked out of hydrogen molecules by fast electrons, and Doppler-shifted wings from fast atoms made when energetic ions steal an electron from the background gas. By joining two existing models of those two processes, the team turn one spectrum plus the electron current into an absolute number of fast ions per cubic metre — about ten to the fourteen at minus five kilovolts and twenty millitorr, rising in step with the current, and agreeing with what probes and drifting dust grains say in similar machines.
Why it matters hereChapter 12 needs to know how many nuclei are actually moving fast enough to fuse, not how bright the glow is, and this paper turns a cheap optical measurement into that number — then shows, in its final section, that the same measurement in deuterium gives the fusion reaction rate directly. Chapter 9 gets something else from it: a self-organising structure inside the discharge, a positive space-charge core the authors call a virtual anode, mapped by nothing more exotic than the shape of a spectral line.
What it claims
01Combining two collisional-radiative models that had previously been used separately — one for the unshifted Balmer alpha peak produced by dissociative excitation of molecular hydrogen by fast electrons, one for the Doppler-shifted wings produced by charge exchange of energetic ions — yields an optical measurement of absolute fast-ion density that needs only two inputs, the current density due to fast electrons and a single Balmer alpha spectrum taken at the anode; the authors state that neither earlier model in isolation can give this result.Abstract; Section I, Introduction, closing paragraphs; Section III
Published and peer-reviewed02In a hollow cathode 4.1 centimetres long and 1 centimetre in radius, biased at minus 5 kilovolts at 20 millitorr and observed at 25 degrees to the emission channel through a 0.5 metre monochromator and linear diode array, the density of fast ions emerging from the cathode is of order one to ten times ten to the fourteen per cubic metre, increasing roughly linearly with current over the 10 to 30 milliampere range, and agreeing with values obtained in similar apparatus from Langmuir probes and from the ion drag force on dust particles.Section II, Experimental setup, Figure 3; Section IV B, Figure 12; Section V, Conclusions
Published and peer-reviewed03The Doppler shift grows with distance from the cathode centre, which implies that most ions are created inside the cathode and charge-exchange as they accelerate outward from a central region of positive space charge — a virtual anode, supported by Langmuir probe measurements of the electric potential in similar apparatus; the authors note in the same passage that recent Doppler spectroscopy and numerical modelling at these pressures challenge the argument that energetic ions are confined at all.Section I, Introduction; Section III C, Figure 4
What to watch04Combining the measured densities with the background gas density gives the fraction of the gas dissociated into fast ions at the cathode, about one to two parts in a million and largely independent of current above 10 milliamperes; the authors then show that in a deuterium discharge this same fraction fixes the deuterium-deuterium reaction rate, since the rate is the fraction times the square of the gas density times the cross section times the ion velocity.Section IV B, Figure 13 and the reaction-rate expression that follows it
Published and peer-reviewed05The method is honest about its own limits: the density values are order-of-magnitude estimates, they hold only where the electron population is roughly monoenergetic and above about 1.5 kiloelectronvolts, and the ion and neutral populations are not perfectly monoenergetic — the Gaussian half-width of about 3 ångström in this discharge corresponds to an energy spread of roughly 100 to 300 electronvolts per peak, some 10 to 20 percent at kiloelectronvolt energies.Section III D, Limitations and uncertainties; Section V, Conclusions
Published and peer-reviewed06The named next measurement is a calibration: because the chosen cathode bias of minus 5 kilovolts is an order of magnitude below that used in inertial electrostatic confinement neutron production, future work will compare the dissociation fraction obtained by emission spectroscopy with the value obtained by nuclear spectroscopy in deuterium at larger cathode bias.Section IV B, final paragraph; Section V, Conclusions
What to watch
Read it · abstract
Abstract
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 Hα 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 Hα 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 −5 kV at 20 mTorr) is in the order 10¹⁴ m⁻³, increasing approximately linearly with current in the 10–30 mA range. Calculated densities agree with values obtained in similar apparatus using Langmuir probes and analysis of dust particle motion.
The way in
https://doi.org/10.1103/physreve.77.066405SOURCE READ IN FULL, REPRODUCED IN PART. The published article carries the line ©2008 The American Physical Society and the APS default licence, with no Creative Commons statement, so only the authors’ own abstract is reproduced here. The complete nine-page article was retrieved on 2026-09-08 from the APS full-text endpoint harvest.aps.org/v2/journals/articles/10.1103/physreve.77.066405/fulltext and read end to end; every claim locator below points to a numbered section, equation or figure of it. The abstract is verbatim, with the publisher’s markup rendered as Greek letters and typographic subscripts and superscripts — the alpha of the Balmer line is set inline rather than as a subscript — and the minus sign on the cathode bias set as a true minus. The authors are at the School of Physics, University of Sydney; initials are left as the journal prints them, and the corresponding author is J. Kipritidis. One point of confusion worth naming: S. Bosi is a co-author of this group’s earlier hollow-cathode papers, which appear in the reference list, but is not an author of this one — the fourth author here is O. Shrier. Companion sheets: ion kinetics in an inertial electrostatic confinement device at /library/stm-0b806244cb, the cylindrical discharge study at /library/stm-218a859c1b, deuterium anions in inertial electrostatic confinement devices at /library/stm-27b0684846, and space charge neutralization in these plasmas at /library/stm-5c07c85688.
How to cite it
J. Kipritidis, J. Khachan, M. Fitzgerald, O. Shrier (2008) Absolute densities of energetic hydrogen ion species in an abnormal hollow cathode discharge. doi:10.1103/physreve.77.066405
Where it sits in the curriculum
Plasmoids, charge clusters and the orbsLattice confinement fusion