Historical research guide · 1076 · 2008
Absolute densities of energetic hydrogen ion species in an abnormal hollow cathode discharge
J. Kipritidis · J. Khachan · M. Fitzgerald · O. Shrier
In one minute
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.
Connection
Chapter 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.
From the source
Combining 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
In 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
The 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
Combining 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
The 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
The 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
The way in
https://doi.org/10.1103/physreve.77.066405How 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