Page 5 - Achievement of Sustained Net Plasma Heating in a Fusion Experiment with the Optometrist Algorithm

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Settings
Metaparameters
Formation: Voltages
34
4
Formation: Timings
80
4
Formation: Gas Pressure
6
1
Formation: Gas Timing
6
1
Equilibrium: Magnets
7
7
Equilibrium: Mirror Field
4
2 (4)
Equilibrium: Electrical Biasing
8
4 (8)
Totals
145
23 (29)
Table 2. Metaparameters for specifying experiments. Values in parentheses indicate asymmetric operation, which was not commonly attempted or required. Note that settings for the equilibrium magnets were not believed to be further reducible. For many experiments there were additional reductions, e.g. not adjusting mirror elds and electrical biasing.
where the total plasma energy had brief increases. We then attempted to improve on this: we achieved a high and rapidly rising ion temperature (see Fig. 2) in addition to the total energy increase (see Fig. 3(b)) in Shot 46366. Both the absolute magnitude and the rate of rise of the temperature were signi cant, because one of the research goals at Tri Alpha Energy is to create hot ions.
While the performance of this Shot 46366 was exemplary, on the same day a repeat and a single further Optometrist step each displayed rising total energy. ree days later, two direct repeats of 46366 again showed this behaviour. In addition, three days prior to taking Shot 46366, we took an Optometrist shot 46226 which was starting to display these excellent characteristics. e behaviour of this shot was repeated more than 10 times during the period of this particular experimental campaign, and before the objectives had to change. e best shots are summarised in Supplementary Table S1. Note in particular that the highest temperatures of the run were achieved by Shot 46366 and its repeat 46453.
Energy in the plasma is set by the di erence between heating and loss rates, given by dE/dt = (vHeat − vLoss)E. roughout this experimental run, heating inputs (particle beams) were not changed compared with standard set- tings. Prior experimental analyses9 place the typical loss rate at ~1,250 s−1. Figure 3(a) shows the normalised distri- bution of the number of shots as a function of peak net heating power for the sequence of shots leading up to the discovery of the new con nement regime. As can be seen, the best shots achieved a period of net heating for the rst time in the history of the apparatus. Comparing the di erence in slopes, ΔdE/dt, between typical shot performance and the record setting series of shots shows that the loss rate, vLoss, was reduced by about 250 s−1 to 1000 s−1 or less.
A complete power balance analysis17 of these shots is beyond the scope of this paper, several conclusions can still be drawn based on prior knowledge of C-2/C-2U transport18. Ions and electrons primarily lose energy through convection, conduction and radiation. Typical total ion and electron cooling rates are about 700 s−1 and 3,500 s−1 (for Ti ≈ 4 * Te), respectively. Particle and radiated power loss rates remain unchanged when comparing values from the new record shots (vp ≈ 400 s−1, vrad ≈ 300 s−1) with typical values. Furthermore, ion heat conduc- tion losses are insigni cant (vq,i ≈ 100 s−1) in C-2U. erefore, the observed record con nement is due to a pro- nounced reduction in electron heat conduction (vq,e), from 2400 s−1 to 1200 s−1. is is a remarkable improvement in plasma con nement and a necessary step towards attaining higher plasma temperatures.
Discussion
e problem of e cient exploration in many dimensions is certainly not unique to a plasma physics setting, and is applicable in many other disciplines. e highly nonlinear interactions innate to a magnetised fusion experiment, however, require systematic exploration. Changing one-variable-at-a-time is simply insu cient for the dimen- sionality of the problem. Blind randomisation is not necessarily the answer, because of concerns for damaging delicate pieces of equipment.
The Optometrist Algorithm complements model-based approaches by performing a thorough explora- tion of parameter space. We have built models of objective metrics on the data gathered from the Optometrist Algorithm. Another positive feature of the Optometrist Algorithm is that the optima of objective metrics may lie near the edge of the possible operating space. e tendency of humans to avoid such edges is counterbalanced by randomised exploration.
e most impactful bene t of the Optometrist Algorithm was the discovery of the unexpected regime of sustained net plasma heating. It is remarkable that this achievement was realised despite an a priori lack of knowl- edge of the causality or physics of the regime.
e Optometrist Algorithm is a solution to the common problem of understanding and optimising complex systems. Stochastic exploration combined with human-guided interpretation of results is a valuable tool that may solve a variety of di cult problems across modern science. We used the Optometrist Algorithm to advance understanding and performance of plasma fusion.
Methods
Metaparameters. Plasma experiments begin with a “formation” phase. First, gas is injected into the forma- tion sections through pu valves. Typically there were 6 active pu valves, each with pressure and timing settings. e rst two MPs unify these into a single injection pressure and time. e gas must then be ionized, controlled
Scientific REPORTS | 7: 6425 | DOI:10.1038/s41598-017-06645-7 5