Page 5 - Inference of field reversed configuration topology and dynamics during Alfvenic transients

NATURE COMMUNICATIONS | DOI: 10.1038/s41467-018-03110-5
ARTICLE
0.35 0.3 0.25 0.2 0.15
2.5 2 1.5 1
1 0.5
√⎯2R0 Rs
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BwR3s/Rw 0(mWb)
b 4 3
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–10 –20
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0.3 0.4 t (ms)
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0 cd 300
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Fig. 4 Inference of Alfvenic oscillations. Inferred plasma variables at the start of the C-2U shot #49040. Solid lines correspond with the expected values of the posterior distribution, and shaded areas are a measure of the uncertainty of the inferred variables corresponding to one standard deviation.
pffiffiffi
a Separatrix radius Rs (blue) and o-point radius R0 times 2 (green). Rs is found to be proportional to the R0, in agreement with Eq. (7). b Trapped flux
(blue) and the trapped flux approximation for a long FRC (green). c Separatrix length (distance between x-points). d Total plasma current. e o-point z position. f Vessel current imbalance
on Hooke’s constant and the axial force exerted on the plasma as a result of its axial displacement are shown in Fig. 5. Axial force and displacement are linearly dependent in a range of +/−1 m around the mid-plane, so plasma dynamics can be approximated by a linear partial differential equation in this range. This is interesting for the future plasma control goals, since control theory and practice are well established for linear systems22.
The Hooke’s constant is positive due to the axially stabilizing external field and therefore consistent with an axially stable magnetic configuration that reaches the mid-plane after a few oscillations, as observed. The inferred value of about 1000 N/m is in agreement with the results obtained using the Lamy Ridge code23. The inference method can also provide the axial stability properties of the magnetic configuration. This is an important information for plasma control of future devices, which will require to establish and sustain an axially unstable plasma in equilibrium around the mid-plane z=024. A method to determine the axial stability properties of the magnetic config- uration will be therefore required.
Comparison with plasma imaging. High-speed imaging of visible plasma emission is an independent technique that can yield information about the plasma dimensions. In this study, qualitative agreement between visible light emission from intrinsic oxygen impurity ions and the dynamics of the inferred poloidal flux contours serve as additional validation of the pro- posed inference method. Photons emitted from the 3d→3p
transition (at 650.0 nm) of O4+ were measured using a filtered high-speed camera with a radial view of the plasma25.
Emissivity of this spectral line was reconstructed (assuming axis symmetry) using the Simultaneous Algebraic Reconstruction Technique26. The core FRC electron temperature and density are more than sufficient to ionize the O4+ charge state and populate higher charge states via electron impact excitation; therefore, minimal emission from this spectral line is found in the core. Instead, emission is peaked in the SOL where the electron temperature and density are lower and diffusive transport from boundary sources competes with ionization to higher charge states.
An example comparing the results of the magnetic inference method with the emissivity reconstruction for this spectral line is shown in Fig. 6. A relatively high-density plasma discharge (#48269) was chosen so that the emission measurement had good signal. Good agreement in the temporal dynamics of the reconstructed poloidal flux and emissivity is observed. This agreement provides further validation of the proposed inference method and is all the more encouraging since the two reconstructed quantities are derived from independent measure- ments (magnetics vs. photons) and analysis procedures.
The overall consistency of inferred results (Fig. 7) is also good, with the following highlights: (a) Rs 1⁄4 p2R0 is really a very good
approximation, within one sigma. (b) The long FRC trapped flux (Eq. (9)) ψ 0 1⁄4 Bw R3s =Rw is also a very good approximation, being its overall magnitude in agreement with similar results obtained
NATURE COMMUNICATIONS | (2018)9:691 | DOI: 10.1038/s41467-018-03110-5 | www.nature.com/naturecommunications 5
Zo (m) L (m) (m)
I v(kA) I p(kA)
0(mWb)