Summary of C-2W Field-Reversed Configuration Experiment Diagnostic Systems and Results

Application of Bayesian inference for reconstruction of FRC plasma state in C-2W
P.C. Norgaard1, M. Dikovsky1, I. Langmore1, T. Madams1, Y. Carmon1, E.A. Baltz1, J. Romero2, M.C. Thompson2, E. Trask2, H. Gota2, and the Google/TAE Team1,2 (1) Google LLC, 1600 Amphitheatre Parkway, Mountain View, CA 94043
(2) TAE Technologies, Inc., 19631 Pauling, Foothill Ranch, CA 92610
60th Annual Meeting of the APS Division of Plasma Physics, November 5-9, 2018 • Portland, Oregon
Abstract
Bayesian methods are used to infer Field Reversed Configuration (FRC) plasma properties for the C-2W machine at TAE Technologies. The approach starts with a statistical distribution of possible plasma states, where physically-motivated constraints are imposed through the Bayesian prior. Possible states are processed by a forward model for the relevant instruments to assess agreement with corresponding measured experimental data. The resulting probability distribution is known as the posterior, from which the most likely plasma state and the corresponding statistical confidence are extracted. Plasma state reconstruction from multi-instrument Bayesian inference are presented in this study, implemented for the upgraded diagnostics that have come online for C-2W. FIR interferometry, Thomson scattering, Bremsstrahlung radiation measurement, and secondary electron emission detection from the neutral beams are used in reconstruction near the FRC midplane. Magnetic probes and imaging from a high-speed camera provide 3D data throughout the main confinement vessel. This study aims to further the understanding of plasma properties and dynamics, such as electron and ion densities, electron temperature, plasma current, and magnetic field topology.
Bayesian Inference
We employ Bayesian inference to obtain a distribution of plasma states consistent with the plasma diagnostic measurements. The method is described here for determining electron density from 14 chords of interferometry.
Parameterization
Create a parameterized representation of the plasma state (z). The electron density is represented as a set of values on 32 concentric annular rings. Together with radial shift coordinates (x,y), this forms a set of parameters to solve for.
Prior
The prior specifies conditions on the space of possible parameter values. In this case, a prior is defined to penalize density outside of the confinement vessel and also to encode expectation of smoothness into a covariance matrix, similar to the GPT method1.
Forward Model
Samples taken from the prior, p(z) are possible plasma states. 1) J. Svensson, JET Internal Report EFDA-JET-PR24 (2011)
The forward model transforms a set of parameter values to a corresponding set of measurements. For interferometry, the density is integrated along the laser path. Noise terms are needed to provide for discrepancy between the parameterized representation and real physical system.
Posterior
The posterior is obtained from the defined prior and forward model, and allows for statistical sampling of the parameterization (z) given a set of instrument measurements (mtrue). We use Hamiltonian Monte Carlo (HMC) to sample the posterior.
Samples taken from the posterior, p(z|m_true) are possible plasma states given the measurements. Since the interferometry chords are collinear, the inference cannot distinguish between these.
Output
With sufficient samples of the posterior, the reconstructed profile and credibility bounds are obtained from the mean value and quantiles. The predicted measurement interval is computed by running posterior samples through the forward model - this allows for comparison to the plasma diagnostic measurements.
The blue points are the measurements from the interferometry chords. The blue shading is the predicted measurement interval, which is computed by running posterior samples through the forward model. Having the measurement data inside this interval provides trust in the reconstruction output.
The red line is the radial density profile from the plasma center, computed as the mean of the posterior samples. The red shading is the credibility interval, which is similar to one standard deviation error bounds.
Confidential + Proprietary
Bremsstrahlung
The bremsstrahlung diagnostic optical mount holds collimation and focusing lenses for 15 fiber bundles. The view chords are spaced across half of the vessel, giving greater observation of the edge plasma. This system has seven fibers per bundle to enable different detectors. These include notch filters to observe bremsstrahlung emissivity at 523.5 nm and 1000 nm.
Camera
A Phantom Micro Lab 310 camera with 384 x 384 px resolution sampling a 19.5 kfps is used with a 130 deg field of view lense to record emissivity via a notch O4+ filter (650.0 nm). Though computationally intensive, this large field of view can be used to infer midplane emissivity profile and plasma location.
Results
M. Nations et al, REVIEW OF SCIENTIFIC INSTRUMENTS 89, 10D130 (2018)
The Bayesian inference process is initialized when C-2W instrument data and machine settings are uploaded to Google servers immediately after an experiment shot. The computation is typically extremely fast as it employs TensorFlow and can be distributed across multiple nodes of CPUs and GPUs. An hdf5 file of the reconstructed plasma profile results and html page of figures are created and downloaded to TAE. The html includes a sequence of videos that display in the TAE control room. The image below shows one video frame of electron density reconstruction.
Acknowledgements
The authors wish to thank the many team members at TAE and Google who contributed significant work, including the
images here, to make the poster publication possible.
Confidential + Proprietary
Diagnostics
The C-2W midplane has the most instruments and measurements of any section of the confinement vessel, making it optimal for reconstruction of the plasma profile.
An electron density profile is reconstructed from interferometry and Thomson scattering. Emissivity measurements from bremsstrahlung diagnostics or a fast camera have been used to assist in determining the profile radial shift. In future work we plan to incorporate additional diagnostics and couple physics variables together in the Bayesian inference.
Interferometry
Seven chords of FIR interferometry measure chord-integrated electron density perpendicular to the machine axis, while 7 more are tilted 15 degrees. We project the latter to get 14 chords in the plane with 8.1 cm spacing.
B. H. Deng et al, REVIEW OF SCIENTIFIC INSTRUMENTS 89, 10B109 (2018)
Thomson Scattering
The central Thomson Scattering system measures Te and ne profiles at 16 locations along the laser path,
with up to 35 snapshots at up to 20 kHz.
K. Zhai et al, HTPD2018, 2018