For more than 70 years, plasma physicists have dreamed of controlled “breakeven” fusion, where a system is capable of releasing more energy in a fusion reaction than it takes to initiate and sustain those reactions. The challenge is that the reactor must create a plasma at a temperature of tens of millions of degrees, which requires a highly complex, finely tuned system to confine and sustain. Further, creating the plasma and maintaining it, requires substantial amounts of energy, which, to date, have exceeded that released in the fusion reaction itself. Nevertheless, if a “breakeven” system could be achieved, it could provide ample zero-carbon electricity, the potential impact of which has driven interest by government laboratories, such as ITER and the National Ignition Facility, as well as several privately funded efforts.
Today we highlight two recently published papers arising from our collaboration with TAE Technologies1, which demonstrate exciting advancements in the field. In “Overview of C-2W: High-temperature, steady-state beam-driven field-reversed configuration plasmas,” published in Nuclear Fusion, we describe the experimental program implemented by TAE, which leverages our improved version of the Optometrist Algorithm for machine optimization. Due in part to this contribution, the current state-of-the-art reactor is able to achieve plasma lifetimes up to three times longer than its predecessor. In “Multi-instrument Bayesian reconstruction of plasma shape evolution in the C-2W experiment,” published in Physics of Plasmas, we detail new methods developed for analyzing indirect measurements of plasma to reconstruct its properties in detail. This work enabled us to better understand how instabilities in the plasma arise and to understand how to mitigate these perturbations in practice.
Optimizing the Next Generation Fusion Device
The C-2W “Norman” machine (named for TAE’s late co-founder Prof. Norman Rostoker) is a nearly complete rebuild of the C-2U machine that we described in 2017. For this updated version, the TAE team integrated new pressure vessels, new power supplies, a new vacuum system, along with other substantial upgrades.
Norman is incredibly complex, with over 1000 machine control parameters, and likewise, it captures extensive amounts of data for each run, including over 1000 measurements of conditions in the plasma alone. And while the measurements of each plasma experiment are extremely rich, there is no simple metric for “goodness”. Further complicating matters, it is not possible to rapidly iterate to improve performance, because only one experiment can be executed every eight minutes. For these reasons, tuning the system is quite difficult and relies on the expert intuition developed by the plasma physicists operating the system. To optimize the new reactor’s performance, we needed a control system capable of handling the tremendous complexity of the system while being able to quickly tune the control parameters in response to the extensive data generated in experiments.
To accomplish this, we further adapted the Optometrist Algorithm that we had developed for the C-2U system to leverage the expertise of the operators. In this algorithm, the physicists compare experiment pairs, and determine whether the trial better achieves the current goals of the experiment, according to their judgment, than the current reference experiment — e.g., achieving increased plasma size at a fixed temperature, increased temperature, etc. By updating the reference accordingly, machine performance improves over time. However, accounting for operator intuition during this process is critical, because the measure of improvement may not be immediately obvious. For example, under some situations, an experiment with much denser plasma that is a little bit colder may, in fact, be “better”, because it may lead to other improvements in subsequent experiments. We further modified the algorithm by fitting a logistic regression to the binary decisions of the expert to guide the trial experiments, making a classic exploration-exploitation tradeoff.
Applying the Optometrist Algorithm to the magnetic field coils that form the plasma, we found a novel timing sequence that provides consistent starting conditions for long-lived plasmas, almost tripling the plasma lifetime when first applied. This was a marked improvement over the regime of net plasma heating first seen on the C-2U machine in 2015.
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| Plasma formation section of the Norman reactor. The outer coils operate for the duration of the experiments while the inner coils accelerate the plasma in less than 10 microseconds. (Photograph by Erik Lucero) |
Bayesian Reconstruction of Plasma Conditions
In addition to optimizing the performance of the machine, we also sought to more thoroughly understand the behavior of the plasmas it is generating. This includes understanding the density profiles, separate electron and ion temperatures, and magnetic fields generated by the plasma. Because the plasma in a fusion generator reaches 30 million Kelvin, which would destroy most solid materials in moments, precise measurements of the plasma conditions are very difficult.
To address this, Norman has a set of indirect diagnostics, generating 5 GB of data per shot, that peer into the plasma without touching it. One of these is a two-story laser interferometer that measures the line-integrated electron density along 14 lines of sight through the plasma, with a sample rate of more than a megahertz. The resulting dataset of line-integrated densities can be used to extract the spatial density profile of the plasma, which is crucial to understanding the plasma behavior. In this case, the Norman reactor generates field-reversed configuration (FRC) plasmas that tend to be best confined when they are hollow (imagine a smoke ring elongated into a barrel shape). The challenge in this situation is that generating the spatial density profiles for such a plasma configuration is an inverse problem, i.e., it is more difficult to infer the shape of the plasma from the measurements (the “inverse” direction) than to predict the measurements from a known shape (the “forward” direction).
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| Schematic of C-2W confinement vessel showing measurement systems: interferometer lines of sight measuring electron density (magenta), neutral particle beam lines of sight measuring ion density (purple) and magnetic sensors (blue). These disparate measurements are combined in the Bayesian framework. |
We developed a TensorFlow implementation of the Hamiltonian Monte Carlo (HMC) algorithm to address the problem of inferring the density profile of the plasma from multiple indirect measurements. Because the plasma is described by hundreds to thousands of variables and we want to reconstruct the state for thousands of frames, linked into “bursts” or short movies, for each plasma experiment, processing on CPUs is insufficient. For this reason, we optimized the HMC algorithm to be executed on GPUs. The Bayesian framework for this involves building “forward” models (i.e., predicting effects from causes) for several instruments, which can predict what the instrument would record, given some specified plasma conditions. We can then use HMC to calculate the probabilities of various possible plasma conditions. Understanding both density and temperature are crucial to the problem of breakeven fusion.
High Frequency Plasma Perturbations
Reconstruction of the plasma conditions does more than just recover the plasma density profile, it also recovers the behavior of high frequency density perturbations in the plasma. TAE has done a large number of experiments to determine if Norman’s neutral particle beams and electrode currents can control these oscillations. In the second paper, we demonstrate the strong mitigating effects of the neutral beams, showing that when the neutral beams are turned off, fluctuations immediately begin growing. The reconstruction allows us to see how the radial density profile of the plasma evolves as the perturbations grow, an understanding of which is key to mitigating such perturbations, allowing long-lived stable plasmas. Following a long tradition of listening to plasma perturbations to better intuit their behavior (e.g., ionospheric “whistlers” have been captured by radio operators for over a century), we translate the perturbations to audio (slowed down 500x) in order to listen to them.
| Movie showing spectrogram of magnetic oscillations, played as audio 500 times slower. Different colors indicate different shapes. There is a whistle as the plasma forms, as well as low drum sounds followed immediately by chirps when the plasma destabilizes and recovers. Headphones / earbuds recommended; may annoy pets and humans. |
The Future Looks Hot and Stable
With our assistance using machine optimization and data science, TAE achieved their major goals for Norman, which brings us a step closer to the goal of breakeven fusion. The machine maintains a stable plasma at 30 million Kelvin for 30 milliseconds, which is the extent of available power to its systems. They have completed a design for an even more powerful machine, which they hope will demonstrate the conditions necessary for breakeven fusion before the end of the decade. TAE has succeeded with two complete machine builds during our collaboration, and we are really excited to see the third.
Acknowledgments
We wish to thank Michael Dikovsky, Ian Langmore, Peter Norgaard, Scott Geraedts, Rob von Behren, Bill Heavlin, Anton Kast, Tom Madams, John Platt, Ross Koningstein, and Matt Trevithick for their contributions to this work. We thank the TensorFlow Probability team for considerable implementation assistance. Furthermore, we thank Jeff Dean for visiting TAE’s facility in Southern California and providing thoughtful suggestions. As always we are grateful to our colleagues at TAE Technologies for the opportunity to work on such a fascinating and important problem.
1Google owns stock and warrants in TAE Technologies. ↩
