Demo
P. 1

PHYSICS OF PLASMAS 24, 042504 (2017)
Modeling feedback control of unstable separatrix location in beam-driven
field-reversed configurations
N. Rath,a) M. Onofri, S. A. Dettrick, D. C. Barnes, and J. Romero
Tri Alpha Energy, P.O. Box 7010, Rancho Santa Margarita, California 92688-7010, USA
(Received 30 September 2016; accepted 24 February 2017; published online 31 March 2017)
We present a linear, one-parameter model for rigid displacement of a toroidally symmetric plasma. When the feedback control is feasible, plasma inertia can be neglected, and the instability growth rate is proportional to wall resistivity. We benchmark the linear model against non-linear, hybrid simulations of an axially unstable, beam-driven field-reversed configuration to fix the free parame- ter of the model. The resulting parameter-free model is validated using linear and non-linear closed-loop simulations with active feedback control by voltage-controlled coils. In closed loop simulations, the predictions of the parameter-free linear model agree satisfactory with the non- linear results. Implications for the feedback control of the positional instability in experiments are discussed. The presented model has been used to guide the design of the feedback control hardware in the C-2W experiment. Published by AIP Publishing. [http://dx.doi.org/10.1063/1.4979188]
I. INTRODUCTION
A field-reversed configuration (“FRC”1) is an axisym- metric toroidal confinement scheme. In contrast to the Tokamak, there is no central column (the vacuum chamber is cylindrical) and almost no toroidal field. The configuration is called field-reversed because the total magnetic field on the central machine axis points in the direction opposite to the vacuum field. This reversal is generated by strong toroi- dal plasma currents and results in the formation of a separa- trix that separates a compact toroid with closed field lines from the open-field-line scrape-off layer. The FRC concept has several features that make it attractive as a potential fusion reactor. The weakness of the toroidal magnetic field greatly reduces the chance for disruptive events associated with stored magnetic energy and runaway electrons, the two great challenges facing fusion reactors.2 Of all magnetic con- finement systems, the FRC exhibits the highest b (values of 8–12 are common, cf. Ref. 1), thus allowing for the most efficient use of magnet hardware. The FRC’s simple, linear geometry without center stack and toroidal field coils facili- tates the construction and maintenance and enables an unre- stricted divertor configuration that facilitates energy extraction and ash removal.
FRCs were predicted to be unstable,3 and early FRCs never achieved lifetimes of more than a millisecond.4 However, recent experiments with beam-driven FRCs (like Tri Alpha Energy’s C-2 and C-2U devices5,6) have re-invigorated interest in the FRC as a potential fusion concept.7,8
In C-2, tangential neutral beam injection (20–40keV hydrogen,  4MW total), coupled with electrically biased plasma guns at the plasma ends, magnetic end plugs, and advanced surface conditioning, led to dramatic reductions in turbulence-driven losses and greatly improved plasma stabil- ity.7,9 Under such conditions, FRCs with a significant fast- ion population and a total plasma temperature of up to 1 keV
a)Electronic mail: nrath@trialphanenergy.com
were achieved reproducibly.8 The FRCs were macroscopi- cally stable and decayed on characteristic transport time scales of a few milliseconds.
In C-2U, neutral beams were upgraded to 10 MW and produced a dominant fast ion population with a dramatic beneficial impact on the overall plasma performance.8 Specifically, FRCs were produced and sustained for times significantly longer than all characteristic plasma decay times without the beams, and the sustainment was fully cor- related with neutral beam injection. Furthermore, fast ions’ confinement close to the classical limit and new, benign col- lective fast ion effects were observed.
The exact stabilization mechanisms that are at work in such beam-driven FRCs are not fully understood yet, but large ion gyroradii (in the order of the machine radius) and radial electric potentials are known to play important roles.1,10,11 PIC simulations of the tilt instability identified stabilization effects due to hollow current profiles, self-generated toroidal fields, and finite larmor radii.12–14 Generally, predicting and modelling the stability of an FRC experiment are thus chal- lenging and requires time-dependent, non-linear, 3-D, ion- kinetic codes.15,16
However, there is one kind of instability that is unlikely to be affected by physics beyond basic MHD: the positional instability.17 In Tokamaks (which are topologically identical to FRCs), the positional instability is always along the major axis of the machine and known as the vertical instability. In FRCs, the instability may also be in the radial directions. If the FRC can be moved “as a whole” in a direction that low- ers the total energy, it will move into this direction regardless of the complexity of its internal dynamics. In the previous FRC experiments, this instability has been stabilized by a conducting wall which (on the timescale of the experiments) was acting as a perfect flux conserver. Future progress on beam-driven FRCs, however, will require feedback stabiliza- tion of the positional instability.
The C-2W experiment that is currently under construc- tion at Tri Alpha Energy is designed to evaluate the
1070-664X/2017/24(4)/042504/14/$30.00 24, 042504-1 Published by AIP Publishing.


































































































   1   2   3   4   5