Rotational stability a long field-reversed configuration

PHYSICS OF PLASMAS 21, 032507 (2014)
Hybrid magneto-hydrodynamic simulation of a driven FRC
H. U. Rahman,1,a) F. J. Wessel,1 M. W. Binderbauer,1 F. Conti,2,3 P. Ney,4 A. Qerushi,1 and N. Rostoker1
1Tri Alpha Energy, Inc., P.O. Box 7010, Rancho Santa Margarita, California 92688, USA 2Physics Department “E. Fermi,” University of Pisa, Largo B. Pontecorvo 3, 56127 Pisa, Italy 3Plasma Diagnostics and Technologies Ltd., Via Giuntini 63, 56023 Navacchio (PI), Italy 4Mount San Jacinto College, Menifee, California 92584, USA
(Received 10 December 2013; accepted 3 March 2014; published online 17 March 2014)
We simulate a field-reversed configuration (FRC), produced by an “inductively driven” FRC experiment; comprised of a central-flux coil and exterior-limiter coil. To account for the plasma kinetic behavior, a standard 2-dimensional magneto-hydrodynamic code is modified to preserve the azimuthal, two-fluid behavior. Simulations are run for the FRC’s full-time history, sufficient to include: acceleration, formation, current neutralization, compression, and decay. At start-up, a net ion current develops that modifies the applied-magnetic field forming closed-field lines and a region of null-magnetic field (i.e., a FRC). After closed-field lines form, ion-electron drag increases the electron current, canceling a portion of the ion current. The equilibrium is lost as the total current eventually dissipates. The time evolution and magnitudes of the computed current, ion-rotation velocity, and plasma temperature agree with the experiments, as do the rigid-rotor-like, radial-profiles for the density and axial-magnetic field [cf. Conti et al. Phys. Plasmas 21, 022511 (2014)]. VC 2014 AIP Publishing LLC. [http://dx.doi.org/10.1063/1.4868727]
I. INTRODUCTION
The Field Reversed Configuration (FRC) is a cylindri- cally symmetric, compact-toroid, unity-beta plasma distribu- tion, where b 8pnkT=B2, and n, T, and B are the density, temperature, and magnetic field, respectively.1,2 To form the FRC, an electric field is applied in the presence of pre- magnetized plasma. Plasma rotation is established3 with dia- magnetic currents that sustain a reversed, axial-magnetic field inside the FRC.
Magneto-hydrodynamic (MHD) models are widely used to describe the FRC dynamics; while kinetic4 and full two- fluid5–7 plasma models are also used to a lesser extent. The approach taken here is to simulate the formation and equilib- rium dynamics of the FRC, using a hybrid-MHD model, and to compare the results with measurements obtained on a well-documented experiment.
The experiment uses a coaxial-coil system to form and sustain the FRC, in a quasi-equilibrium state, unlike typical experiments where the FRC simply decays in time. The cen- tral flux-coil (FC) solenoid generates an azimuthal-electric field that ionizes the plasma and forms the FRC in the pres- ence of a pre-formed, axial-magnetic field, produced by an outer limiter-coil (LC) solenoid. Figure 1 is a schematic illustration of the FC-FRC.
Recent experiments at the University of California, Irvine, and Tri Alpha Energy, Inc., agree that FRCs formed in this manner possess significant ion-azimuthal current and plasma rotation.8–10 Measurements also indicate that the ra- dial profiles for the density, axial-magnetic field, and radial- electric field are rigid-rotor like;10 a rigid-rotor plasma is one
where the entire plasma rotates with a uniform-angular fre- quency, independent of radius.11–14
The hybrid simulation presented here uses a modified version of the MACH2 MHD code15,16 and a coupled-circuit model to produce the azimuthal-electric field. MACH2 com- putes three components of the vector fields for velocity and magnetic-field, hence is sometimes described as 2-1/2 dimensional. It solves the dynamic single-fluid, multi-tem- perature, resistive MHD equations, including separate energy equations for the electrons, ions, and radiation field. The MHD equations are closed with an equilibrium equation-of- state and transport coefficients.
The radial and axial formulations in MACH2 remain unchanged in the hybrid simulation, while the azimuthal- momentum equations are decoupled (i.e., as two-fluid). This allows for ion acceleration during the full-life cycle of the FRC, when the electric field is present. The simulated FRC parameters agree with experiments, both qualitatively and quantitatively, including the density, azimuthal-rotation fre- quency, total current, and n(r) and Bz(r) radial profiles.
This paper is organized into five sections, as follows: Sec. I is the introduction, Sec. II describes the derivation of the hybrid, two-fluid MHD equations, Sec. III presents the results of the simulations, Sec. IV compares the simulations with the experimental results, and Sec. V concludes the paper.
II. FORMULATION OF THE HYBRID MODEL
The physics model is two dimensional, in r and z, and assumes azimuthal symmetry in the third dimension h. The standard, two-fluid momentum equations are
@ ~v i
min @t þ~vi r ~vi 1⁄4enðEþ~vi BÞ rpi þPie; (1)
~~
a)
Electronic mail: hrahman@trialphaenergy.com
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