Proceedings of the Fourth Symposium on the Physics and Technology of Compact Toroids

Summary

These proceedings contain review papers, technical presentations, and poster session contributions from the Fourth Symposium on the Physics and Technology of Compact Toroids held at Lawrence Livermore National Laboratory in October 1981. The papers cover theoretical, experimental, and reactor-concept developments in field-reversed configurations (FRC), spheromaks, beam-heated compact toroids, particle ring-plasma hybrids, and anomalous transport phenomena.

Title Page

CONF-811087 DE82 019828

Proceedings of the Fourth Symposium on the Physics and Technology of Compact Toroids Held at Lawrence Livermore National Laboratory October 27-29, 1981

R. F. Post W. C. Turner Editors

Lawrence Livermore National Laboratory Manuscript Date: June 11, 1982

LAWRENCE LIVERMORE LABORATORY University of California • Livermore, California • 94550

Contents Summary

PROGRAM - 1 REVIEW OF SYMPOSIUM - 3 POSTER SESSIONS - 9 SYMPOSIUM PAPERS - 13 I. Field Reversed Theta Pinch-Theory - 13 II. Field Reversed Theta Pinch Experiment - 55 III. Spheromak - Theory - 73 IV. Spheromak - Experiment - 123 V. General - 169 CONFERENCE ATTENDEES - 249

Review of the Fourth Symposium on the Physics and Technology of Compact Toroids (R. F. Post)

Hosted by the Lawrence Livermore National Laboratory, the Fourth Symposium on the Physics and Technology of Compact Toroids took place on the 27-29 October 1981. Attendees, numbering 80, heard 10 review papers in three morning plenary sessions, and interacted in two afternoon poster sessions where some 45 contributions were presented. There were 7 participants from overseas, including 6 scientists from Japan, and 1 from West Germany. Immediately following the Symposium, a two-day Joint U.S./Japan workshop on compact toroid research was held.

The review papers covered mainline approaches to compact torus research—the field-reversed theta pinch and the spheromak configuration—along with related fields (e.g. the reversed-field Z pinch) and common concerns such as particle transport, beam applications, and impurity radiation. Progress in understanding tilting/shifting instabilities, gross MHD stability, and transport scalings was highlighted.

Paper I-1: The Analytical and Numerical Calculations of Field Reversed Theta Pinch Equilibria Based on a Generalized Hill’s Vortex Model

Authors: D. V. Anderson, J. H. Hammer, D. C. Barnes (LLNL & Univ. of Texas). Investigates methods for numerically extending analytical solutions of field-reversed theta pinch equilibria for stability and dynamic studies using SEECOD and CYLEQ codes.

Paper I-2: An Integral Poloidal Flux Squared Invariant Model of the Relaxation of a Field Reversed Theta Pinch

Author: John Brandenburg (LLNL). Proposes a ‘Sonic Bath’ model where closed field line plasma forms an unstable intermediate equilibrium after axial contraction and relaxes to a state of minimum magnetic energy through shear Alfvén turbulence.

Paper I-3: Rotational Instabilities in the FRC: Results of Hybrid Simulations

Author: Douglas S. Harned (UC Berkeley / LANL). Uses the AQUARIUS quasineutral hybrid simulation code to show that m = 2 rotational instabilities can occur for ion rotation levels well below thresholds predicted by previous finite Larmor radius (FLR) theory.

Paper I-4: Equilibrium and Power Balance Constraints on a Quasi-Static, Ohmically-Heated FRC

Authors: K. F. McKenna, D. J. Rej, M. Tuszewski (LANL). Analytically investigates quasi-static formation of FRC plasmas under constraints of radial equilibrium and energy losses, including rotating-magnetic-field (RMF) current drive techniques.

Paper I-5: Nonadiabatic Scattering and Transport at the Spindle Cusp

Authors: R. W. Moses, D. W. Hewett (LANL). Discusses nonadiabatic collisionless processes occurring at a spindle cusp that transfer ions and electrons across a separatrix.

Paper I-6: Ion Kinetic Effects on the Tilt Mode in FRCs

Authors: J. L. Schwarzmeier, C. E. Seyler, D. C. Barnes (LANL, Cornell, Univ. of Texas). Employs the Vlasov-fluid dispersion functional to evaluate finite Larmor radius and equilibrium profile effects on the internal tilt mode stability.

Paper I-7: Quasistatic Evolution of Compact Toroids

Authors: A. G. Sgro, R. L. Spencer, C. Lilliequist (LANL). Simulates post-formation resistive-timescale evolution of compact toroids using a 1-1/2 D transport code with singular geometry handling at the separatrix.

Paper I-8: Multiple Solutions of a Free Boundary FRC Equilibrium Problem in a Metal Cylinder

Authors: Ross L. Spencer, Dennis W. Hewett (LANL). Solves the Grad-Shafranov equation for a step-function current profile in an infinitely long flux-conserving cylinder, finding up to four solutions including elongated racetrack equilibria near a bifurcation point.

Paper I-9: Plasma Transport Modeling of a Field-Reversed Theta Pinch

Authors: Loren C. Steinhauer, Richard D. Milroy, Alan L. Hoffman (Mathematical Sciences Northwest, Inc.). Develops quasi-steady and time-dependent 1-D/2-D models to explain particle and poloidal flux loss rates observed in FRX-B and TRX-1 experiments.

Paper I-10: Particle Transport in Field Reversed Configurations

Authors: M. Tuszewski, R. K. Linford, J. Lipson, A. G. Sgro (LANL). Presents steady-state 1-D particle transport models based on lower-hybrid-drift (LHD) turbulence saturation mechanisms, comparing scaling laws (R^2/rho_i0) with FRX-B experimental data.

Paper II-1: Initial Operation of FRX-C

Authors: W. T. Armstrong et al. (LANL). Reports preliminary operation of the FRX-C large theta-pinch facility (45 cm diameter, 2 m length), demonstrating stable lifetimes of 70-100 microseconds with densities ~ 4 x 10^15 cm^-3.

Paper II-2: Compact Toroid Formation Using Barrier Fields and Controlled Reconnection in the TRX-1 Field Reversed Theta Pinch

Authors: Alan L. Hoffman, W. T. Armstrong (MSNW). Demonstrates triggered reconnection and octopole barrier field techniques in the TRX-1 device to optimize flux trapping efficiency and plasma heating.

Paper II-3: Onset Time of n = 2 Rotational Instability of FRC Plasma

Authors: Y. Nogi et al. (Nihon Univ., Nagoya Univ., Osaka Univ.). Investigates onset times and scaling laws of the n = 2 rotational instability across NUCTE, STP-L, and PIACE experiments in Japan.

Paper II-4: Reconnection Studies in a Low-Compression Theta Pinch

Authors: E. Sevillano, F. L. Ribe, H. Meuth (Univ. of Washington). Studies spontaneous and delayed magnetic field reconnection and plasma confinement in the High Beta Q Machine (HBQM).

Paper III-1: Analytic Model of Radiation-Dominated Decay of a Compact Toroid

Author: Steven P. Auerbach (LLNL). Formulates an analytical model showing that impurity radiation (predominantly oxygen and carbon) explains finite lifetimes, linear current decay, and density insensitivity in coaxial-gun spheromak experiments.

Paper III-2: A Theory of the Relaxation of Finite Beta Toroidal Plasmas

Author: John Brandenburg (LLNL). Generalizes Taylor’s minimum energy relaxation theory by introducing the ‘Laminativity’ invariant to include finite-beta effects in compact tori and reversed-field pinches.

Paper III-3: Compressible MHD Fluctuations

Authors: Eliezer Hameiri, Harvey A. Rose (Courant Institute & LANL). Constructs a nonlinear statistical mechanics model of compressible magnetohydrodynamic fluctuations using discrete lattice-Fourier conservation variables and Gibbs distribution ensembles.

Paper III-4: Current Drive, Heating and Fueling by Compact Torus Injection

Authors: James H. Hammer, Charles W. Hartman (LLNL). Explores injecting magnetized compact toroids into tokamaks and other toroidal devices to supply magnetic helicity for steady-state current drive, heating, and fueling.

Paper III-5: A New Type of Collective Accelerator

Authors: Charles W. Hartman, James H. Hammer (LLNL). Proposes accelerating magnetically confined plasma rings in coaxial electrode structures or magnetic gradients up to 10 MJ kinetic energy for ICF drivers, fusion reactor fueling, and nuclear synthesis.

Paper III-6: MHD Simulation and the Implication in Reactor Concept of Merging Spheromaks

Authors: M. Katsurai, K. Katayama, T. Sato (Univ. of Tokyo & Hiroshima Univ.). Examines merging of two spheromaks via 2-D MHD simulations, observing that toroidal flux is doubled while poloidal flux is conserved, discussing implications for steady-state reactor designs.

Paper III-7: Resistive MHD Stability Calculations of Force-Free Spheromak Configurations

Authors: A. I. Shestakov, N. J. O’Neill (LLNL). Employs the RIPPLE VI linear resistive stability code to analyze n = 1 tilt and shift modes across five prolate-to-oblate spheromak equilibrium configurations.

Paper III-8: Numerical Simulation of a Beam Heated Compact Torus

Authors: D. E. Shumaker, B. McNamara, W. C. Turner (LLNL). Uses the 1-1/2 D transport code FRT to model neutral beam injection (4 MW at 12 keV) into magnetized coaxial gun-formed compact toroids, studying beta limits and thermal transport.

Paper III-9: Numerical Simulation of the Energy Balance in the Proto S-1C Spheromak

Authors: Y. C. Sun, S. C. Jardin, D. Heifetz, M. Yamada, D. E. Post (PPPL). Models spheromak formation and energy loss in Proto S-1C including 2-D resistive MHD, coronal non-equilibrium impurity radiation (C and O), and Monte Carlo neutral charge exchange/ionization.

Paper IV-1: Plasma Impurity Control Studies in CTX

Authors: Cris W. Barnes et al. (LANL). Reports on hydrogen glow discharge cleaning in the CTX coaxial gun spheromak facility, achieving lifetime extension up to 550 microseconds and dramatic reduction in carbon radiation.

Paper IV-2: Metallic Liner, Electrode Material and Stabilization Coil Studies in the PS-1 Experiment

Authors: H. Bruhns et al. (Univ. of Maryland). Evaluates stainless steel liners, elkonite/carbon electrodes, and Figure-8 passive stabilization coils for tilt and shift mode control in the PS-1 spheromak.

Paper IV-3: Properties of Spheromaks Generated by a Magnetized Coaxial Source

Authors: H. W. Hoida et al. (LANL). Details measurements of magnetic configuration lifetimes, snipper coil reconnection, and pyroelectric bolometer radiation power in CTX spheromaks.

Paper IV-4: Spheromak Experiments in Proto S-1C

Authors: A. Janos et al. (PPPL). Describes experimental results from Proto S-1C (R = 12 cm, a = 6-8 cm, I_p = 60 kA) utilizing inductive flux-core formation, analyzing MHD stability and impurity radiation barriers.

Paper IV-5: Creation of a Spheromak by a Conical Theta-Pinch

Authors: K. Kawai, Z. A. Pietrzyk (Univ. of Washington). Demonstrates generation and translation of spheromak plasmoids with embedded toroidal fields generated from a conical theta-pinch discharge into an aluminum flux conserver.

Paper IV-6: RF Heating Plans for CTX

Authors: S. O. Knox, B. L. Wright (LANL). Outlines designs for low-frequency and fast magnetosonic / shear Alfvén wave RF heating systems (0.1-10 MHz) in CTX using equatorial antenna straps.

Paper IV-6 / IV-7 (Cont.): MHD Stability Studies in Proto S-1 A/B & Impurity Control Concepts

Authors: C. Munson et al. (PPPL); R. F. Post, W. C. Turner (LLNL). Investigates experimental tilt stabilization via Figure-8 coils in Proto S-1 A/B and proposes titanium-hydride coated electrodes to desorb pure hydrogen during gun discharge to mitigate impurity influx.

Paper IV-8: Beta II Compact Torus Experiment Plasma Equilibrium and Power Balance

Authors: W. C. Turner et al. (LLNL). Analyzes magnetic helicity efficiency (K_p/K_in ~ 0.5), pyroelectric radiation measurements, and density scaling with gas puffing and discharge cleaning in Beta II.

Paper IV-9: Experiments on CT Plasma Merging in the CTCC-1

Authors: K. Watanabe et al. (Osaka Univ.). Examines successive injection and merging of two CT plasmas in an oblate flux conserver, finding doubled toroidal flux and slow interior field reconnection over 100 microseconds.

Section V & Review Papers: General Concepts & Anomalous Diffusion

Contains presentations on: Traveling Mirror Adiabatic Compressors (P. M. Bellan); Analytic Field-Reversed Mirror Equilibria (J. K. Boyd); Relativistic Electron Beam (REB) ring studies at Nagoya University (M. Hasegawa et al.); Review of Anomalous Diffusion in Toroidal Plasma (N. A. Krall); MeV/GeV Ion Layers for Fusion (J. R. McNally, Jr.); Intense Ion Beam Propagation (S. Robertson et al.); Microsecond Rotating REB Generation (G. Saenz); Prototype Moving-Ring Reactor Design (A. C. Smith, Jr. et al.); and a Comprehensive Review of Japanese Compact Torus Research (K. Watanabe).