LA-8944-C Conference UC-20g Issued: January 1962 DCf2 O0Gf57 Proceedings of the Reversed-Field Pinch Theory Workshop Held at Los Alamos National Laboratory April 29— May 2, 1980 Compiled by H. Ralph Lewis NOTICE PORTIONS Or THIS PEP0BT ABE ILLBMMJE. It h»s been renrodwcel fnm the fcetf awIlrtH capy to permit the liTMiwI ptiriMs «•*• ability. -•'•£ SaCli^PTF TS Los Alamos National Laboratory Los Alamos, New Mexico 87545 ATTENDEES NAME INSTITUTION Thomas Armstrong Los Alamos National Laboratory Stefano Atzenl University of Rome Don Baker Los Alamos National Laboratory Daniel Barnes Los Alamos National Laboratory Herb Berk Lawrence Livermore National Laboratory M- K. Bevlr Culham Laboratory Amltava Bhattacharjee Princeton University A. Bondeaon University of Maryland Allan Boozer Princeton Plasma Physics Laboratory Lou Burkhardt Los Alamos National Laboratory Nelson Byrne Science Applications Inc. Edward Caramana Los Alamos National Laboratory P. G. Carol an Culham Laboratory Morrell Chance Princeton University Chla Lul Chang University of Maryland Richard Christian Purdue University Chang Chu General Atomic Company John Chu Columbia University Ming S. Chu General Atomic Company J. P. Christiansen Culham Laboratory William Condit Lawrence Livermore National Laboratory J. W. Connor Princeton University iv RostoB Dagazlan Los Alaaos National Laboratory Joseph DIHarco LOB Alamos National Laboratory Jacques Denavlt Northwestern University Harry Drelcer Los Alamos National Laboratory Richard Gerwin Los Alamos National Laboratory C* G. Glablett Culhata Laboratory Nuvel T. Gladd University of Maryland George C. Goldenbaum University of Maryland Harold Grad New York University Ray Grimm Princeton University Albert Haberstich Los Alamos National Laboratory Randy L. Hagenson Los Alamos National Laboratory Selshl Hamasaki Jaycor Dennis Hewett Los Alamos National Laboratory R. B. Howe11 Los Alamos National Laboratory Abram R. Jacobson Los Alamos National Laboratory Tom Jarboe Los Alamos National Laboratory John L. Johnson Princeton University Abe Kadlsh Science Applications, Inc. Ichiro Kawakami Nihon University Robert A. Krakowskl Los Alamos National Laboratory H. Ralph Lewis Los Alamos National Laboratory Carl Lllllequist Los Alamos National Laboratory Ralph Llnsker Princeton Plasma Physics Laboratory H. C. Lul Columbia University Wallace M. ManhelMer Naval Research Laboratory George J. Marklln University of Maryland William Matthaeus College of William and Mary Georgb H. Miley University of Illinois Guthrie Miller - Los Alamos National Laboratory J. P. Mondt Los Alamos National Laboratory David C. Montgomery College of William and Mary Ronald Moses Los Alamos National Laboratory Don Monticello Frinceton University Glanfranco Nalesso University of Padua Richard Nebel Los Alamos National Laboratory A. A. Newton Culham Laboratory Michlo Okabayshl Princeton Plasma Physics Laboratory Thomas Oliphant Los Alamos National Laboratory Sergio Ortolan! University of Padua Ken D. Partain General Atomic Company Francis W. Perkins Princeton Plasma Physics Laboratory James A. Phillips Los Alamos National Laboratory Warren Qulnn Los Alamos National Laboratory S. Nell Rasband Brigham Young University Allan H. Relman Cornell University Keith Roberts Culham Laboratory Harvey Rose Los Alamos National Laboratory Michael G. Rusbridge UMIST (Manchester, UK) Michael J. Schaffer General Atomic Company Theo J. Schep FOM - Jutphaas Dalton Schnack Lawrence Livermore National Laboratory Kurt F. Schoenberg Los Alamos National Laboratory Anthony Sgro Los Alamos National Laboratory vi W. R. Spears Culham Laboratory Ross L. Spencer Los Alamos National Laboratory J. Bryan Taylor Culham Laboratory Keith S. Thomas Los Alamos National Laboratory Alan M* Todd Grumman Aerospace Corporation Leaf Turner Los Alamos National Laboratory William C. Turner Lawrence Livermore National Laboratory Robert C. Watt Los Alamos National Laboratory Michael R. C. Watts Culham Laboratory Paul Webber Los Alamos National Laboratory Tomejlro Yaaagishi General Atomic Company CONTENTS ABSTRACT 1 SESSION 1A - THE RFP AS A REACTOR Chairman: R. A. Krakowski Los Alamos National Laboratory Physics Considerations of the Reversed-Field Pinch Fusion Reactor (R. L. Hagenson and R. A. Krakowski) 2 Recent Culham Reactor Studies With RFP Relevance (W. R. Spears) 8 Ohmic Heating and Ignition Studies (R. Gerwin, R. W. Moses, Jr., R. Spencer, and R. A. Nebel) 13 One Dimensional Burn Computations for RJPR (R. A. Nebel, G. H. Miley, R. W. Moses, and R. L. Hagenson) 19 The Compact Reversed Field Pinch (CRFP) Reactor Concept (George H. Miley and Richard A. Nebel) 24 Ignition and Burn in RFP Reactors (P. G. Carolan) 29 Plasma Power Balance of a Pulsed RFP Reactor (J. P. Christiar.^»n and K. V. Roberts) 34 Alpha-Particle Consideratior.s Relevant to the Reversed-Field Pinch Reactor (RFPR) (Ronald L. Miller) 39 SESSION IB - RESULTS OF RFP EXPERIMENTS Chairman: J. A. Phillips Los Alamos National Laboratory Measurements of Volt-Seconds in ZETA and the Setting Up Phase (A. A. Newton and E. P. Butt) 44 Programming and Self-Reversed Pinches in the ETA-BETA II Experiment (A. Buffa, S. Costa, R. De Angelis, L. Giudicctti, C. W. Gowers, G. F. Nalesso, S. Ortolani, M. Puiatti, P. Scarin, and M. R. C. Watts) 49 Optimization and Properties of Reversed Field Pinches in the ETA-BETA II Experiment (A. Buffa, S. Costa, R. De Angelis, L. Giudicotti, C. W. Gowers, G. F. Nalesso, S. Ortolani, M. Puiatti, P. Scarin, and M. R. C. Watts) .... 53 Plasma Resistance Behavior During the Linear Decay Phase of RFPs in ETA-BETA II (G. F. Nalesso) 60 ix Experimental Status of ZT-40 (A. Haberstich, D. A. Baker, M. D. Bausraan, C. J. Buchenauer, L. C. Burkhardt, G. I. Chandler, J. N. DiMarco, J. N. Downing, C. A. Ekdahl, P. R. Forman, K. B. Freese, R. F. Gribble, R. B. Howell, A. R. Jacobson, F. C. Jahoda, K. A. Klare, E. M. Little, G. Miller, S. Ortolani, J. A. Phillips, A. E. Schofield, K. S. Thomas, R. G. Watt, P. G. Weber, R. W. Wilkins, and Y. Yoshida) 65 Transient Phenomena on ZT-40 (A. R. Jacobson and C. J. Buchenauer) . 70 SESSION 2A - EQUILIBRIUM AND STABILITY Chairman: C. K. Chu Columbia University Progress on RFP Stability Problems Since the Padua Workshop (D. C. Robinson) . , 75 The Kink Tearing Mode in the Reversed Field Pinch (Rostom Y. Dagazian) . 79 Stability Analysis of Plasmas Limited by a Resistive Wall of Finite Thickness (G. F. Nalesso) 86 Dispersion Differential Equation for a Straight Vlasov-Fluid RFP With Small lor. Gyroradius (H. Ralph Lewis) 88 Low-Frequency Microinstabilities in Cylindrically Symmetric Systems with Arbitrary 0 and Strong Magnetic Shear (Ralph Linsker) 93 The Nonlinear Evolution of Resistive Interchange Modes in Reversed Field Pinches (D. D. Schnack and J. Killeen) 97 A Comparison of the m = 0 Resistive Interchange Mode as Simulated by Nonlinear Hybrid and MHD Codes (D. W. Hewett and D. D. Schnack) 102 Electron Temperature Gradient Effect on Resistive-G Mode (C. L. Chang, N. T. Gladd, and C. S. Liu) 107 MHD Equilibrium and Interchange Stability of Helical Configurations With "Pitch Reversal" (M. S. Chu, C. Chu, R. Goforth, F. W. McClain, M. Schaffer, and T. Ohkawa) 113 Dynamical Determination of Ohmic States of a Cylindrical Pinch (D. D. Schnack) , 118 On A Helical Ohmlc State for Reversed Field Pinches (Rostom Y. Dagazian) 123 Magnetic Islands and Stochastic Field Lines in the RFP (Ross L. Spencer) 129 SESSION 2B - RELATED CONCEPTS Chairman: G. C. Goldenbaum University of Maryland Force-Free Equilibria In Cylindrical Geometry (Z. G. An, A. Bondeson, H. H. Chen, Y. C. Lee, C. S. Liu, and E. Ott) 135 Stability of a Force-Free Cylindrical Spheromak (G. J. Marklin and C. S. Liu) 140 Studies of the Formation of Field Reversed Plasma by a Magnetized Co-Axial Plasma Gun (W. C. Turner, E. H. A. Granneman, C. W. Hartman, D. S. Prono, J. Taska, and A. C. Smith, Jr.) 144 Gun-Generated Compact Tori at Los Alamos (T. R. Jarboe, I. Henins, H. H. Hoida, R. K. Linford, J. Marshall, D. A. Platts, and A. R. Sherwood) 149 Two-Dimensional Modeling of the Formation of the S-l Spheromak (S. C. Jardin, H. P. Furth, M. Okabayashi, W. Park, and M. Yamada) 155 The OHTE Plasma Confinement Concept (M. J. Shaffer, M. S. Chu, C. Chu, R. R. Goforth, R. La Haye, T. Ohkawa, and T. Yamagishi) 161 SESSION 3A - RFP STARTUP Chairman: R. W. Moses, Jr. Los Alamos National Laboratory Setting Up Reversed Field Pinches (A. A. Newton and J. W. Johnston) ........ 166 Energy and Flux Loss Considerations for RFP Startup (D. A. Baker, L. W. Mann, T. A. Oliphant, and J. A. Phillips) 171 Relaxation, Flux Consumption and Quasi Steady State Pinches (M. K. Bevir and J. W. Gray) 176 The Edge Region of RFP and Spheromak Plasmas (F. W. Perkins and E. J. Caramana) 181 Startup of the RFP in a Quasi-Adiabatic Mode (E. J. Caramana) 187 ZT-40 Startup Calculations With Various Anomalous Transport Models (R. N. Byrne and C. K. Chu) - 192 Ideal MHD Stable Start-up (R. A. Nebel, R. W. Moses, and G. H. Miley) 196 SESSION 4A - HEATING AND TRANSPORT OF REVERSED-FIELD PINCH DISCHARGES Chairman: Richard S. Christian Purdue University Classical Transport in the Reversed Field Pinch (A. H. Boozer) 201 xi Current Decay and tj; Scaling Laws Applied to RFP Transport Calculations (J. P. Christiansen and K. V. Roberts) 206 Effect from Impurities in RFP Discharges (V. Piotrowicz and J. P. Christiansen) , 209 The Simulation on Formation of RFP Plasmas (H. Matsuda, S. Ido, and I. Kawakami) c... 214 Mean Field Electrodynamics Applied to the Reversed-Field Pinch: Anisotropic Effects (S. N. Rasband) 219 The Role of Impurities in Producing Thermal Instability in the RFP (E. J. Caramana and F. W. Perkins) 2?.4 Numerical Modeling of Plasma Motion in RFP Experiments (T. A. Oliphant) .... 229 The Boundary Problem in RFP Diffusion (R. Christian) 234 SESSION 5A - RELAXATION AND TURBULENCE OF REVERSED-FIELD PINCH DISCHARGE Chairman: D. Montgomery College of William and Mary Relaxation Revisited (J. B. Taylor) 239 Incomplete Relaxation and Finite Beta Plasmas (L.