**Carl Sovinec's Research Activities**

Isosurfaces of parallel current density from a NIMROD spheromak simulation.

**Interests**

- computational plasma physics and magnetohydrodynamics (MHD)
- plasma theory
- computational fluid dynamics
- numerical methods for partial differential equations

- Department of Engineering Physics, College of Engineering, Univ. of WI-Madison
- Center for Plasma Theory and Computation (CPTC), Univ. of WI-Madison
- Department of Physics, College of Letters and Science, Univ. of WI-Madison

**Active collaborations outside CPTC**

- NIMROD code development project
- Center for Extended Magnetohydrodynamic Modeling (CEMM)
- Center for Magnetic Self-Organization in Laboratory and Astrophysical Plasmas
- Plasma Science and Innovation Center
- Plasma Theory Group at LLNL

**Personal plasma research history**

- MHD shock dynamics, USAF Phillips Laboratory, 1987-1991
- Reversed-field pinch (RFP) dynamics, Madison Symmetric Torus (MST) group, Univ. of WI, 1991-1995
- NIMROD code development and spheromak dynamics, T-15, LANL, 1996-2001
- RFP, spheromak, and tokamak MHD, NIMROD development, CPTC, Univ. of WI, 2001-present

**Graduate students**

- Kyle Bunkers (Physics)
- Eric Howell (Engineering Physics)
- Jeff Kollasch (Engineering Physics)
- John O'Bryan (Engineering Physics)
- Josh Sauppe (Physics)

**Selected presentations and talks**

- "Numerical Analysis of the NIMROD Formulation," with Alan Glasser, International Sherwood Fusion Theory Conference, Madison, WI, 1997. (poster--pdf)
- "Three-dimensional Resistive MHD Investigation of Spheromak Sustainment," presented at the Centennial Meeting of the American Physical Society, Atlanta, Georgia, 1999. Bulletin of the American Physical Society 44, no. 1, Part I, paper IB21 4, March 1999. (talk--pdf)
- "Nonlinear Fusion Magnetohydrodynamics with Finite Elements," International Sherwood Fusion Theory Conference, Los Angeles, CA, 2000. (poster--pdf)
- "A Comparison of MHD Activity and Nonlinear Dynamics in RFPs and Electrostatically Sustained Spheromaks," presented at Confinement and Stability of Alternative Fusion Concepts, Varenna, Italy, October 2000. (talk--pdf)
- "Toroidal Geometry Effects in the Low Aspect Ratio RFP," International Sherwood Fusion Theory Conference, Santa Fe, NM 2001. (poster--pdf)
- "Simulating Extreme Anisotropy without Mesh Alignment," MHD Working Group, Long Beach, October 28, 2001. (talk--pdf)
- "Simulating RFP and Spheromak Relaxation with Thermal Transport," Innovative Confinement Concepts Workshop, College Park, MD, 2002. (poster--pdf)
- "NIMROD: a Computational Laboratory for Studying Nonlinear Fusion Magnetohydrodynamics," presented at the 44th Annual Meeting of the Division of Plasma Physics of the American Physical Society, Orlando, Florida, 2002. Bulletin of the American Physical Society 47, no. 9, paper GI1 4, November 2002. (talk minus movie--pdf)
- "Use of Nonsymmetric Algebraic Operators in a Semi-implicit MHD Advance," International Sherwood Fusion Theory Conference, Corpus Christi, TX, 2003. (poster--pdf)
- "Spheromak Transients and Energy Transport," Innovative Confinement Concepts Workshop, Madison, WI, 2004. (invited talk--pdf)
- "Spheromak Energy Confinement in Sustained and Transient Conditions," IEEE Intl. Conference on Plasma Science, Baltimore, MD, 2004. (invited talk--pdf) (version given at PPPL NSTX-Theory seminar July 1, 2004--pdf) (associated animation--mpeg)
- "Comparing Transient High-Confinement States in Spheromak and RFP Discharges," presented at the 9th Easter Meeting on Stability and Confinement of Magnetized Plasmas Turin, Italy, March 30-April 1, 2005. (talk--800 Kb pdf)
- "Nonlinear Extended MHD Simulation Using High-Order Finite Elements," Scientific Discovery through Advanced Computing, San Francisco, CA, June 26-30, 2005. ( invited talk--6.8 Mb pdf) version presented to the Math and Computer Science Division of Argonne National Laboratory, July 7, 2005 (talk--2.7 Mb pdf )
- "Implementation and Verification of Two-fluid Modeling in NIMROD," International Sherwood Fusion Theory Conference, Dallas, TX, 2006. (poster--2.3 Mb pdf)
- "Numerical Computation for Two-Fluid Reconnection and Dynamo," Center for Magnetic Self-Organization General Meeting, Chicago, IL, Aug 2-4, 2006. (poster--4.1 Mb pdf)
- "Numerical Results on Two-fluid Reconnection and Relaxation with Guide Field," International Sherwood Fusion Theory Conference, Annapolis, MD, 2007. (poster--4.2 Mb pdf)
- "Simulating Macroscopic Dynamics in Magnetically Confined Plasmas: an overview of the NIMROD project," UW Plasma Seminar, October 29, 2007. (slides--11.4 Mb pdf)
- "Recent Two-Fluid Simulation Results on Internal Kink and Dynamo," UW Plasma Seminar, February 2, 2009. (slides--9.7 Mb pdf)
- "Three-Dimensional Computation of Toroidal Two-Fluid Internal Kink," International Sherwood Fusion Theory Conference, Denver, CO, 2009. (poster--6.7 Mb pdf)
- "Numerical Computation for Low-Frequency Dynamics in Magnetized Plasma," Applied Math and PDE Seminar, Univ. of Wisconsin-Madison Dept. of Mathematics, December 18, 2009. (slides--11 Mb pdf)
- "Some Mechanics of MHD and How it Affects Plasma Simulation," Dept. of Engineering Physics Colloquium, Univ. of Wisconsin-Madison, November 20, 2012. (slides--5.9 Mb pdf)
- "Simulated Flux-Rope Evolution during Non-Inductive Startup in Pegasus," Center for Plasma Theory and Computation Seminar, Univ. of Wisconsin-Madison, October 14, 2013. (slides--6.8 Mb pdf)
- "Verification of Spectral Stabilization and Numerically Modeled External Vacuum in NIMROD," presented at the 55th Annual Meeting of the American Physical Society, Division of Plasmas Physics, Denver, CO, November 11-15, 2013. (poster--4.7 Mb pdf)

**Unpublished notes and reports**

- "1-D Tests of the NIMROD 2-Fluid Algorithm," June, 1996. (pdf)
- "New Results with Line Jacobi Preconditioning," May, 1999. (pdf)
- "Parallel Global Line Jacobi Preconditioning in NIMROD," June, 1999. (pdf)
- "Sound Waves, Thermal Conduction, and the Continuity Equation," August, 2000. (pdf)
- "Kinetic Energy Error in the NIMROD Spheromak Simulations," October, 2000. (pdf)
- "Computations of Temperature Profiles in Spheromak Configurations with Open Field Lines," October, 2000. (pdf)
- "A Tutorial on NIMROD Physics Kernel Code Development," report UW-CPTC 01-3, August, 2001. (pdf)
- "Implementing a Stress Tensor Force in NIMROD," January, 2003. (pdf)
- "SuperLU Implementation and Timings," August, 2003. (talk-pdf)
- "Finite Element Basis Function Continuity Discussion," April, 2004. (talk-pdf)
- Updates on parallel scaling: ("NIMROD Scaling Information for Nonlinear Tokamak Simulations Using SLU," 8/13/04, pdf) ("NIMROD Processor-Layer Scaling on Seaborg," 10/4/04 pdf)
- "Ohmic Current Drive in NIMROD Simulations," October, 2005. (pdf)
- "Axisymmetric Interchange Calculations with NIMROD," report UW-CPTC 07-1, January 9, 2007. (pdf)
- "A Formulation of Fluid Parallel Electron Viscosity for NIMROD," April, 2007. (pdf)
- "Final Report, Center for Extended MHD Modeling Cooperative Agreement," DOE/ER/54668-7 May, 2008. (pdf)
- "Note on Kinetic Alfven Waves," report UW-CPTC 09-2, February 27, 2009. (pdf)
- "Parallel Scaling of the NIMROD Code to 10k Processor Cores," September 8, 2009. (pdf)
- "Using Trigonometric Cardinal Functions in Doubly Periodic Configuraions," NIMROD Team Meeting presentation, April 13, 2013, Santa Fe, New Mexico. (slides--1.3 Mb pdf)

**Journal publications**

- J. H. Degnan, R. E. Peterkin, Jr., G. P. Baca, J. D. Beason, D. E. Bell, M. E. Dearborn, D. Dietz, M. R. Douglas, S. E. Englert, T. J. Englert, K. E. Hackett, J. H. Holmes, T. W. Hussey, G. F. Kiuttu, F. M. Lehr, G. J. Marklin, B. W. Mullins, D. W. Price, N. F. Roderick, E. L. Ruden, C. R. Sovinec, P. J. Turchi, G. Bird, S. K. Coffey, S. W. Seiler, Y. G. Chen, D. Gale, J. D. Graham, M. Scott, and W. Sommars, "Compact Toroid Formation, Compression, and Acceleration," Physics of Fluids B 5, 2938 (1993).
- J. S. Sarff, S. A. Hokin, H. Ji, S. C. Prager, and C. R. Sovinec, "Fluctuation and Transport Reduction in a Reversed Field Pinch by Inductive Poloidal Current Drive," Physical Review Letters 72, 3670 (1994).
- E. Uchimoto, M. Cekic, R. W. Harvey, C. Litwin, S. C. Prager, J. S. Sarff, and C. R. Sovinec, "Lower-Hybrid Poloidal Current Drive for Fluctuation Reduction in a Reversed Field Pinch," Physics of Plasmas 1, 3517 (1994).
- S. Hokin, J. Sarff, C. Sovinec, and E. Uchimoto, "Confinement Improvement with rf Poloidal Current Drive in the Reversed-Field Pinch," Nuclear Fusion 34, 1447 (1994).
- J. S. Sarff, A. F. Almagri, M. Cekic, C.-S. Chaing, D. Craig, D. J. Den Hartog, G. Fiksel, S. A. Hokin, R. W. Harvey, H. Ji, C. Litwin, S. C. Prager, D. Sinitsyn, C. R. Sovinec, J. C. Sprott, and E. Uchimoto, "Transport Reduction by Current Profile Control in the Reversed-Field Pinch," Physics of Plasmas 2, 2440 (1995).
- C. R. Sovinec and S. C. Prager, "Magnetohydrodynamic Simulations of Direct Current Helicity Injection for Current Drive in Tokamaks," Physics of Plasmas 3, 1038 (1996).
- G. Fiksel, R. D. Bengtson, M. Cekic, D. J. Den Hartog, S. C. Prager, P. Pribyl, J. Sarff, C. Sovinec, M. R. Stoneking, R. J. Taylor, P. W. Terry, G. R. Tynan, and A. J. Wootton, "Measurement of Magnetic Fluctuation-induced Heat Transport in Tokamaks and RFP," Plasma Physics and Controlled Fusion 38, A213 (1996).
- J. M. Finn and C. R. Sovinec, "Nonlinear Tearing Modes in the Presence of Resistive Wall and Rotation," Physics of Plasmas 5, 461 (1998).
- R. E. Peterkin, Jr., M. H. Frese, and C. R. Sovinec, "Transport of Magnetic Flux in an Arbitrary Coordinate ALE Code," Journal of Computational Physics 140, 148 (1998).
- A. H. Glasser, C. R. Sovinec, R. A. Nebel, T. A. Gianakon, S. J. Plimpton, M. S. Chu, D. D. Schnack, and the NIMROD Team, "The NIMROD Code: A New Approach to Numerical Plasma Physics," Plasma Physics and Controlled Fusion 41, A747 (1999).
- C. R. Sovinec and S. C. Prager, "Magnetohydrodynamic Effects of Current Profile Control in Reversed-field Pinches," Nuclear Fusion 39, 777 (1999).
- J. M. Finn, C. R. Sovinec, and D. del-Castillo-Negrete, "Chaotic Scattering and Self-organization in Spheromak Sustainment," Physical Review Letters 85, 4538 (2000).
- C. R. Sovinec, J. M. Finn, and D. del-Castillo-Negrete, "Formation and Sustainment of Spheromaks in the Resistive MHD Model," Physics of Plasmas 8, 475 (2001).
- E. D. Held, J. D. Callen, C. C. Hegna, and C. R. Sovinec, "Conductive Electron Heat Flow along Magnetic Field Lines," Physics of Plasmas 8, 1171 (2001).
- F. Ebrahimi, S. C. Prager, and C. R. Sovinec, "Resistive-Ideal Transition of Pressure-Driven Instabilities in Current-Carrying Plasmas beyond the Suydam Criterion," Physics of Plasmas 9, 2470 (2002).
- C. R. Sovinec, T. A. Gianakon, E. D. Held, S. E. Kruger, D. D. Schnack, and the NIMROD Team, "NIMROD: a Computational Laboratory for Studying Nonlinear Fusion Magnetohydrodynamics," Phys. Plasmas 10, 1727(2003).
- R. H. Cohen, H. L. Berk, B. I. Cohen, T. K. Fowler, A. H. Glasser, E. B. Hooper, L. L. LoDestro, E. C. Morse, L. D. Pearlstein, T. D. Rognlien, D. D. Ryutov, C. R. Sovinec, and S. Woodruff, "Theoretical Investigation of Field-Line Quality in a Driven Spheromak," Nuclear Fusion 43, 1220 (2003).
- P. Martin, L. Marrelli, G. Spizzo, P. Franz, P. Piovesan, I. Predebon, T. Bolzonella, S. Cappello, A. Cravotta, D. F. Escande, L. Frassinetti, S .Ortolani, R. Paccagnella, D. Terranova, B. E. Chapman, D. Craig, S. C. Prager, J. S. Sarff, P. Brunsell, J.-A. Malmberg, J. Drake, Y. Yagi, H Koguchi, Y. Hirano, R. B. White, C. Sovinec, C. Xiao, R. A. Nebel, D. D. Schnack, and the RFX, MST, EXTRAP T2R, and TPE-RX teams, "Overview of Quasi Single Helicity Experiments in Reversed Field Pinches," Nuclear Fusion 43, 1855 (2003).
- C. R. Sovinec, A. H. Glasser, T. A. Gianakon, D. C. Barnes, R. A. Nebel, S. E. Kruger, D. D. Schnack, S. J. Plimpton, A. Tarditi, M. Ch u, and the NIMROD Team, "Nonlinear Magnetohydrodynamics Simulation using High-Order Finite Elements," Journal of Computational Physics 195, 355 (2004).
- E. D. Held, J. D. Callen, C. C. Hegna, C. R. Sovinec, T. A. Gianakon, and S. E. Kruger, "Nonlocal Closures for Plasma Fluid Simulations," Physics of Plasmas 11, 2419 (2004).
- C. C. Kim, C. R. Sovinec, S. E. Parker, and the NIMROD Team, "Hybrid Kinetic-MHD Simulations in General Geometry," Computer Physics Communications 164, 448 (2004).
- S. E. Kruger, C. R. Sovinec, D. D. Schnack, and E. D. Held, "Free Boundary Simulations of DIII-D Plasmas with the NIMROD Code," Computer Physics Communications 164, 34 (2004).
- C. R. Sovinec, B. I. Cohen, G. A. Cone, E. B. Hooper, and H. S. McLean, "Numerical Investigation of Transients in the SSPX Spheromak," Physical Review Letters 94, 35003 (2005).
- B. I. Cohen, E. B. Hooper, R. H. Cohen, D. N. Hill, H. S. Mclean, R. D. Wood, S. Woodruff, C. R. Sovinec, and G. A. Cone, "Simulation of Spheromak Evolution and Energy Confinement," Physics of Plasmas 12, 56106, (2005).
- S. E. Kruger, D. D. Schnack, and C. R. Sovinec, "Dynamics of the Major Disruption of a DIII-D Plasma," Physics of Plasmas 12, 56113 (2005).
- E. B. Hooper, T. A. Kopriva, B. I. Cohen, D. N. Hill, H. S. McLean, R. D. Wood, S. Woodruff, and C. R. Sovinec, "Magnetic Reconnection during Flux Conversion in a Driven Spheromak," Physics of Plasmas 12, 92503 (2005).
- D. D. Schnack, D. C. Barnes, C. C. Hegna, E. D. Held, C. C. Kim, S. E. Kruger, A. Y. Pankin, and C. R. Sovinec, "Computational Modeling of Fully Ionized Plasmas Using the Fluid Approximation," Physics of Plasmas 13, 58103 (2006).
- Y.-M. Huang, E. G. Zweibel, and C. R. Sovinec, "m=1 Ideal Internal Kink Modes in a Line-Tied Screw Pinch," Physics of Plasmas 13, 92102 (2006).
- P. Zhu, C. C. Hegna, and C. R. Sovinec, "Nonlinear Growth of a Line-Tied g-Mode near Marginal Stability," Physics of Plasmas 13, 102307 (2006).
- P. Zhu, C. C. Hegna, C. R. Sovinec, A. Bhattacharjee, and K. Germaschewski, "Intermediate Nonlinear Regime of a Line-Tied g-mode," Physics of Plasmas 14, 055903 (2007).
- A. I. D. Macnab, R. D. Milroy, C. C. Kim, and C. R. Sovinec, "Hall Magneto-hydrodynamics Simulations of End-Shorting Induced Rotation in Field-Reversed Configurations," Physics of Plasmas 14, 092503 (2007).
- P. Zhu, C. R. Sovinec, C. C. Hegna, A. Bhattacharjee, K. Germaschewski, "Nonlinear Ballooning Instability in the Near-Earth Magnetotail: Growth, Structure, and Possible Role in Substorms," J. Geophys. Res. 112, A06222 (2007).
- E. B. Hooper, B. I. Cohen, H. S. McLean, R. D. Wood, C. A. Romero-Talamas, and C. R. Sovinec, "NIMROD Resistive Magnetohydrodynamic Simulations of Spheromak Physics," Physics of Plasmas 15, 032502 (2008).
- N. A. Murphy and C. R. Sovinec, "Global Axisymmetric Simulations of Two-fluid Reconnection in an Experimentally Relevant Geometry," Physics of Plasma 15, 042313 (2008).
- J. M. Reynolds, C. R. Sovinec, and S. C. Prager, "Nonlinear Magnetohydrodynamics of Pulsed Parallel Current Drive in Reversed-field Pinches," Physics of Plasmas 15, 062512 (2008).
- P. Zhu, D. D. Schnack, F. Ebrahimi, E. G. Zweibel, M. Suzuki, C. C. Hegna, and C. R. Sovinec, "Absence of Complete Finite-Larmor-Radius Stabilization in Extended MHD," Physical Review Letters 101, 085005 (2008).
- J. A. Breslau, C. R. Sovinec and S. C. Jardin, "An Improved Tokamak Sawtooth Benchmark for 3D Nonlinear MHD," Communications in Computational Physics 4, 647 (2008).
- J.-Y. Ji, E. D. Held, and C. R. Sovinec, "Moment approach to deriving parallel heat flow for general collisionality," Physics of Plasmas 16, 22312 (2009).
- P. Zhu, C. C. Hegna, and C. R. Sovinec, "Exponential Growth of Nonlinear Ballooning Instability," Physical Review Letters 102, 235003 (2009).
- C. S. Carey and C. R. Sovinec, "Rotational Stabilization of Magnetically Collimated Jets," Astrophysical Journal 699, 362 (2009).
- P. Zhu, C. C. Hegna, C. R. Sovinec, A. Bhattacharjee, and K. Germashewski, "Intermediate Nonlinear Regimes of Line-tied g mode and Ballooning Instability, "Nuclear Fusion 49, 095009 (2009).
- T. G. Jenkins, S. E. Kruger, C. C. Hegna, D. D. Schnack, and C. R. Sovinec, "Calculating Electron Cyclotron Current Drive Stabilization of Resistive Tearing Modes in a Nonlinear MHD Model," Physics of Plasmas 17, 12502 (2010).
- B. J. Burke, S. E. Kruger, C. C. Hegna, P. Zhu, P. B. Snyder, C. R. Sovinec, and E. C. Howell, "Edge localized linear ideal magnetohydrodynamic instability studies in an extended-magnetohydrodynamic code," Physics of Plasmas 17, 32103 (2010).
- C. R. Sovinec, J. R. King, and the NIMROD Team, "Analysis of a Mixed Semi-Implicit/Implicit Algorithm for Low-Frequency Two-Fluid Plasma Modeling," Journal of Computational Physics 229, 5803 (2010).
- R. D. Milroy, C. C. Kim, and C. R. Sovinec, "Extended magnetohydrodynamic simulations of field reversed configuration formation and sustainment with rotating magnetic field current drive," Physics of Plasmas 17, 62502 (2010).
- N. A. Murphy, C. R. Sovinec, and P. A. Cassak, "Magnetic Reconnection with Asymmetry in the Outflow Direction," Journal of Geophysical Research 115, A09206 (2010).
- J. R. King, C. R. Sovinec, and V. V. Mirnov, "First-Order Finite-Larmor-Radius Effects on Magnetic Tearing in Pinch Configurations," Physics of Plasmas 18, 042303 (2011).
- R. A. Bayliss, C. R. Sovinec, and A. J. Redd, "Zero-# Modeling of Coaxial Helicity Injection in the HIT-II Spherical Torus," Physics of Plasmas 18, 94502 (2011).
- P. Zhu, C. C. Hegna, and C. R. Sovinec, "Stabilizing Effects of Edge Current Density on Pedestal Instabilities," Physics of Plasmas 19, 032503 (2012).
- J. R. King, C. R. Sovinec, and V. V. Mirnov, "First-Order Finite-Larmor-Radius Modeling of Tearing and Relaxation in a Plasma Pinch," Physics of Plasmas 19, 055905 (2012).
- J. B. O'Bryan, C. R. Sovinec, and T. M Bird, "Simulation of Current-Filament Dynamics and Relaxation in the Pegasus Spherical Tokamak," Physics of Plasmas 19, 080701 (2012).
- M. G. Schlutt, C. C. Hegna, C. R. Sovinec, J. D. Hebert, and S. F. Knowlton, "Numerical Simulation of Current Evolution in the Compact Toroidal Hybrid," Nuclear Fusion 52, 103023 (2012).
- E. B. Hooper, R. H. Bulmer, B. I. Cohen, D. N. Hill, C. T. Holcomb, B. Hudson, H. S. McLean, L. D. Pearlstein, C. A. Romera-Talamás, C. R. Sovinec, B. W. Stallard, R. D. Wood, and S. Woodruff, "Sustained Spheromak Physics Experiment (SSPX): Design and Physics Results," Plasma Physics and Controlled Fusion 54, 113001 (2012).
- P. Zhu, J. Raeder, C. C. Hegna, and C. R. Sovinec, "Nature of axial tail instability and bubble-blob formation in near-Earth plasma sheet," Journal of Geophysical Research: Space Physics 118, 653 (2013).
- M. G. Schlutt, C. C. Hegna, C. R. Sovinec, E. D. Held, and S. E. Kruger, "Self-consistent simulations of nonlinear magnetohydrodynamics and profile evolution in stellarator configurations," Physics of Plasmas 20, 056104 (2013).
- F. Ebrahimi, E. B. Hooper, C. R. Sovinec, and R. Raman, "Magnetic reconnection process in transient coaxial helicity injection," Physics of Plasmas 20, 090702 (2013).
- E. B. Hooper, C. R. Sovinec, R. Raman, F. Ebrahimi, and J. E. Menard, "Resistive MHD simulations of helicity-injected startup plasmas in NSTX," Physics of Plasmas 20, 092510 (2013).
- J. B. O'Bryan and C. R. Sovinec, "Simulated flux-rope evolution during non-inductive startup in Pegasus," Plasma Physics and Controlled Fusion 56, 064005 (2014).
- E. C. Howell and C. R. Sovinec, "Solving the Grad-Shafranov equation with spectral elements," accepted for publication in Computer Physics Communications, 2014.

**Other links**