The toroidal current is consistent with numerical estimates of bootstrap current

1. Measurement of the Pfirsch-Schlüter and Bootstrap Currents in HSX J.C. Schmitt, J.N. Talmadge, P.H. Probert, S.F. Knowlton*, D.T. Anderson HSX Plasma Laboratory, Univ. of Wisconsin – Madison, WI USA *Physics Department, Auburn Univ. – Auburn, AL USA HSX Magnetics and Computational Modeling Operating Parameters & Diagnostics Bootstrap Current Pfirsch-Schlüter Current • Majority of HSX plasmas are in long mean free path (LMFP) regime • Magnetic diffusivity varies across the confinement volume • The Pfirsch-Schlüter current exhibits dipole behavior and rotates with the |B| contours 1/6 FP • B0 = 1 Tesla • 50 kW ECR Heating (1st Harmonic) • 10-chord Thomson Scattering • Te(ρ) and ne(ρ)profiles • Rogowski coil – External • Toroidal current • Low-frequency response • dB/dt triplet array – External • MHD and bootstrap currents • Low-frequency response • Poloidal and toroidal measurements • The Helically Symmetric eXperiment has • Quasi-Helically Symmetric axis: (n,m)=(4,1) • No toroidal curvature • The Pfirsch-Schlüter current • Rotates with toroidal angle • Is reduced by a factor of compared to a conventional stellarator • The bootstrap current • Is in opposite direction than that of a tokamak • Reduces the rotational transform in HSX • VMEC • Calculates free-boundary MHD Equilibrium • Inputs are measured Te & ne profiles and assumed Ti & ni (Zeff≈ 1) • BOOTSJ • Calculates bootstrap current profile from VMEC results. Results may be input back into VMEC as toroidal current profile. • V3FIT • Computes response function for diagnostic coils • Expected magnetic signals are computed from response functions and VMEC output 50 kW ECRH heated plasma JPS 1/6 FP 16 Profiles obtained during resonance heating location scan Poloidal Station # Poloidal Rotation of Null Point in Bθ 1 1/2 FP 16 1/2 FP 2 1 2 Offset in measured Bθ due to toroidal bootstrap current Temporal Evolution of Currents in HSX HSX Vacuum Vessel and Diagnostic Coils VMEC equilibrium, JBS=JBOOTSJ BOOTSJ: 478 A Numerical Model and Measurement • BOOTSJ calculates the bootstrap current; Assumes LMFP regime • BOOTSJ provides an upper limit to the bootstrap current • The toroidal current rises throughout the majority of the shot • Steady state reached only in coldest plasmas • Decaying exponential growth is observed in many cases: projections are based this model • Special thanks to Steve Knowlton and the V3FIT team 1/2 FP 1/6 FP Summary + Future Directions Near-axis ECRH • The toroidal current is consistent with numerical estimates of bootstrap current • The measured magnetic diagnostic signals match predictions of V3FIT • Comparisons with and without toroidal bootstrap current show agreement • Helical nature of Pfirsch-Schlüter current in HSX has been confirmed • Future modeling and measurement • Temporal evolution of toroidal current will be studied – Poloidal flux diffusion • Effects of toroidal current on rotational transform will be studied • Configuration Flexibility: HSX can alter the magnetic spectrum with a set of auxiliary coils • Mirror: The helical symmetry is spoiled by introducing (n,m) = (4,0) component (and harmonics) into the magnetic spectrum, affecting the equilibrium and bootstrap currents • Well/Hill: Rotational transform profile may be raised/lowered, adjusting the location of the = 1 resonant surface Off-axis ECRH • Diagnostic signals and toroidal current evolution • t = 10. ms: MHD equilibrium established, bootstrap current still small • t = 50. ms: ECH turn-off, bootstrap current has grown to 450 A • The diagnostic signals agree well with the V3FIT numerical results • Toroidal current is still evolving – Radial profile information is not yet known • The bootstrap current is the upper limit for the measurements to date • Projected steady state values exceed bootstrap current estimate • Decaying exponential growth is not appropriate for most cases – may overestimate steady state value 49th Annual Meeting of the Division of Plasma Physics, November 12-16, 2007, Orlando, Florida