Modeling, measurement, and 3-D equilibrium reconstruction of the bootstrap current in the Helically Symmetric Experiment

Abstract

The bootstrap current for three electron cyclotron resonance heated plasma scenarios in a quasihelically symmetric stellarator (the Helically Symmetric Experiment) are analyzed and compared to a neoclassical transport code PENTA. The three conditions correspond to 50 kW input power with a resonance that is off-axis, 50 kW on-axis heating and 100 kW on-axis heating. When the heating location was moved from off-axis to on-axis with 50 kW heating power, the stored energy and the extrapolated steady-state current were both observed to increase. When the on-axis heating power was increased from 50 kW to 100 kW, the stored energy continued to increase while the bootstrap current slightly decreased. This trend is qualitatively in agreement with the calculations which indicate that a large positive electric field for the 100 kW case was driving the current negative in a small region close to the magnetic axis and accounting for the decrease in the total integrated current. This trend in the calculations is only observed to occur when momentum conservation between particle species is included. Without momentum conservation, the calculated bootstrap current increases monotonically. We show that the magnitude of the bootstrap current as calculated by PENTA agrees better with the experiment when momentum conservation between plasma species is included in the calculation. The total current was observed in all cases to flow in a direction to unwind the transform, unlike in a tokamak in which the bootstrap current adds to the transform. The 3-D inductive response of the plasma is simulated to predict the evolution of the current profile during the discharge. The 3-D equilibrium reconstruction code V3FIT is used to reconstruct profiles of the plasma pressure and current constrained by measurements with a set of magnetic diagnostics. The reconstructed profiles are consistent with the measured plasma pressure profile and the simulated current profile when the reconstruction is constrained by the measured data from a diagnostic array that is internal to the vacuum chamber.

Advancing the physics basis for quasi-helically symmetric stellarators

“…2001), smaller Pfrisch–Schlüter (Boozer 1981; Schmitt, Talmadge & Anderson 2013) and bootstrap currents (Boozer & Gardner 1990; Schmitt et al. 2014) and reduced Shafranov shift compared to an equivalent sized tokamak for the same parameters. This is quantified by the ‘effective’ rotational transform , where is the periodicity of the stellarator.…”

“…The MHD properties of quasi-helical stellarators (Nührenberg & Zille 1988) are somewhat distinct from those of other classes of optimized stellarators. The relatively reduced connection length (the distance along the field line between B max and B min ) implies that quasi-helical stellarators have reduced banana widths, reduced orbit drifts for passing particles (Talmadge et al 2001), smaller Pfrisch-Schlüter (Boozer 1981;Schmitt, Talmadge & Anderson 2013) and bootstrap currents (Boozer & Gardner 1990;Schmitt et al 2014) and reduced Shafranov shift compared to an equivalent sized tokamak for the same parameters. This is quantified by the 'effective' rotational transform ι eff = (ι − N), where N is the periodicity of the stellarator.…”

Magnetic diagnostic optimization for plasma equilibrium reconstruction in the HSX stellarator

“…It was also shown in HSX that the bootstrap current is in good agreement with a neoclassical calculation [14]. V3FIT was applied to the RFX-mod to demonstrate that a single helicity state in an RFP can be detected using a combination of magnetic and kinetic diagnostics [15].…”

“…Because the bootstrap current is strongly dependent on the density and temperature gradient, the possible current profiles, given by equation (5) and (6), encompass a range of profiles that are compatible with the density and temperature derivative. To encompass current density profiles that are not unidirectional, for example when local regions of the bootstrap current density are in the opposite direction or in the current evolution phase when shielding currents exist [14], additional free parameters may be required.…”

Advancing the understanding of plasma transport in mid-size stellarators

“…Critical to the proper operation of the island divertor in W7-X is control of the edge rotational transform as the bootstrap current evolves. On HSX 3D equilibrium reconstruction was used to obtain the bootstrap current profile and to demonstrate the critical role of the radial electric field on that profile [10]. Finally, it was demonstrated that optimization of the position of magnetic diagnostics used to perform the reconstruction can reduce the uncertainty in the plasma pressure and current profiles [11].…”