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Feasibility of Negative Triangularity Equilibria in the SPARC Tokamak

Narin Yüksek, Theodore Golfinopoulos

Abstract

We investigate the feasibility of negative triangularity (NT) plasma configurations in the SPARC tokamak, a compact, high-field device (up to 12.2 T) designed for positive triangularity (PT) operation. Using the FreeGS free-boundary equilibrium solver, we systematically explore the parameter space through 600+ equilibrium calculations spanning triangularity (-0.7-0.7) and elongation (1.0-2.1) while respecting SPARC's coil current limits and first-wall constraints and selecting a reduced-field 8 T operating point. We find that moderate NT double-null plasmas (delta = -0.35, kappa = 1.68) are achievable at 8 T with plasma currents of 2.1 MA. However, NT operation requires 43% plasma volume reduction (from 20.0 to 11.4 m$^3$) compared to the baseline PT design due to vessel walls optimized for PT conformity, and connection lengths are reduced by 40% due to geometric mismatch with the PT-optimized divertor. Central solenoid current requirements decrease by 54% in NT configurations, though specific shaping coils (PF3) require a factor of 5.5 higher currents. All equilibria satisfy fundamental MHD stability criteria with comfortable margins. Thus, while performance is degraded relative to baseline design, these results demonstrate SPARC's potential as a high-field experimental bridge between contemporary NT experiments and proposed NT reactor concepts, capable of testing whether NT's operational advantages (ELM-free operation, favorable impurity transport) persist under reactor-relevant conditions provided by SPARC.

Feasibility of Negative Triangularity Equilibria in the SPARC Tokamak

Abstract

We investigate the feasibility of negative triangularity (NT) plasma configurations in the SPARC tokamak, a compact, high-field device (up to 12.2 T) designed for positive triangularity (PT) operation. Using the FreeGS free-boundary equilibrium solver, we systematically explore the parameter space through 600+ equilibrium calculations spanning triangularity (-0.7-0.7) and elongation (1.0-2.1) while respecting SPARC's coil current limits and first-wall constraints and selecting a reduced-field 8 T operating point. We find that moderate NT double-null plasmas (delta = -0.35, kappa = 1.68) are achievable at 8 T with plasma currents of 2.1 MA. However, NT operation requires 43% plasma volume reduction (from 20.0 to 11.4 m) compared to the baseline PT design due to vessel walls optimized for PT conformity, and connection lengths are reduced by 40% due to geometric mismatch with the PT-optimized divertor. Central solenoid current requirements decrease by 54% in NT configurations, though specific shaping coils (PF3) require a factor of 5.5 higher currents. All equilibria satisfy fundamental MHD stability criteria with comfortable margins. Thus, while performance is degraded relative to baseline design, these results demonstrate SPARC's potential as a high-field experimental bridge between contemporary NT experiments and proposed NT reactor concepts, capable of testing whether NT's operational advantages (ELM-free operation, favorable impurity transport) persist under reactor-relevant conditions provided by SPARC.
Paper Structure (8 sections, 20 equations, 4 figures, 1 table)

This paper contains 8 sections, 20 equations, 4 figures, 1 table.

Table of Contents

  1. Introduction
  2. Methods
  3. Scaling plasma current and pressure
  4. Stability Limits
  5. Results
  6. Discussion
  7. Conclusion
  8. Acknowledgments

Figures (4)

  • Figure 1: FreeGS equilibrium for the nominal 12.2 T SPARC V2 PRD case overlaid with SPARC layout with PF, CS, and divertor coils labeled.
  • Figure 2: FreeGS equilibrium for the NT 8 T case with $\delta=-0.37$ and $\kappa=1.68$.
  • Figure 3: FreeGS equilibrium for the PT 8 T case with $\delta=3.7$ and $\kappa=1.75$.
  • Figure 4: Separatrix for all three cases: the black line corresponds to the PRD case, the brown line corresponds to the 8 T PT case, and the red line corresponds to the 8 T NT case.