DESC Stellarator Code Showcase¶
This page details key publications detailing the capabilities of the DESC code. For the full list, see the DESC docs
Core DESC Equilibrium and Optimization Capabilities¶
DESC Equilibrium Solver Fundamental Details — Dudt, D.W. & Kolemen, E. (2020)¶
DESC introduces a pseudo-spectral equilibrium solver that directly minimizes the MHD equilibrium force-balance residual, demonstrating accurate computation of fully three-dimensional MHD equilibria.
Citation: Dudt, D.W. & Kolemen, E. (2020). DESC: A stellarator equilibrium solver. Physics of Plasmas. https://doi.org/10.1063/5.0020743
Equilibrium Solving — Panici, D. et al. (2023)¶
DESC's equilibrium solver compares well against the VMEC equilibrium solver and has been verified to be accurate, particularly near the magnetic axis. DESC's accuracy highlights how important correctly solving equilibria is, and how equilibrium accuracy can affect derived metrics such as Mercier stability.
Basic equilibrium tutorial link
Citation: Panici, D., Conlin, R., Dudt, D.W., Unalmis, K.E., & Kolemen, E. (2023). The DESC Stellarator Code Suite Part I: Quick and accurate equilibria computations. Journal of Plasma Physics. https://doi.org/10.1017/S0022377823000272
Equilibrium Perturbation & Continuation Methods — Conlin, R. et al. (2023)¶
DESC utilizes novel perturbation and continuation methods that efficiently traverse solution branches to produce families of equilibria, leveraging DESC's automatic differentiation to locate nearby equilibria without restarting a full force-balance solve.
Continuation & perturbation tutorial link
Citation: Conlin, R., Dudt, D.W., Panici, D., & Kolemen, E. (2023). The DESC Stellarator Code Suite Part II. Journal of Plasma Physics. https://doi.org/10.1017/S0022377823000399 (pdf: https://arxiv.org/abs/2203.15927)
Stage-One Optimization — Dudt, D.W. et al. (2023)¶
Using DESC's differentiable equilibrium solver together with perturbation methods, DESC can perform efficient stellarator optimization which needs only one equilibrium solve per optimization step, dramatically improving performance over finite-difference approaches.
Stage-one optimization tutorial link
Citation: Dudt, D.W., Conlin, R., Panici, D., & Kolemen, E. (2023). The DESC Stellarator Code Suite Part III. Journal of Plasma Physics. https://doi.org/10.1017/S0022377823000235
Recent advances and applications¶
Omnigenity Optimization — Dudt, D.W. et al. (2024)¶
DESC first introduced a method to optimize for general omnigenity (including toroidal and helical forms in addition to poloidal/QI), using a parametrization based on the Cary–Shasharina mapping. The accompanying paper demonstrated successful optimizations across six omnigenity types (QA, QH, QP and their OT, OH, OP generalizations).
Citation: Dudt, D.W., Goodman, A.G., Conlin, R., Panici, D., & Kolemen, E. (2024). Magnetic Fields with General Omnigenity. Journal of Plasma Physics. https://doi.org/10.1017/S0022377824000151 (pdf: https://arxiv.org/abs/2305.08026)
Turbulence Optimization — Kim, P. et al. (2024)¶
DESC allows for coupling of external codes into the optimization framework, enabling new complex integrated optimizations. The 2024 work from the group, led by Patrick Kim, integrates the nonlinear flux-tube turbulence solver GX into the optimization loop to directly minimize nonlinear turbulent heat flux, demonstrating reductions in turbulent transport and improved ion-temperature profiles in coupled T3D simulations.
Citation: Kim, P. et al. (2024). Optimization of Nonlinear Turbulence in Stellarators. Journal of Plasma Physics. https://doi.org/10.1017/S0022377824000369
Constrained Optimization — Conlin, R. et al. (2024)¶
DESC allows for constrained optimization formulations to be used, which enable intuitive optimization problem setups based on physics and engineering constraints. The first paper from the group on the subject incorporates an augmented Lagrangian constrained optimization method into DESC to handle general nonlinear constraints (e.g., quasisymmetry, curvature, stability), and shows how Lagrange multiplier estimates can help visualize conflicts between objectives.
Constrained optimization tutorial
Citation: Conlin, R., Kim, P., Dudt, D.W., Panici, D., & Kolemen, E. (2024). Stellarator optimization with constraints. Journal of Plasma Physics. https://doi.org/10.1017/S0022377824000655 (pdf: https://arxiv.org/abs/2403.11033)
Differentiable Ballooning Stability — Gaur, R. et al. (2024)¶
This paper applies a differentiable ideal-ballooning stability metric within DESC to optimize for omnigenity, Mercier stability and ideal ballooning stability, reporting improved KBM stability and evidence of a possible second-stability regime at high pressure gradients.
Citation: Gaur, R., Conlin, R., Dickinson, D., Parisi, J.F., Dudt, D.W., Panici, D., Kim, P., Unalmis, K.E., Dorland, W.D., & Kolemen, E. (2024). Omnigenous stellarators with improved ideal and kinetic ballooning stability. https://iopscience.iop.org/article/10.1088/1361-6587/ae1e9e
Efficient and Differentiable Bounce Averaging — Unalmis, K.E. et al. (2024)¶
This work details a spectrally accurate reverse-mode differentiable bounce-averaging operator implemented in DESC that attains fast, accurate bounce-averaged quantities with superior convergence; it can be used in optimization loops to target confinement proxies such as effective ripple. The bounce-averaging framework is generally applicable and may be built upon to implement other bounce-integral-dependent metrics in an efficient and differentiable manner.
Citation: Unalmis, K.E., Gaur, R., Conlin, R., Panici, D., & Kolemen, E. (2024). Spectrally accurate reverse-mode differentiable bounce-averaging operator and its applications. https://arxiv.org/abs/2412.01724
Near-Axis-Constrained Equilibria — Panici, D. et al. (2025)¶
This paper introduces a method for computing global ideal MHD equilibria constrained by near-axis-expansion (NAE) theory, producing equilibria that retain their near-axis characteristics even at low aspect ratios where traditional NAE-to-global conversions fail.
Near-axis-constrained equilibrium tutorial
Citation: D. Panici, E. Rodríguez, R. Conlin, D. Dudt, & E. Kolemen. (2025). Extending near-axis equilibria in DESC. Journal of Plasma Physics. 91(6):E149. https://doi.org/10.1017/S0022377825100901
Deflation Techniques for Stellarator Optimization — Panici, D. et al. (2026)¶
Stellarator optimization problems often involve non-convex objective landscapes with multiple local minima. Exploring these landscapes has traditionally involved using large amounts of initial guesses, or varying systematically the relative weights in an objective function. Deflation techniques offer a more efficient method of exploring the stellarator design space, by discouraging the optimizer away from already-found minima.
Citation: D. Panici, B. Jang, R. Conlin, D. Dudt, Y.G. Elmacioglu & E. Kolemen. (2026). Deflation Techniques for Stellarator Equilibrium and Optimization. arXiv:2602.09957