36 research outputs found
The DESC Stellarator Code Suite Part III: Quasi-symmetry optimization
The DESC stellarator optimization code takes advantage of advanced numerical
methods to search the full parameter space much faster than conventional tools.
Only a single equilibrium solution is needed at each optimization step thanks
to automatic differentiation, which efficiently provides exact derivative
information. A Gauss-Newton trust-region optimization method uses second-order
derivative information to take large steps in parameter space and converges
rapidly. With just-in-time compilation and GPU portability, high-dimensional
stellarator optimization runs take orders of magnitude less computation time
with DESC compared to other approaches. This paper presents the theory of the
DESC fixed-boundary local optimization algorithm along with demonstrations of
how to easily implement it in the code. Example quasi-symmetry optimizations
are shown and compared to results from conventional tools. Three different
forms of quasi-symmetry objectives are available in DESC, and their relative
advantages are discussed in detail. In the examples presented, the triple
product formulation yields the best optimization results in terms of minimized
computation time and particle transport. This paper concludes with an
explanation of how the modular code suite can be extended to accommodate other
types of optimization problems.Comment: 18 pages, 5 figures, 2 tables, 2 listing
The DESC Stellarator Code Suite Part I: Quick and accurate equilibria computations
3D equilibrium codes are vital for stellarator design and operation, and
high-accuracy equilibria are also necessary for stability studies. This paper
details comparisons of two 3D equilibrium codes, VMEC, which uses a
steepest-descent algorithm to reach a minimum-energy plasma state, and DESC,
which minimizes the MHD force error in real space directly. Accuracy as
measured by final plasma energy and satisfaction of MHD force balance, as well
as other metrics, will be presented for each code, along with the computation
time. It is shown that DESC is able to achieve more accurate solutions,
especially near-axis. DESC's global Fourier-Zernike basis also yields the
solution everywhere in the plasma volume, not just on discrete flux surfaces.
Further, DESC can compute the same accuracy solution as VMEC in an order of
magnitude less time
Optimization of Nonlinear Turbulence in Stellarators
We present new stellarator equilibria that have been optimized for reduced
turbulent transport using nonlinear gyrokinetic simulations within the
optimization loop. The optimization routine involves coupling the
pseudo-spectral GPU-native gyrokinetic code GX with the stellarator equilibrium
and optimization code DESC. Since using GX allows for fast nonlinear
simulations, we directly optimize for reduced nonlinear heat fluxes. To handle
the noisy heat flux traces returned by these simulations, we employ the
simultaneous perturbation stochastic approximation (SPSA) method that only uses
two objective function evaluations for a simple estimate of the gradient. We
show several examples that optimize for both reduced heat fluxes and good
quasisymmetry as a proxy for low neoclassical transport. Finally, we run full
transport simulations using T3D to evaluate the changes in the macroscopic
profiles
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A robust solution for the resistive MHD toroidal Δ′ matrix in near real-time
We introduce a new near real-time solution for the tokamak resistive MHD Δ′ matrix. By extending state transition matrix methods introduced in [Glasser et al., Phys. Plasmas 25(3), 032507 (2017)] and leveraging the asymptotic methods of [A. H. Glasser, Phys. Plasmas 23, 072505 (2016)], we have developed STRIDE—State Transition Rapid Integration with DCON (Asymptotic) Expansions—a code that solves for Δ′ in <500 ms. The resistive MHD stability remains a foremost challenge in successful tokamak operation, and its numerically demanding analysis has received attention for many years. Our code substantially improves upon the speed and robustness of earlier Δ′ calculation methods, affording solutions for previously intractable equilibria and helping enable the real-time control of ideal and resistive MHD tokamak stability. In this paper, we pedagogically review tearing stability analysis and motivate and define Δ′ in the slab, cylindrical, and toroidal geometries. We also benchmark STRIDE against the calculations of [Nishimura et al., Phys. Plasmas 5, 4292–4299 (1998)] and Furth et al. [Phys. Fluids 16, 1054 (1973)] for Δ′ in a cylindrical geometry, and the Δ′ matrix calculations of [A. H. Glasser, Phys. Plasmas 23, 112506 (2016)] in the full toroidal geometry
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Optimization of the snowflake divertor for power and particle exhaust on NSTX–U
In this paper, simple analytical modeling and numerical simulations performed with the multi-fluid edge transport code UEDGE are used to identify optimal snowflake divertor (SFD) configurations for heat flux mitigation and sufficient cryopumping performance on the National Spherical Torus eXperiment Upgrade (NSTX–U). A model is presented that describes the partitioning of sheath-limited SOL power and particle exhaust in the SFD as a result of diffusive transport to multiple activated strike points. The model is validated against UEDGE predictions and used to analyze a database of 70 SFD-minus equilibria. The optimal location for the entrance to a divertor cryopumping system on NSTX–U is computed for enabling sufficient pumping performance with acceptable power loading in a variety of SFD-minus configurations. UEDGE simulations of one promising equilibrium from the database indicate that a significant redistribution of power to the divertor legs occurs as a result of neutral particle removal near one of the SFD-minus strike points in the outboard scrape-off layer. It is concluded that pump placement at the optimal location is advantageous as the large number of compatible equilibria reduces the precision required of real-time SFD configuration control systems and enables acceptable divertor solutions even if UEDGE-predicted power redistribution slightly reduces the achievable pumping performance
Hamilton-Jacobi Modelling of Stellar Dynamics
Abstract One of the physical settings emerging in the galaxy and stellar dynamics is motion of a single star and a stellar cluster about a galaxy center. The potential availability of analytical treatment of this problem stems from the smallness of mass of the star and cluster relative to the galactic mass, giving rise to Hill's restricted three-body problem in the galaxy-cluster-star context. Based on this observation, this paper presents a Hamiltonian approach to modelling stellar motion by the derivation of canonical coordinates for the dynamics of a star relative to a star cluster. First, the Hamiltonian is partitioned into a linear term and a high-order term. The HamiltonJacobi equations are solved for the linear part by separation, and new constants for the relative motions are obtained, called epicyclic orbital elements. The effect of an arbitrary cluster potential is incorporated into the analysis by a variation of parameters procedure. A numerical optimization technique is developed based on the new orbital elements, and quasiperiodic stellar orbits are found