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QO/QP stellarator optimization methods and unique physics properties

Don Spong (ORNL)

Simons Greifswald Stellarator Retreat

July 8, 2022

ORNL is managed by UT-Battelle, LLC for the US Department of Energy

Work supported by U.S. Department of Energy, Office of Science

under DE-FC02-04ER54698, DE-AC52-07NA27344, DE-FG02-07ER54917,

DE-SC00-16268, and DE-AC05-00OR22725

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Some stellarator projects I’ve been involved with

ATF (Advanced toroidal facility)

ORNL stellarator from mid 1980’s to mid 1990’s
Similar to LHD, but 12 field periods and R₀ ~ 2m

SMARTH – (Small Aspect Ratio Toroidal Hybrid)

First attempt at a compact follow-on to ATF
But poor confinement

QOS (Quasi Omnigenous Stellarator)

First application of STELLOPT
Tried to improve over SMARTH confinement by using J, B_min, B_max, etc. optimization targets

QPS (Quasi Poloidal Stellarator)

Low aspect ratio: A = 2.7
Coil engineering R&D project indicated costs would be a challenge
Project stopped in 2007

ATF coils

QPS coil structure

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Post QPS – exploration of extended racetrack (aka “paper clip” configurations

D. A. Spong, J. Harris, Plasma and Fusion Research, Volume 5, S2039 (2010)

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Quasi-omnigeneous stellarator design

Several optimization targets were used:

B_min, B_max contour alignment with flux surfaces
J* alignment with flux surfaces over a range of 𝜺/𝝁 values
Worked best for one well in |B| per field period

D. A. Spong, et al., Phys. Plasmas 5, 1752 (1998)

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QP-symmetry features: neoclassical flows are dominantly poloidal – shearing from neoclassical drives can be comparable to ITG growth rates (PENTA transport model, 2004)

D. Spong, “Generation and damping of neoclassical plasma flows in stellarators,” Phys. Plasmas 12, 056114 (2005)

Net flow velocities within a flux surface

(ExB + Pfirsch-Schlüter + diamagnetic)

Ambipolar electric field

for different heating scenarios

Near the edge flow shearing

can exceed ITG growth rate

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QP-symmetry features: access to second stability regime for ballooning modes – high 𝜷 operation

A. S. Ware, et al., ”Second ballooning stability in high-𝜷

compact stellarators”, Phys. Plasmas 11, 2453 (2004)

QPS

NCSX

HSX

stable

unstable

QPS ballooning stability growth rates – shows

access to 2^nd stability for 𝜷 between 5 and 6%

Other results showed full 2^nd stability access over narrow range of i’ - S. R. Hudson et al 2004 Plasma Phys. Control. Fusion 46 869

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Micro-instability properties of QP systems

ITG analysis of Rewoldt indicated stability threshold for QPS
Trapped particles in QP systems can be localized in straight (low curvature)sections => mitigate drive for trapped particle instabilites
Possibility for maximum J configurations

G. Rewoldt, et al., Phys. Plasmas 12, 102512 (2005)

QPS stability threshold

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QP systems allow suppression of bootstrap current and Pfirsch-Schlüter currents

<β> = 0.01 0.02 0.05

QPS

4 field

period QP/QI configuration

Bootstrap current levels

relative to tokamak

Shafranov shift variation with 𝜷

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Some other potential features of QP/QI systems

Exact QP symmetry would make P_𝜽 a constant of the motion => deviation from flux surfaces ≃ O(gyroradius) => classical rather than neoclassical transport

Magnetic geometry could be optimized for magnetic beach ICRF heating => attractive because ions are directly heated (more efficient for fusion than other methods that must heat electrons first)

Unique divertor designs possible

Bundle divertors instead of X-point or island divertors
Compatible with QP-symmetry, but not QH or QA
Could possibly spread the heat out over a larger area

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Other comments

Near axis analysis useful for intuition and starting point, but

Ideally it would be best to have good symmetry further out in radius and not so good symmetry near the axis (e.g., spread out alphas in reactor)
Finite beta and nonlinear equilibrium couplings not taken into account in near axis analysis – these can be important further out for suppressing undesireable modes

For QP systems may need to generalize quasi-symmetry to consider optimial phase space distributions

For example, make corner regions higher magnetic field than side regions
To keep trapped particles localized to side regions where QP symmetry is higher and only allow passing particles to pass through corner regions

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