Advancing Fusion Science with CGYRO using GPU-Based Leadership - PowerPoint PPT Presentation

Advancing Fusion Science with CGYRO using GPU-Based Leadership Systems by J. Candy 1 , I. Sfiligoi 2 and E. Belli 1 . 1 General Atomics, San Diego, CA 2 San Diego Supercomputer Center, San Diego CA Presented at GTC 2019 San Jose, CA 18-21 March 2019 ID: S9202 1 Candy / GTC / March 2019 / S9202

Sincere thanks to • Chris Holland (UCSD) • Orso Meneghini, Sterling Smith, Ron Waltz, Gary Staebler (GA) • Nathan Howard, Alessandro Marinoni (MIT) • Walter Guttenfelder, Brian Grierson (PPPL) • George Fann (ORNL) • Klaus Hallatschek (IPP, Germany) 2 Candy / GTC / March 2019 / S9202

OUTLINE 1 Who is General Atomics? 3 Candy / GTC / March 2019 / S9202

OUTLINE 1 Who is General Atomics? 2 The case for fusion energy 4 Candy / GTC / March 2019 / S9202

OUTLINE 1 Who is General Atomics? 2 The case for fusion energy 3 Mathematical formulation and GPU-based numerical solution 5 Candy / GTC / March 2019 / S9202

OUTLINE 1 Who is General Atomics? 2 The case for fusion energy 3 Mathematical formulation and GPU-based numerical solution 4 Simulation of turbulent energy loss in a tokamak plasma 6 Candy / GTC / March 2019 / S9202

OUTLINE 1 Who is General Atomics? 2 The case for fusion energy 3 Mathematical formulation and GPU-based numerical solution 4 Simulation of turbulent energy loss in a tokamak plasma 5 GPU performance: development and results 7 Candy / GTC / March 2019 / S9202

Who is General Atomics? 8 Candy / GTC / March 2019 / S9202

Who is General Atomics? 1 General Atomics (GA) is a private contractor in San Diego 9 Candy / GTC / March 2019 / S9202

Who is General Atomics? 1 General Atomics (GA) is a private contractor in San Diego 2 The GA Magnetic Fusion division does DOE-funded research 10 Candy / GTC / March 2019 / S9202

Who is General Atomics? 1 General Atomics (GA) is a private contractor in San Diego 2 The GA Magnetic Fusion division does DOE-funded research 3 Hosts DIII-D National Fusion Facility 11 Candy / GTC / March 2019 / S9202

Founded on July 18, 1955 (photo 1957) The General Atomic Division of General Dynamics 12 Candy / GTC / March 2019 / S9202

Laboratory formally dedicated on June 25th, 1959 John Jay Hopkins Laboratory for Pure and Applied Science 13 Candy / GTC / March 2019 / S9202

Present-day Campus (2019) Retains feel of early architecture 14 Candy / GTC / March 2019 / S9202

Doublet III (1974) 15 Candy / GTC / March 2019 / S9202

DIII-D (Present day) 16 Candy / GTC / March 2019 / S9202

The case for fusion energy 17 Candy / GTC / March 2019 / S9202

Energy Use by Technology and Year energy.mit.edu/news/limiting-global-warming-aggressive-measures-needed 18 Candy / GTC / March 2019 / S9202

Surface Temperature Anomaly energy.mit.edu/news/limiting-global-warming-aggressive-measures-needed 19 Candy / GTC / March 2019 / S9202

Plasma theory in closed fieldline region well-understood 20 Candy / GTC / March 2019 / S9202

Helical field perfectly confines plasma (almost) 21 Candy / GTC / March 2019 / S9202

There is a small amount of radial energy / particle loss • Collisions (1970s): Γ collision • Turbulence (1980s): Γ turbulence • Both exhibit gyroBohm scaling Γ ∼ v ( ρ/ a ) 2 flux a 3 τ = a confinement time Γ ∼ v ρ 2 • a = torus radius • ρ = particle orbit size • v = particle velocity 22 Candy / GTC / March 2019 / S9202

Tokamak physics spans multiple space / timescales Core-edge-SOL (CESOL) region coupling CESOL Core Edge SOL Profile Ψ 23 Candy / GTC / March 2019 / S9202

Tokamak confinement improves with LARGE PLASMA VOLUME 24 Candy / GTC / March 2019 / S9202

ITER Facility (35 nations) under construction in France GOAL: Simulate turbulent plasma in core (magenta) region 25 Candy / GTC / March 2019 / S9202

Mathematical formulation and GPU-based numerical solution 26 Candy / GTC / March 2019 / S9202

Gyrokinetic Theory for Magnetized Plasma The Cooper / Kripke Inversion 27 Candy / GTC / March 2019 / S9202

Gyrokinetic equation for plasma species a a = ( deuterium, carbon, electron ) Typically: ∂ � h a ∂τ − i Ω s X � Ψ a + Ω NL ( � h a − i ( Ω θ + Ω ξ + Ω d ) � H a − i Ω ∗ � h a , � Ψ a ) = C a Symbol definitions h a + z a T e H a = � � � particles Ψ a T a 28 Candy / GTC / March 2019 / S9202

Gyrokinetic equation for plasma species a a = ( deuterium, carbon, electron ) Typically: ∂ � h a ∂τ − i Ω s X � Ψ a + Ω NL ( � h a − i ( Ω θ + Ω ξ + Ω d ) � H a − i Ω ∗ � h a , � Ψ a ) = C a Symbol definitions h a + z a T e H a = � � � particles Ψ a T a � � + v 2 φ − v � J 1 ( γ a ) � δ � c δ � ⊥ δ � fields Ψ a = J 0 ( γ a ) A � B � Ω ca c γ a 29 Candy / GTC / March 2019 / S9202

Electromagnetic GK-Maxwell Equations Coupling to fields is a MAJOR complication! � � � � T e d 3 v f 0 a d 3 v f 0 a � � δ � J 0 ( γ a ) � k 2 ⊥ λ 2 z 2 D + φ = z a H a a T a n e n e a a � v � 2 d 3 v f 0 a � s δ � J 0 ( γ a ) � k 2 ⊥ ρ 2 A � = z a H a β e ,unit n e c s a � m a v 2 2 B � d 3 v f 0 a J 1 ( γ a ) δ � ⊥ � − B � = H a β e ,unit B unit n e T e γ a a 30 Candy / GTC / March 2019 / S9202

Gyrokinetic equation for plasma species a Typically, deuterium, some carbon, and electrons ∂ � h a ∂τ − i Ω s X � Ψ a + Ω NL ( � h a − i ( Ω θ + Ω ξ + Ω d ) � H a − i Ω ∗ � h a , � Ψ a ) = C a E × B flow − i Ω s = − i k θ L a γ E 2 π c s 31 Candy / GTC / March 2019 / S9202

Gyrokinetic equation for plasma species a Typically, deuterium, some carbon, and electrons � � ∂ � h a ∂τ − i Ω s X � Ψ a + Ω NL ( � H a − i Ω ∗ � � h a , � h a − i Ω θ + Ω ξ + Ω d Ψ a ) = C a Streaming − i Ω θ = v � ∂ w s ∂θ 32 Candy / GTC / March 2019 / S9202

Gyrokinetic equation for plasma species a Typically, deuterium, some carbon, and electrons � � ∂ � h a ∂τ − i Ω s X � Ψ a + Ω NL ( � H a − i Ω ∗ � � h a , � h a − i Ω θ + Ω ξ + Ω d Ψ a ) = C a Trapping � 1 − ξ 2 � ∂ ln B − i Ω ξ = − v ta u a ∂ √ w s ∂θ ∂ξ 2 � � √ v � � 1 − ξ 2 � ∂ − 1 ∂λ a ∂ 2 v ta + 2 u a ∂θ w s ∂ u a w s ∂ξ 33 Candy / GTC / March 2019 / S9202

Gyrokinetic equation for plasma species a Typically, deuterium, some carbon, and electrons � � ∂ � h a ∂τ − i Ω s X � Ψ a + Ω NL ( � H a − i Ω ∗ � � h a , � h a − i Ω θ + Ω ξ + Ω d Ψ a ) = C a Drift motion � � � 1 + ξ 2 � ∇ B − i Ω d = av ta a ξ 2 8 π u 2 B + u 2 B 2 ( ∇ p ) e ff · i k ⊥ ρ a b × a c s � R � 2 av � ∂ R ∂θ ∇ ϕ − B t + M a b × B ∇ R · i k ⊥ ρ a c s R 0 J ψ B � � + a − v ta F c + c b × · i k ⊥ ρ a B ∇ Φ ∗ c s T a 34 Candy / GTC / March 2019 / S9202

Gyrokinetic equation for plasma species a Typically, deuterium, some carbon, and electrons ∂ � h a ∂τ − i Ω s X � Ψ a + Ω NL ( � h a − i ( Ω θ + Ω ξ + Ω d ) � H a − i Ω ∗ � h a , � Ψ a ) = C a Gradient drive � a � � � + a a − 3 a RB t u 2 − i Ω ∗ = + γ p v � ik θ ρ s v 2 L na L Ta 2 R 0 B ta � a � z a e R 2 − R ( θ 0 ) 2 �� Φ ∗ − M 2 � a + 2 R 2 L Ta T a 0 R 2 − R ( θ 0 ) 2 � � � aR ( θ 0 ) dR ( θ 0 ) a + M 2 + M a γ p ik θ ρ s a R 2 v ta R 2 dr 0 0 35 Candy / GTC / March 2019 / S9202

Gyrokinetic equation for plasma species a Typically, deuterium, some carbon, and electrons ∂ � h a ∂τ − i Ω s X � Ψ a + Ω NL ( � h a − i ( Ω θ + Ω ξ + Ω d ) � H a − i Ω ∗ � h a , � Ψ a ) = C a Nonlinearity � � � Ψ a ) = ac s � Ω NL ( � h a , � b · k ′ ⊥ × k ′′ Ψ a ( k ′ ⊥ ) � h a ( k ′′ ⊥ ) ⊥ Ω cD k ′ ⊥ + k ′′ ⊥ = k ⊥ 36 Candy / GTC / March 2019 / S9202

Gyrokinetic equation for plasma species a Typically, deuterium, some carbon, and electrons ∂ � h a ∂τ − i Ω s X � Ψ a + Ω NL ( � h a − i ( Ω θ + Ω ξ + Ω d ) � H a − i Ω ∗ � h a , � Ψ a ) = C a Cross-species collision operator � � � H a , � � C L C a = H b ab b � � �� ν � 1 − ξ 2 � ∂ � v 4 ∂ � H b ) = ν D � ∂ ∂ξ + 1 H a ∂ ∂ v + m a H a v 5 � C L ab ( � H a , � ab ab H a v 2 2 ∂ξ ∂ v 2 T b � 1 − ξ 2 �� v 2 � 1 + ξ 2 � � + ν � − � + R mom ( � H b ) + R ene ( � H a k 2 ⊥ ρ 2 ν D H b ) a ab 4 v 2 ab ta 37 Candy / GTC / March 2019 / S9202

Sonic Transport Fluxes These are inputs to an independent TRANSPORT CODE � � � � d 3 v � H ∗ a c 1 a � particle flux Γ a = Ψ a k ⊥ � � � � d 3 v � a c 2 a � H ∗ energy flux Q a = Ψ a k ⊥ � � � � d 3 v � a c 3 a � H ∗ momentum flux Π a = Ψ a k ⊥ 38 Candy / GTC / March 2019 / S9202