Verication of Continuum Kinetics in NIMROD

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1 Verication of Continuum Kinetics in NIMROD CEMM Meeting, New Orleans, LA E. Held 1 J.Y. Ji 1 S. Kruger 2 NIMROD Team 1 Department of Physics Utah State University 2 Tech-X Corp. October 26, 2014

2 Electron, ion and hot particle DKEs in NIMROD Hazeltine's form for the rst-order drift kinetic equation in energy, ε, and magnetic moment, µ, variables: ( ) f + t (v + vd) f + µ B + t e(v + vd) f E ε = C(f ) 1 ξ 2 2ξ Transforming to pitch-angle, ξ = v /v, and normalized speed, s = v/v 0, variables yields f + t (v + vd) [ f 1 ξ 2 2ξ [ ξ 2 b B B + t s 2 [ (1 ξ 2 ) b B B t + ] lnb f ξ s lnt 2 0 f s q s 2 T (v 0 + vd) E + ξ 2 E B lnb B 2 C(f )+ ] f ξ + q s 2 T (v 0 + vd) E+(1+ξ 2 ) E B lnb B 2 ] f s = 0 where [ (1 v D = E B B 2 + T 0s 2 ) ] qb + ξ 2 2 b B + 2ξ 2 µ 0J + (1 ξ 2 )µ 0J + mv 0sξ qb 2 b B. t

3 Continuum Electron and Ion DKE verication Quantitative agreement between NIMROD and NEO for (1) high aspect ratio circular equilibrium, (2) high-beta, DIII-D like equilibrium, and (3) NSTX equilibrium. Consistent bootstrap currents: NIMROD, NEO, DK4D, NCLASS and Sauter. Paper written and soon to be submitted.

4 Equations for NIMROD/NEO Benchmark Solve simplied DKEs: t f 1 + v f 1 (v lnb ) 1 ξ 2 2ξ ξ f 1 C aa C ab = vd f 0 + sv D lnv 0 s f 0 e 2ε 0 s v (E ) A φ 1 s f 0. Using g 1 = f 1 (eφ 1 /T 0 )f 0 and assuming steady-state yields (Belli and Candy, 51 PPCF 2009): v g 1 v lnb 1 ξ 2 2ξ ξ g 1 C aa C ab = vd f 0 + sv D lnv 0 s f 0 e 2ε 0 s v E A s f 0.

5 High-β Equilibrium T on axis 7.5 KeV Z(m) ν i a/v Ti T/T 0 n/n 0 f t ν i a/v Ti R(m) R(m)

6 Bootstrap Currents and Parallel Ion Flows J B = b q b B d vv g 1b, V i B = (B/n) d vv g 1i. 2.0E E+04 <J B>(AT/m 2 ) <u B>(mT/s) 1.0E E+04 NIMROD NEO Sauter NCLASS NIMROD NEO Sauter NCLASS 0.0E R(m) 0.0E R(m)

7 Ion Distribution Functions g 1i shown near outboard midplane: R=2.16, Z=

8 Ion Distribution Functions g 1i shown near outboard midplane: R=2.16, Z= NIMROD g 1i NEO g 1i v /v v /v v /v 0 v /v 0

9 NSTX Benchmark NSTX equilibrium provided by Brendan Lyons (Phys. Plasmas 19, (2012)) Z(m) ν i (a/v Ti ) T/T 0 n/n 0 f t ν i (a/v Ti ) R(m) R(m)

10 Bootstrap Currents and Parallel Ion Flows J B = b q b B d vv g 1b, V i B = (B/n) d vv g 1i. 6.0E+04 <J B>(AT/m 2 ) 3.0E+04 <u B>(mT/s) NIMROD NEO Sauter NCLASS NIMROD NEO Sauter NCLASS DK4D 0.0E R(m) R(m)

11 Verication paper to be submitted

12 Continuum Hot Particle DKE verication Ideal kink benchmark with NIMROD (continuum and δ f -PIC) and M3D (δ f -PIC) done. Verication and validation of NIMROD's continuum and δ f -PIC hot particle algorithms for giant sawteeth (GS) in DIII-D in progress. Verication and validation of NIMROD's continuum hot particle algorithm with GYRO, GTC and TAEFL for reversed shear Alfven eigenmodes (RSAE) in DIII-D in progress.

13 Agreement on Ideal Kink Benchmark Ideal kink benchmark with NIMROD (continuum andδ f -PIC) and M3D (δ f -PIC).

14 Sawteeth stabilized by fast ions in shot #96043 Toroidal precession of high-energy tail stabilizes small sawteeth but results in giant sawteeth (Choi et al. POP, 2007).

15 NIMROD results for GS Continuum andδ f -PIC growth rates for slowing-down f 0 in the same ballpark. Thermal ions and RF-driven high energy tail in beam distribution important for stabilization.

16 High-energy tail Implemented in NIMROD for GS Continuum linear simulations with high-energy tail matching Orbit-RF calculations in progress. Good scaling to 20,000 procs but signicant compute time needed.

17 GS calculations need signicant compute time Step function in June was GS calculations with 20,000 cores. (4 hours used) * (2 for MCF) * (20,000 cores) * (0.6 for regular queue) = 100,000 MPP hours.

18 Verify hot particles in NIMROD on RSAE case From Verication and validation of linear gyrokinetic simulation of Alfven eigenmodes in the DIII-D tokamak, Spong, et al., Phys. Plasmas 19, (2012) Fully self-consistent simulation of energetic particle turbulence and transport in burning plasmas must incorporate three new physics elements: kinetic eects of thermal particles at the thermal ion gyro-radius (micro scale), nonlinear interactions of many meso scale (energetic particle gyro-radius) shear Alfvén waves induced by the kinetic eects at the micro scale, and meso-micro couplings of the micro-turbulence and shear Alfvén wave turbulence. The large dynamical ranges of spatial-temporal processes further require global simulation codes to be ecient in utilizing massively parallel computers. Therefore, the studies of energetic particle physics in the burning plasma regime require a new approach using gyrokinetic turbulence simulation. In this paper, we document progress in the verication and validation of the simulation of Alfvén eigenmodes using the advanced tokamak regime of the DIII-D experiment as a reference case.

19 Beam Ions Drive RSAE's in DIII-D (#142111) RSAE's driven by 4.6 MW of deuterium neutrals injected at kev. Verication uses Maxwellian fast particles although TRANSP-NUBEAM predicts anisotropic distribution.

20 Hot particle Maxwellian used in benchmark E. Held, J.Y. Ji, S. Kruger, NIMROD Team Veri cation of Con

21 Growth and rotation rates change with q min TAE real frequency changes as minimum in q decreases.

22 NIMROD/GYRO Eigenmode Comparisons

23 Future Work on Fast Particle Benchmarks Write fast particle verication paper that includes ideal kink benchmark (NIMROD continuum, NIMROD δ f -PIC, and M3D δ f -PIC) and RSAE results (verication with GTC, GYRO and TAEFL and validation with DIII-D). Collaborate with Tech-X and Wisconsin on Giant Sawteeth problem with continuum hot particles.

24 Theory work related to CEMM Jeong-Young Ji has two papers in preparation: Electron Parallel Closures for Arbitrary Collisionality provides tted kernel functions for evaluating integral electron closures. Electron Heat Transport in a Stochastic Magnetic Field uses the electron parallel heat ow closure to estimate radial heat transport in the presence of magnetic eld line uctuations.

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