J. R. KingWith contributions from

E. Howell, S. Kruger & A. Pankin (Tech-X); K. Burrell, X. Chen, A. Garofalo, R. Groebner (General Atomics);

Jim Callen (U. Wisconsin); B. Grierson & S. Haskey (PPPL);U. Shumlak & S. Taheri (U. Washington);

Work supported by the US Department of Energy, Fusion Energy SciencesComputational support from NERSC

Update on QH-mode modeling

NIMROD Team Meeting

Previous results of QH-mode modeling

● Hypothesis: the saturated pert. drives particle and thermal transport to maintain steady state pedestal profiles [Snyder NF 2007]

● How well can MHD modeling characterize the low-n perturbations observed during QH-mode?

● Published nonlinear results: NIMROD code [King NF 57 2017] & JOREK code [Liu NF 2015]

[K. Burrell PoP 2016]

A Pankin

Linear analysis shows near marginal stability with flow

Kinetic efit with best fit to measurement data is analyzed

Without toroidal and poloidal flows linear analysis:Growth rates monotonically increase with mode #

With flows:n<4 are stable Growth rates for othermodes are significantlyreduced

Kinetic efit includes effect of MHD instability transport

Growth rates w/o flows

flows stabilize

Need to control instability driveA Pankin

New kinetic EFIT is generated

In order to have a better control over equilibrium, new kinetic equilibria generated ● Nonlinear relaxation

expected to relax plasma profiles to bring them close to the original profiles

● Density and temperature fits are modified to reduce the pedestal width

The width reduced from ~0.93 of normalized poloidal flux to ~0.96

4.5

3.0

1.5

0.0

0.00 0.25 0.50 0.75 1.00 ρ

4

3

2

1

00.00 0.25 0.50 0.75 1.00 ρ

Linear analysis without flows

ELITE code is used to compute the growth rates w/o flow effects:● Original equilibrium if marginally unstable

● Account for diamagnetic effects brings this equilibrium below the peeling-ballooning boundary

● Growth rates are larger by factor of ~105 in the modified equilibrium

Original Modified

50% Pedestal Width

Comparison of simulations with 50% and 70% of the initial pedestal width

50% Pedestal Width 70% Pedestal WidthLarge-Amplitude Turbulent Low-amplitude Laminar

Does one better match experiment?

Large perturbations relax profiles towards the measured state

50% pedestal width 70% pedestal width

Synthetic diagnostic update

Nonlinear simulation shows large density perturbations: consistent with BES?

JRK: Move to 400 usShow density movie from 145098

50% Pedestal Width

Density at ~440μsec

Comparison of simulations with 70% and 50% of the initial pedestal width

n=1 mode n=1 mode

Final density perturbations differ signifi-cantly depend-ing on initial conditions:~5% for50% width>1% for70% widthComparison with BESmeasurement can beused in order to set correct initial profiles

Density perturbations rotate: Can be detected with synthetic BES

Such rotation has been also observed in broadbandsimulations ● J. King [PoP 2017]● Video: https://www.youtube.com/watch?

v=2X1gyaI_3VMRotation might be better resolved with better aligned BES diagnostics in co-Ip QH discharges that are being considered for this year

J. Beodo [PoP 2004]

BES synthetic diagnostic workflow in NIMROD

BES synthetic diagnostic post-processing is implemented in the NIMROD analysis workflow● Density is evaluated on (R,Z) grid● Synthetic density computed with PSF functions used in experimental

data analysis

● Unperturbed synthetic density <ns>

can be computed by averaging using● Synthetic density values at different time

slices (time averaging)● Synthetic density values at random toroidal

angles ● Cross correlation is computed for

synthetic density fluctuations ns-<n

s>

BES Synthetic is applied to 70% pedestal case:Large slowly rotating coherent structures observed

Transport Update

Core transport based on beam/RF sources and stiff gradients

● King NF/PoP 2017: used annulus for particle/energy source

● Present simulations: no annulus, no source

● Plan: Use large n=0 diffusivities that act on perturbation from the “top” of the pedestal into the core with a heuristic source inside Ψ ~ 0.4:

● Similar for momentum (?) LCFS

Perturbations

Time- andflux-surface-average profiles

Density (m-3)

Prevent this withassumption of stifftransport

King NF/PoP 2017

Thermal conduction and sound-wave mixing probably sufficient in SOL

King et al. NF 2017; King et al. PoP 2017

● Present simulations use uniform parallel viscosity

● This causes parallel sound-wave damping in the SOL and inhibits transport

● Plan to switch to profile dependent parallel viscosity

Separation of fields in perturbed and steady-state leads to implicit sources

● These sources are meant to heuristically represent effects outside the model (e.g. bootstrap current, neoclassical poloidal flow, Er well generation, high-k turbulence, neutral beam and RF sources and hot-particle transport/stresses, the loop voltage)

Separation of fields in perturbed and steady-state leads to implicit sources

Without incompressible flow within a flux-surface, many terms drop out

Grad-Shafranov equilibrium = 0

Small with

Without flow, the model is more reasonable

Without flow…

Grad-Shafranov equilibrium = 0

Small with

But flow is critical to H-mode, and clearly influences the MHD dynamics

Energy-balance also affected by sources

● Derived from the above equations:

● Top line is energy-flow with implicit sources

● Second line is additional effects related to profile changes

– Only n=0 modification survive toroidal average (except a density term) *density diffusion

neglected but canbe added

Where are the “implicit” source large?

Sources largest when gradients are large!

163518 @ 2350 ms

Consider a heuristic density source

n n’

Ψ

Consider note that : it includes contributions from the flux!

Ψ 0

n’’

Ψ

sink

source

How can we do better?

● EASY: Include effects for transport with explicit, not implicit, sources!

– (not easy)

● Split this discussion into three parts: core, pedestal, SOL

● Core:

– Expect dominant particle/energy source in core from neutral beams

– Heuristically stiff transport from high-k turbulence limits gradients

● Pedestal (this is the hard part):

– (1) Need bootstrap current and poloidal flow drives

– (2) Neutrals and impurities

– Is MHD enough otherwise for QH-mode pedestal transport?

● SOL:

– Interaction with neutrals, parallel thermal conduction and sound wave mixing important in SOL

Two approaches for neoclassical effects

● (1) Use Callen-like [UW-CPTC 09-06R] heuristic closures

– Need to add Ion-orbit loss (IOL)

● (2) Use Chapman-Enskog-like closures by solving suitable DKE equation [Ramos PoP 10/11]

– Held/Spencer (USU)

– Effectively full-f DKE eqn: will include ion-orbit loss

– More computationally expensive than (1)

Neutral solutions are possible in DIII-D cases but require careful attention to profiles

Te(wall)=10 eV

● Enhanced diffusion used for stability● Likely required due to temperature “notch” at ped. top● Require an impurity model to eliminate● Poloidal asymmetry near divertor is from Grad-Shafranov

SOL assumption and is not realistic

Initial stateFinal state

Temp. notchdrives “+” flow

Use of an impurity model would enable better match to data

● NIMROD (no impurities):

– p=pi+pe

● Reality:

– p=pi+pe+pz+ph

● Good model if hot-particle fraction is small

● Profile-dependent Zeff excluded by quasineutrality

● Impurity continuity eqn with COM velocity is valid and is a good first step

Need impurity model

Working on low-frequency impurity model

● Formulation excludes light/plasma waves

– Drops displacement current and assumes quasineutrality

● Natural to use differential velocity of impurity with respect to ions

● Motivated by main-ion CER measurements showing different Carbon/Deuterium rotation [e.g. Haskey BO5.00011 APS-DPP 2018]

Additional forces for impurities without same charge-to mass ration as main-ion species

With Carbon6 and Deuterium eqns simplify

● Temperature/density are straight-forward

Summary

● Control of instability drive (profiles) leads to differing QH-mode dynamics

● Validation with BES planned to determine which state best matches experimental observations

● Inconsistent power-flow equations with flow and steady-state sources make the need for a better transport model clear

– Requires a multitude of physics outside of MHD:● neoclassical drift-kinetics ● main-ion neutral interaction ● Impurities● High-k turbulence (important in edge during QH?)

● Drop by my Sherwood poster for more details on the transport part of this talk