J. R. KingWith contributions from

E. Howell, S. Kruger & A. Pankin (Tech-X); B. Grierson, S. Haskey (PPPL); R. Groebner (General Atomics);

J. Callen (U. Wisc); U. Schumlak & S. Taheri (U. Washington);

Work supported by the US Department of Energy, DE-SC0018311, DE-SC0018313 and DE-FC02-04ER54698Fusion Energy SciencesComputational support from NERSC

Testing models of ion orbit loss (IOL)

APS-DPP 2019

Our understanding of the interaction between flow and extended-MHD dynamics is limited

● For fast MHD dynamics (e.g. disruption simulation) and transport time scales separated by multiple orders of magnitude

● Long time-scale MHD simulations run on the flow evolution time– NTM, QH, RMP simulations routinely run 1 to 100 of milliseconds

– NTM, QH, RMP dynamics critically depend on flow

● Predictive modeling of MHD dynamics requires models for flow in next generation devices

● Anticipate many relevant physics effects: – e.g. Ion-orbit loss (IOL), neoclassical poloidal flow, fast parallel, neutral

particle, and neutral beam torques

We work to incorporate IOL and other flow drives into extended-MHD simulations with the NIMROD code

Focus on validation with DIII-D shot 164988

Multispecies (D+C6 here) model required for correct collisionality parameters (T

i and Z

*)

Single species (deuterium)

Multi-species (D + C6)

Inclusion of Carbon permits profiles consistent with transport analysis in reconstructed state

All subsequent slides use multispecies

Particle drifts lead to trapping and ion orbit loss

● Particle orbits depend on combination of drifts

● Dominant drift from ExB is from ErBpol and within a flux surface

● The loop voltage (Eφ) provides a small confining cross-field drift

● Cross field drifts (GradB and curvature) combine with mirror force to cause trapped ‘banana’ orbits

● Near the LCFS particles drift to open field lines and cause prompt losses

Consider single particle motion to establish conceptual picture

Particle motionequations:(neglect ExBdrift for now)

Start near LCFS:

Track 4 particles with speed =

Passing Trapped in

Trapped out

Lost

-1.8 -0.77 0.62 1.8

Mapping out phase space establishes a “loss cone”

Trajectories at s=2.63 vTi

(blue line in lower left fig)

Lost

Trapped in

Passing

Trapped out

If particle hits wall: lostOtherwise do 3 outboard midplane crossingsIf u

|| changes sign: trapped

Otherwise: passing

Orbit losses vanish away from the separatrix

Most Ions with s<2.6 vTi NOT lost

Most thermal ions in loss cone lost

Passing

Trapped

Lost

A culinary representation of IOL

Shaing develops closure for IOL

FSA particleloss rate

Without collisions no pitch-angle scattering into loss cone

Losses are limited by collisions and distance from LCFS

S is ‘orbit-squeezing’ factor that decreases IOL outside minimum of E

r well

IOL particle flux acts like a current

IOL leads to viscous forces &co-current torque

Shaing et al., PFB 2 June (1990); Shaing PFB 2 Jan (1992); Shaing PFB 2 Oct (1992)

Collisionality limits IOL in DIII-D shot 164988

IOL rate is slightly limited by orbit squeezing

Orange – no orbit squeezing

IOL torque is not “turned off” by orbit squeezing from the generation of E

r

Need balancing torques

Torque balance establishes flow – need to consider neoclassical poloidal flow damping

Callen UW-CPTC 09-06R

Residual stress leadsto neoclassical offset torquetowards offset velocity

Fast parallel viscous damping

Poloidal flow damping alone does not set the poloidal flow

Neutrals also provide edge torque

Neutral closures

1D neutral test with frozen plasma establishes neutral profiles

wall (neutral source)

Ballistic expansion

Inwardparticle flux

Initial state is local EQ:

Ionization in SOL

Te(wall)=10 eV

(sets wallneutral density) N

n ~ 1016 m-3

core

Time dependence:Red (initial)

toBlue (final)

Freeze plasma profiles similar to 164988 and establish neutral steady state

x (m)x (m)

Local ODE equations become stiff at low T

Time-centered neutral implementation numerically unstable at low Te / low neutral population for this test case

New time-split algorithm extendsNIMROD’s implicit leapfrog:

Computation with low neutral temperatures now tractable

Ballistic expansion

Inwardparticle flux

Initial state is local EQ:

Ionization in SOL & pedestal

Te(wall)=1.25 eV

(sets wallneutral density)N

n ~ 1019 m-3

core

wall (neutral source)

Time dependence:Red (initial)

toBlue (final)

Freeze plasma profiles similar to 164988 and establish neutral steady state

x (m)x (m)

Next steps

● Add neutral beam torque

● Compute 2D neutral state

● Run time-dependent simulation for the steady-state flow in for 164988 with IOL, neoclassical poloidal flow, fast parallel viscous, neutral particle and neutral beam torques

● Compare to flows measured by CER (right)

Summary

● Flow critical to MHD edge-mode dynamics on millisecond time scales

● Moving toward predictive modeling requires a model for the underlying flow

● Ion-orbit loss (IOL) produces a significant edge co-current torque

● This balances neoclassical poloidal flow, fast parallel, neutral particle, and neutral beam torques

● Work underway to include these effects in NIMROD simulations

Extra slides (not included in poster)

Trapping fraction calculations

FSA magnetic field calculation

Nustar and collisionality regimes

Plateau Pfirsch-Schluter(collisional)