Impact of penalized SOL boundary conditions on plasma turbulence

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Submitted on 27 Apr 2020

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Impact of penalized SOL boundary conditions on plasma turbulence

E. Caschera, G. Dif-Pradalier, P Ghendrih, V. Grandgirard, P. Donnel, X. Garbet, C. Gillot, G. Latu, C. Passeron, Y. Sarazin

To cite this version:

E. Caschera, G. Dif-Pradalier, P Ghendrih, V. Grandgirard, P. Donnel, et al.. Impact of penalized SOL boundary conditions on plasma turbulence. 46th European Physical Society Conference on Plasma Physics (EPS 2019), Jul 2019, Milan, Italy. �cea-02555086�

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E. Caschera, G. Dif-Pradalier, P. Ghendrih, V. Grandgirard, P. Donnel, X. Garbet, C. Gillot, G. Latu, C. Passeron, Y. Sarazin

Impact of penalized SOL

boundary conditions

on plasma turbulence

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HPC plasma modeling

| PAGE 2

• Electrostatic ITG

• Global

• 5D full-f

10 millions h/monoproc 104processors

GYrokinetic SEmi LAgrangian

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Penalization for plasma-wall interaction

| PAGE 3 Flux-driven

[Dif-Pradalier PFR 2017]

─ Plasma open system boundary = Heat sink ─ Affect edge-core turbulence

─ Realistic boundary = 2 directions

─ Penalized immersed boundaryas edge fluid codes [Bufferand, JNM, 2013], [Isoardi, JPC,2010]

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Realistic heat sink = poloidal asymmetry

| PAGE 4

o Heat sink = Cold

o Resolution demanding 𝑣_∥, 𝜇 & (𝑟, 𝜃)

o ∥ transport in SOL, interrupts current loop o Adiabatic electrons = NO ⊥ 𝑒− transport

" 2D SOL-like" Poloidal asymmetry −𝜈(𝑓 − 𝑓_{𝑐𝑜𝑙𝑑}) " symmetric SOL" Poloidal symmetry −𝜈(𝑓 − 𝑓 𝑒−𝜆𝑟)

o Restoring towards exponential profiles

[Caschera, 2018]

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The reversed Er builds a

transport barrier

𝑣_𝐷 + + + + +

- -

-

- -

-

- -

_-

-

— ∥ electron dynamic in the SOL → 𝜙 _𝐹𝑆 = Λ𝑇_𝑒 — 𝑐𝑜𝑟𝑒 dominated by ion physics

— Reversed Er self-consistently generated (as experimental measurements)  Edge transport barrier (not steady state simulation)

| PAGE 5

𝐸(𝑟) Reversal

𝐸_𝑟 ∼ 𝛻𝑝𝑖 𝑛_𝑒 𝐸_𝑟 ∼ Λ𝛻𝑇_𝑒 Ra dial elec tric field 𝑬(𝒓) Reversal Initial 𝑡 = 104Ω_𝑖−1 Temperature gradient Ion dynamics ∥ electron dynamics Electric potential

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A strong

𝑬 × 𝑩shear

drives axisymmetric instability

| PAGE 6 • Threshold on ExB shear

• ExB shear = poloidal velocity  Kelvin-Helmholtz

 Axisymmetric simulation, evolving only n=0  « Neoclassical »

 Turbulence activity in neoclassical SOL

Poloidal spectum

(PVG

[D’angelo, PoF, 1965], [Garbet, Fenzi, PoP, 1999])

−0,1 0,1 Potential fluctuations 𝑡 = 4000Ω_𝑖−1 𝑇_𝑒𝛿𝑛_𝑒 𝑒𝑛_𝑒

 Plasma polarization is sufficient to drive turbulence

GAM Small

scales eddies

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SOL is determinant for edge turbulence

| PAGE 7

 SOL impact on turbulent fluctuations [Kadomtsev 65; Garbet NF 94, Hahm PoP 05]

Potential fluctuations

−𝟎, 𝟎𝟐

𝟎, 𝟎𝟐

𝑇_𝑒𝛿𝑛_𝑒 𝑒𝑛_𝑒

o Non-linear dynamics, SOL-evolving o Only with SOL boundary [Holland PoP 11]

Potential fluctuations −𝟎, 𝟎𝟐 𝟎, 𝟎𝟐 𝑇_𝑒𝛿𝑛_𝑒 𝑒𝑛_𝑒 • ITG modes

• Same core turbulence

T urbulenc e int ensity 0.95 0.1 1D SOL 2D Observed dynamics: Shear @ separatrix Turbulence Inward (Edge) Turbulence Outward (SOL)

o Tore Supra profiles, Edge linearly stable o Edge turbulence only with SOL+Limiter

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| PAGE 8

Global = core + edge + SOL

1) Transient barrier by Er reversal

2) Instability even in axisymmetric framework 3) Qualitative 𝛿𝑛/𝑛 experimental trend

Potential fluctuations

−𝟎, 𝟎𝟐

𝟎, 𝟎𝟐

𝑇_𝑒𝛿𝑛_𝑒 𝑒𝑛_𝑒

Limiter boundary leads to new physics in GYSELA simulations

― Many different non-linear phenomena at a time: Kelvin-Helmholtz, ITG, spreading, flows ― Push towards steady-state boundary layer

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| PAGE 9

Back-up slides

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Evidence of edge-core interplay

| PAGE 10

T

urbul

en

ce

drive

𝜌 = 𝑟/𝑎

T

urbul

ence

in

tensity

[Dif-Pradalier, 2017]

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The weak transport barrier

depends on core dynamics

| PAGE 11 Initial 𝐸_𝑟 𝑟 > 𝑎 = 0 𝐸_𝑟 𝑟 > 𝑎 = Λ𝑇_𝑒 T em pera ture gradient Initial

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𝑬

_𝒓

Reversal at separatrix modifies SOL

poloidal symmetries

Vertical drift + + + + + +

-

- -

-

- -

-

−𝜈𝑀(𝑓 − 𝑓_{𝑐𝑜𝑙𝑑})

o Slow dynamic in the limiter

o Strong polarization on SOL flux surfaces o Particles loss at r max

| PAGE 12 SOL Polarization

Inverse rotation btw core/SOL

Reversed 𝐸_𝑟 ↔ v_𝜃

• Vertical drift + SOL flows • HFS density accumulation • Barrier at separatrix

 Polarization of the LIMITER (grounded)

𝑬

_𝒁

< 𝟎

𝝓 > 𝟎

𝜙 = 0

⊙ 𝑩 𝐄

𝒗

_𝑬×𝑩

LIMITER brakes the current loop → SOL poloidal asymmetries

Normalized radius r/a

Initial

De

nsity

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Initial transient in the SOL

| PAGE 13

log (𝑛)

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Axisymmetric simulations:

barrier on the profiles

| PAGE 14

Density

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Recovering

𝜹𝒏/𝒏 behavior

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3D IMAGES

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Self-organized heat sink

| PAGE 17

1. Heat & momentum sink  Cold immersed boundary  Poloidally asymmetric  ∥ transport in SOL

Adiabatic electrons

NO Particle sink,

Constrained ⊥ particle transport NO recombination Open system Confined plasma 𝑃_𝑎𝑑𝑑 _𝑃_{𝑙𝑜𝑠𝑠} 𝑊 Heat source Heat loss

−𝜈(𝑓 − 𝑓

_{𝑐𝑜𝑙𝑑}

)

Poloidal section/ Mask

Self-organized

Heat Source

Heat Sink

 All heat reaching the limiter is removed  SOL = boundary for core

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Different SOL equilibrium

| PAGE 18

Density Temperature Pressure

𝜌 = 𝑟/𝑎 𝜌 = 𝑟/𝑎 𝜌 = 𝑟/𝑎

Initial Initial Initial

Adiabatic electrons