Recent Developments of Integrated Data Analysis at ASDEX Upgrade

R. Fischer, A. Bock, S.S. Denk, M. Dunne, J.C. Fuchs, L. Giannone, B. Kurzan, K. Lackner, P.J. McCarthy, A. Mlynek, R. Preuss, M. Rampp,

U. Stroth, M. Weiland, M. Willensdorfer, E. Wolfrum, H.-P. Zehrfeld, and ASDEX Upgrade Team

Max-Planck-Institut für Plasmaphysik, Garching

EURATOM Association

Nice, France, Jun 01-03, 2015

9th Workshop on Fusion Data Processing, Validation and Analysis(1st IAEA Technical Meeting)

IDA at ASDEX Upgrade

➢Lithium beam impact excitation spectroscopy (LIB)

➢Interferometry measurements (DCN)

➢Electron cyclotron emission (ECE)

➢ Thomson scattering (TS)

➢ Reflectometry (REF)

➢ Beam emission spectroscopy (BES)

(1) multi-diagnostic profile reconstruction: ne , Te

(2) Equilibrium reconstructions for diagnostics mapping: New and flexible equilibrium code IDE

R. Fischer et al., Integrated data analysis of profile diagnostics at ASDEX Upgrade, Fusion Sci. Technol., 58, 675-684 (2010)

➢Garching Parallel Equilibrium Code (GPEC)

➢Pressure profiles (electron, ion, and fast ions)➢ iso-flux constraints from Te(ECE) measurements

➢toroidal plasma flow

➢current diffusion + Kadomtsev reconnection

IDA: LIB + DCN + ECE: New LIB Optics

➔ additional midplane LIB optics :✔ large signal-to-noise ratio ✔ density profiles consistent

➔ turbulence studies (200 kHz data sampling)

old LOSnew

data, fit, residues

M. Willensdorfer

IDA: LIB + DCN + ECE: New central DCN channel

H-1

H-2

H-3

H-4

H-0

H-5

A. Mlynek

Shift of one DCN channel (H-0) closer to the center→ smaller uncertainty in center→ core density variations of 10% significantly observable

Bi-notch filter on H-0 signal (mirror vibrations at 123 ± 18 Hz and 280 ± 40

Hz):→ large spurious oscillations in central density suppressed

IDA: New central DCN channel → sawteeth in density

without H-0

Sawtooth crashes clearly seen in core density

with H-0

Soft X-ray core channel

IDA: LIB + DCN + ECE: radiation transport

• ECE assumptions: local emission and black-body radiation (optically thick plasma)• Optically thin plasma (edge and core)

→ EC emission depends on Te and ne

→ combination with data from density diagnostics is mandatory → calculate broadened EC emission and absorption

profiles by solving the radiation transport equation

→ electron cyclotron forward model (ECFM) in the framework of Integrated Data Analysis (S.K. Rathgeber et al., PPCF 55 (2013) 025004; S. Denk, to be published)

dI ω(s)ds

= jω( s ;ne ,T e)−αω(s ;ne ,T e) I ω( s)

s LOS coordinateI ω spectral intensityjω emissivityαω reabsorption

ECE: Core shine-through

ECE core hfs-lfs loop if small optical depth in core (small ne) and large core T

e-gradient:

→ extended microwave emission region

→ high-field side: Trad

< Te due to shine-through of smaller (outer) temperatures

→ low-field side: Trad

> Te due to shine-through of larger (inner) temperatures

[“Non-thermal electron distributions measured with ECE”, S. Denk, Master thesis, 2014]

fieldside

high low

The Magnetic Equilibrium

➢Tokamak equilibrium (Grad-Shafranov equation)

➢ Various codes: EFIT, CLISTE, JANET, IDE, …

➢ External constraints: Magnetic probe and flux loop measurements → ill-posed equilibrium (core)

➢ Internal constraints: Motional Stark effect (MSE, iMSE) → frequently cumbersome to be calibrated

➢ Additional inner constraints:

✗ Pressure profile (electrons, ions, fast particles)

✗ Edge pressure profiles (thermal electrons + ions) → reconstruct edge current distribution

✗ Core pressure profiles (+ fast particles from TRANSP)

✗ Faraday rotation, divertor tile currents, q, q0, MSE, loop voltage, …

✗ Geometric information about the shape of magnetic surfaces (iso-flux)

from multiple measurements of Te on the same flux surface, but

✔ ECE Te needs proper forward modeling

✗ Extension: Equilibrium with rotational plasma flows

➢ Extension of equilibrium equation:

✗ toroidal flows

✗ current diffusion

(R ∂∂ R

1R

∂∂ R

+∂ ²∂ z ² )Ψ=−(2π) ²μ0R

2P '+μ0FF '

Pressure: Edge constraint

Kinetic profile constraints

pe = n

e*T

e {IDA}, p

i = f(n

e, Z

eff, T

i ) {CEZ, IDZ}, p

fast {TRANSP} → p = p

e + p

i + p

fast

→ Improves definition of edge pressure and current density profiles

→ resolves full ELM cycle

M. Dunne

Core pressure constraint → current, q0

Sawtooth with pressure degradation in core

with subsequent recovery within ~5-10 ms:

→ core current degradation

→ increase of q0

IDE

IDE

IDE

IDE

Core Thomson scattering alignment

EQH: magn. data

IDE: magn. + pressure

2.6 cm

TS16

Profile alignment:

Radial inward shift of

edge channels of core TS

in the order of 3 cm

necessary (B. Kurzan)

TS15

2.4 cm

→ can be explained (partly) by the equilibrium

separatrix

➢ rigid rotation on flux surface → angular velocity Ω(Ψ) = vT/R

➢ centrifugal force → re-distribution of particles on flux surface →

➢ Mach number and velocity of sound →

➢ T(Ψ), ps(Ψ) and M

t(Ψ) are assumed to be flux surface quantities, p is not

➢ Grad-Shafranov equation with centrifugal pressure term:

➢ included in IDE equilibrium code

➢ validated with DIVA-Flow code (H.-P. Zehrfeld; L. Hauertmann, Bachelor work)

Tokamak equilibrium with toroidal flow

=−(2π) ²μ0 R2(∂ p s∂Ψ

+ps2R ²

Ra2

∂M t2

∂Ψ )exp (M t2R ²

2 Ra2 )−μ0F

∂F∂Ψ

p= p sexp (M t2R ²

2 Ra2 )

(R ∂∂ R

1R

∂∂ R

+∂ ²∂ z ² )Ψ=−(2π)²μ0R

2 p '−μ0FF '

p= p sexp (mR2Ω2

2 kT )

M t=RaR

vtc s

cs2=kTm

Problem: ECE core loop → (shine through or) position magnetic axis wrong?

→ iso-flux measurements (ECE Te)

→ but, is the Grad-Shafranov equation correct?

What about plasma flow?

Equilibrium and toroidal rotation

asymmetry of density on flux surface

CEZ

CEZ

Equilibrium and toroidal rotation

➢ increase of Rin and R

aus

→ might be relevant for alignment of edge diagnostic

measured

➢ increase of Rmag

, minor changes in: zmag

, volume, ellipticity, … → relevant for iso-flux constraints

➢ increase of flux gradient → plasma stability

Mt=0Mt= measuredMt= meas. ✕2

Equilibrium and current diffusion

➢equilibrium typically evaluated without temporal correlation → unphysically large jumps in core current density due to lack of proper measurements

➢include temporal correlation by coupling the equilibrium code with thepoloidal flux diffusion equation:

σ||

∂ψ

∂ t=R0 J

2

μ0ρ∂∂ρ

(G2

J∂ψ∂ρ

)−V '2 πρ

( j bs+ jcd ) (F. Felici et al., NF 51 (2011) 083052; this workshop)

➢use the previous equilibrium Ψ,ti), calculate the current distribution for the next time point, and use this

current distribution as a constraint for the next equilibrium Ψ,ti+1

)➢#31113, counter ECCD for t > 1.5s → current hole → reversed shear

standard equilibrium: equilibrium with current diffusion:

Summary: IDA at ASDEX Upgrade

✔ Lithium beam: new optic✔ interferometry: new core channel

➢ diagnostic improvements → ne

➢ ECE forward modelling → Te

➢ IDA and magnetic equilibrium✔ Consistency of profiles and equilibrium (Thomson scattering)

✔ core and edge pressure profiles (→ q-profile, sawtooth, edge current density, ELM)

✔ rotational flows (→ diagnostic alignment, flux surface geometry, iso-flux constraints, plasma stability)

✔ current diffusion (+ Kadomtsev reconnection model for sawtooth)

✔ solving the radiation transport equation

✔ needs ne: combination with density diagnostics (LIB, DCN)

✔ edge and core shine-through