Recent Developments of Integrated Data Analysis at ASDEX Upgrade R. - - PowerPoint PPT Presentation

Recent Developments of Integrated Data Analysis at ASDEX Upgrade

• R. Fischer, L. Barrera, A. Burckhart, M.G. Dunne, C.J. Fuchs, L.

Giannone, J. Hobirk, P.J. McCarthy,

• M. Rampp, S.K. Rathgeber, R. Preuss, W. Suttrop, P. Varela,
• M. Willensdorfer, E. Wolfrum, and ASDEX Upgrade Team

Max-Planck-Institut für Plasmaphysik, Garching EURATOM Association

Frascati, Mar 26-28, 2012

7th Workshop on Fusion Data Processing, Validation and Analysis

Multi-diagnostic profile reconstruction

➢ Lithium beam impact excitation spectroscopy ➢ Interferometry measurements (DCN)

➢ Electron cyclotron emission (ECE)

Forward modelling of the electron cyclotron

radiation transport

→ Te at optically thin plasma edge ➢ Thomson scattering (TS)

➢ Reflectometry (REF)

→ ne at plasma edge

➢Equilibrium reconstructions for diagnostics

mapping (LiB)

• 1. ECE forward modelling
• Magnetic fusion: Understanding and control of plasma edge
• Large variations of plasma parameters within a very thin layer
• Reliable electron density, temperature and pressure profiles

with high spatial and temporal resolution

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

→ EC emission depends on density → combination with data from density diagnostics → calculate broadened EC emission and absorption profiles depending on Te and ne → solve radiation transport equation → forward modelling in the framework of Integrated Data Analysis

ECE forward modelling

• S. K. Rathgeber, et al., to be published
• S. K. Rathgeber, PhD thesis

Electron cyclotron intensity

Radiation transport equation: dI s ds = js−sI s

s LOS coordinate I  spectral intensity j emissivity  reabsorption

Emissivity: j m=e

2m 2 c 2

8

20

m

2m−1

m−1!

2 sin  2m−1cos 21

×∫[1−∥cos]−m   ⊥ 2 

2m

f ∥ ,⊥2⊥ d ⊥ d ∥

m  m=meB me 

−2=1− 2=1−∥ 2−⊥ 2

∥, ⊥=v∥, ⊥ c f ∥, ⊥

mth harmonic angle to magn.field

• freq. cold resonance

Maxwell distribution

Absorption

(Kirchhoff's law for thermal equilibrium):

= j I BB I BB= 

2

8

3c 2 k BT e

Black-body intensity

(in Rayleigh-Jeans approximation):

Electron cyclotron emissivity

Emissivity for 2nd harmonic in X-mode =

7/2

∫[1−∥cos]−2X

 exp−[⊥

2 ∥ 2]⊥ 5 d ⊥ d ∥

j 2X=2X jne  2X=1 2 1 8 sin

4cos 2

cos

21cos 2 1

16 sin

4

2nd harmonic in X-mode fraction only jne= e 2X 4

2 ne

0c sin

2cos 21

total emissivity shape function = mec² 2k BT e Shape function can be integrated analytically ...

Electron cyclotron emissivity

= 

3/2

cos

5[exp−1−

−sin

2



 

2

−3−2sin

2



F ]1

 2

Shape function: = mec² 2k BT e =  2X

2

=1−∥cos

2

=1cos

2

1/2=1−∥,1/2cos

2

∥,1/2=cos∓1−sin

2

1cos

2

F  Dawson integral (efficient subroutines and approximations) → fast forward model for the EC radiation transport in the plasma

• S. K. Rathgeber, et al., to be published

IDA: LIB + DCN + ECE(radiation transport)

✔ Efficient ECE radiation

transport forward modeling

✔ High temporal (32 μs) and

spatial (5 mm) resolution of edge temperature profiles

✔ Combination with density

diagnostics (LIB, DCN)

✔ Quantitative reproduction of

EC emission for all frequencies resonant in between the vessel walls

✔ shine-through peak

explained without needing supra-thermal electrons

✔ shine-through peak provides

important information about the pedestal Te gradient

IDA: LIB + DCN + ECE(radiation transport)

✔ Reveals steeper pedestal Te gradients compared to conventional analysis ✔ Pressure profiles and gradients at plasma edge

IDA: LIB + DCN + ECE(radiation transport)

✔ Provides information about diagnostics alignment

➔ Relative shift between ne and Te → minimum in data residues

✔ Sensitivity study:

➔ Profile parameterization with cubic spline (number and position of knots) ➔ Amplitude and alignment of electron density ➔ Reflection on the vessel wall (tungsten) ➔ Antenna pattern ➔ Additional 1st O-mode contribution

• S. K. Rathgeber et al., to be published; PhD thesis

• 2. Reflectometry forward modelling
• Goal: ne profiles, plasma position control (ITER)
• Classical analysis: Abel inversion (O-mode)

→ location of cutoff layer

• Problems:
• Multiple analysis steps (phase of reflected wave → group delay → density)
• error treatment/propagation; profile uncertainties
• density initialization outside first cutoff layer
• unphysical profiles
• IDA
• Forward modelling of measured data for given density profile
• Benefit:
• Additional data (density initialization, complementary at pedestal top)
• Alignment

Reflectometry forward modelling

Time delay of the reflected beam (group delay):  f = 1 2 ∂ ∂ f Phase of reflected beam: =4 f c

∫

rc f  r1

rdr− 2 r= 1− nr nc f  ; nc f = 4

20me f 2

e

2

Refractive index:  f , nr=2 c ∫

rc−r1

2 x

1−nrc−x

2

nc dx Forward model for group delay for a given density profile:

IDA: LIB + DCN + Reflectometry

IDA: LIB+DCN RPF (Abel inv.) IDA: LIB+DCN+RPF

• Only physically reasonable

profiles possible (spline)

• Alignment is ok (< 5 mm)
• Modification of ne at

pedestal top

IDA: LIB + DCN + Reflectometry

• Systematic deviance in REF residue
• Minor changes in LIB residue due to

modification of ne at pedestal top

• SNR(REF) < SNR(LIB)

• 3. IDA and the Magnetic Equilibrium

➢ Combine profile diagnostics LIB, DCN, ECE, TS, REF(new) → ne and Te profile fits to all data at once (IDA shotfile) ➢ Mapping on a common coordinate grid using an existing equilibrium (EQH/EQI/FPP) ➢ Inconsistency: Equilibrium is not evaluated with kinetic profiles from IDA ✗ Position of magnetic axis, separatrix, inner flux surfaces? ✗ DCN: H2-H3 vertical plasma position often seems to be wrong up to ~1cm. ✗ ECE: (r,z) depends on equilibrium ✗ TS: vertical system relies very much on equilibrium ✗ Alignment of TS, ECE, LIB (with separatrix Te) → uncertainties in the equilibrium ??? ➢ Goal: combine data from profile diagnostics with magnetic data for a joint estimation of profiles and the magnetic equilibrium ➢ Needs equilibrium code: ✗ CLISTE very successful, but code too sophisticated to be adapted to the IDA code ✗ New code based on the ideas (success) of CLISTE (P. McCarthy, L. Giannone, P. Martin, K. Lackner, S. Gori) ✗ Extra: Parallel Grad-Shafranov solver (R. Preuss, M. Rampp, K. Hallatschek, L. Giannone)

1) Grid MxN (typically: radially 65 x vertically 128) 2) (a) Garchinger Equilibrium Code (GEC: Lackner et al, 1976) based on cyclic reduction (b) Garchinger Parallel Equilibrium Code (GPEC: Preuss et al, 2012) 3) CLISTE “Fast Mode”: solve Ψ individually for Np+NF basis functions π and Ф (cubic spline (CLISTE), Bernstein polynomials (Giannone), Fourier-Bessel polynom.) for p' and FF' [P.J. Mc Carthy, W. Schneider, P. Martin, "The CLISTE interpretive equilibrium code",

IPP laboratory report 5/85 (1999).]

4) SOL: P' and FF' ≠ 0 5) Linear regression to data (Bpol , Dpsi , Iext , pressure profile, ...)

Grad-Shafranov solver

R ∂

∂ R 1 R ∂ ∂ R ∂² ∂ z²=−2²0R

2 P '0 FF '

Grad-Shafranov equation: Ideal magnetohydrodynamic equilibrium for poloidal flux function Ψ for axisymmetric geometry p ' =∑

h=1 N p

chh FF ' =∑

k=1 N F

d k k    c , d   

IDE: data and residues

Bpol measured Bpol fitted Bpol residue Dpsi measured Dpsi fitted Dpsi residue

#25764

Residues in the order of ~mT

IDE: external currents and residues

Iext measured Iext fitted Iext residue Iext measured and fitted: V1o, V1u, V2o, V2u, V3o, V3u, OH1 = OH3o = OH3u = OH, OH2o = OH + dOH2s, OH2u = OH + dOH2s + dOH2u, Coiu, Coiu, Ipslon, Ipslun

Comparison EQH/IDE: pressure and poloidal current

Net poloidal plasma current (wo external currents)

➢ Center: Pressure constraints reduce Ipol,net ➢ Edge: Opposite direction

Pressure profile and IDA pressure constraints (Ti = Te, Zeff = 1.5, uncertainty 50%)

➢ Center: Pressure gradient → p' ➢ Edge: p and p'

Grad-Shafranov: p' FF'

Comparison EQH/IDE: flux contour and separatrix

EQH IDE

Comparison EQH/IDE: Temperature and density

edge

#25764, 2.0s

core

~5cm ~5mm

IDA(EQH) IDA(IDE)

Summary: IDA at ASDEX Upgrade

✔ Solving the radiation transport equation ✔ Combination with density diagnostics (LIB, DCN) ✔ shine-through peak (no supra-thermal electrons, pedestal Te gradient) ✔ Diagnostic alignment ✔ sensitivity study

➢ ECE forward modelling ➢Reflectometry forward modelling

✔ Group delay for given density profile ✔ error propagation → uncertainty of profiles ✔ redundant information → resolve data inconsistencies ✔ Complementary information → pedestal-top density

➢ IDA and magnetic equilibrium

✔ New equilibrium code with parallel Grad-Shafranov solver ✔ Consistency of profiles and equilibrium ✔ Reduction of ill-posedness ✔ Edge current distributions