w m doppler reflectometry simulations e d t r a for...

C. Lechte et al., Doppler Reflectometry Simulations, TMIAEA2015 Nice 1

Institute of Interfacial Process Engineering and Plasma Technologyw

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w Doppler Reflectometry Simulations for ASDEX Upgrade

C. Lechte

Institute of Interfacial Process Engineering and Plasma Technology IGVPUniversity of StuttgartPfaffenwaldring 31, 70569 Stuttgart | GermanyPhone +49 711 685 – 62306 | Fax +49 711 685 – 63102

G. D. Conway, T. Görler, C. Tröster, and the ASDEX Upgrade Team

Max-Planck-Institut für PlasmaphysikBoltzmannstr. 2, 85748 Garching | Germany



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Outline

Doppler reflectometry

Role of simulations

Simulation of plasma turbulence

Simulation of Doppler scattering

Properties of the turbulence

Simulation results for the perpendicular wavenumber spectrum

position of the 'knee'

roll-off at large k (spectral index)

Conclusions



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Doppler Reflectometry as a Turbulence Diagnostic

Millimeter waves reflected at cutoff

Backscattering on fluctuations, wavenumber resolved Pol. velocity from Doppler shift: ω

D ≈ -2 k

in v

perp sin(θ)

Scattering condition: kfluct

= -2 Nkin = -2 k

in sin(θ)

already widely used on fusion experiments robust diagnostic for poloidal rotation for fluctuations + transport + correlations, large interest

in simulations

Scan θ, kin S

fluct(k)

Simulate ñe(k) S

fluct(k)

[C. Tröster, PhD Thesis 2008]

vpol

from shift

of fitted peak

Sfluct

from area

of fitted peak



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Overall Goal for Doppler Reflectometry Simulations

Experiment

Plasma turbulenceS(k) spectrum

Doppler wavescattering F(S(k))

Received Dopplerspectrum (exp.)

Simulation

Turbulence code(s)S(k) spectrum

Reflectometry codeF(S(k))

Received Doppler spectrum (sim.)

Information known?

✓

✓

✓✓

Comparison at level of received signal: Synthetic Diagnostic

Explore characteristics of exp. diagnostics F(·)

Validate turbulence codes



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Plasma Turbulence Simulations: The Gyrokinetic Code GENE

GENE is a physically comprehensive Vlasov code [F. Jenko et al., PoP 2000, gene.rzg.mpg.de]

3D in space and 2D in velocity space = 5D

allows for kinetic electrons and electromagnetic fluctuations, collisions, and external EB shear flows

coupled to various MHD codes and transport code TRINITY

supports local (flux tube) and global (full torus), gradient and flux driven simulations

uses magnetic equilibrium and profiles from ASDEX Upgrade 2008 campaign

adapted Ti profile to match heat flux

restrict to flux tube due to computational costs



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The Fullwave Code IPF-FD3D Finite difference time domain code

Maxwell equations and plasma currents(cold plasma)

numeric TX and RX antennas, Gaussian beams, all frequencies (= probed wave numbers) in same run

plasma dynamics

fmicrowave

>>> fturbulence

: “frozen” turbulence

run simulations at time points determined by turbulence time scale

assemble complex, time dependent RXsignal from ~1000 runs

IF turbulence has rotation speed: recoverDoppler spectrum

ELSE: std deviation as measure of fluctuation level [E. Blanco, priv. disc.]

AUG lower outer quadrant



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The Finite Difference Time Domain Method for Plasma Waves

Spatial and time derivatives as centered differences, leapfrogging of E, H

Incorporation of J straightforward if no external B0 field

Conditionally stable for small enough dt, second order accuracy

J colocated with Esame time grid as H

En+1 En = dt * Ėn+1/2 Ex += dt * { Hz(y-dy/2, z) – Hz(y+dy/2, z) }/dy + Jx(y, z) n n+1/2 n+1/2 n+1/2

Ex

Hy

Hz

Hy

Hz Ex

Hy

Hy

dxz Hy

y Hz

y

z

dx = c dt

electron eq. of motion



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Magnetised Plasma: X Mode

New type of DE, dJ/dt ~ J: need J from 1/2dt in future

Jx Jy, Jz: not obvious where to locate J components

3 ways of dealing with time dependence:

Runge-Kutta method to advance J by 1 time step (expensive)

substitute “future” J components with finite difference expressions, solve algebraically for new components ("Crank-Nicolson”)

ignore it: works surprisingly well, but wave fronts are slightly distorted (symplectic)

J location: common grid for all J components or colocation with E components?

n, n+1 n+1/2



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Numerical Dispersion in X Mode

Homogenous plasma with cutoff at 141.2 GHz

Needs sophisticated simultaneous J solver (CN)

And correct location or interpolation of J

relatively low resolution is sufficient (ppc=32)

No method is really bad

along major axes along diagonals



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Numerical Dispersion in X Mode

Homogenous plasma with cutoff at 141.2 GHz

Needs sophisticated simultaneous J solver (CN)

And correct location or interpolation of J

relatively low resolution is sufficient (ppc=32)

No method is really bad

Full spatial interpolation[L. Xu, N. Yuan, IEEE Ant. W. Prop. Lett., 2006]

Same special grid for all J

along major axes along diagonals



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Scaling of Scattered Power with Density Fluctuation Strength

Coherent density fluctuations for the probed wavenumber

Received power scales linearly with density 'power' over several orders of magnitude

Eventually, non-linear saturation appears



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The Typical Turbulence Spectrum: Knee And Power Law

ASDEX Upgrade shot 22009ff

Use same setup in fullwave simulations

L mode

k-4 GENE spectrum features similar

characteristics:

spectral index very close

knee position off by significant amount


knee at k where turbulent drive is occurring

nature of turbulent cascade determines slope



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GENE Turbulence: Transformation to Laboratory Frame

export from field aligned coordinate system to R-z frame

< without poloidal rotation

with poloidal rotation >

possibility to capture Doppler shift in fullwave simulation



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Recovery of Doppler Spectrum From Turbulence

GOAL: same signal as in experiment, i. e. Doppler spectrum, fit peaks

Same GENE run, but transform to lab frame including background EB flow First result promising

Prominent Doppler peak with clear shift But too large time step between turbulence snapshots

Clash between good statistics (dt >> turb ,Lturb/v) and good time resolution (dt << Lturb/v)

Experimental Doppler Spectrum:prominent carrier




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Recovery of Doppler Spectrum From Turbulence

GOAL: same signal as in experiment, i. e. Doppler spectrum, fit peaks

Same GENE run, but transform to lab frame including background EB flow First result promising

Prominent Doppler peak with clear shift But too large time step between turbulence snapshots

Clash between good statistics (dt >> turb ,Lturb/v) and good time resolution (dt << Lturb/v)

Experimental Doppler Spectrum:prominent carrier


For now, treat turbulence snapshots as independent and use variance of signal as measure of fluctuation strength



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Presence of ExB Shear in Turbulence Data

ExB shearing is applied discontinuously in GENE for flux-tube simulations

Visible 'jumps' in turbulence movie

Is this a problem for reconstruction of Doppler spectrum?

looks OK

too early to call

similar phenomenon as GAMs

Implications:

ExB shearing is present in reality

If switched off, input parameters have to be tweaked to get same transport

Doppler/k spectrum will be slightly different

1000

100

10

1-1 -0.5 0 0.5 1

Doppler shift (MHz)



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knee to higher k in saturation

Wavenumber Spectrum from Simulated Doppler Reflectometer

Radial position 0.86, X mode

Turbulence amplitude scan to judge linear-ness of scattering process

Interesting phenomenon: knee position moves with fluctuation strength

Explained by non-linear saturation ofreflected power

spectrum 'squished'against maximum

spectral index too high

GENE knee

Experiment knee



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Wavenumber Spectrum from Simulated Doppler Reflectometer

Radial position 0.86, X mode

Turbulence amplitude scan to judge linear-ness of scattering process

Interesting phenomenon: knee position moves with fluctuation strength

Explained by non-linear saturation ofreflected power

spectrum 'squished'against maximum

spectral index too high

knee to higher k in saturationGENE knee

Experiment knee

factor 10000



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Impact of Using Different Solvers

Reference: colocated currents

Compare to: interpolation of J components to different grids

Result: very different spectral indices

Not clear how the impact can be so large when dispersion relation quite similar

Very surprising, working with ERCC members (E. Blanco) to investigate further



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Impact of Using Different Solvers

Reference: colocated currents

Compare to: interpolation of J components to different grids

Result: very different spectral indices

Not clear how the impact can be so large when dispersion relation quite similar

Very surprising, working with ERCC members (E. Blanco) to investigate further

factor 10000



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Unexpected Properties of Turbulence?

Both with k-4 roll-off

Elongated, sheared radial structures vs. isotropic

Radially localised vs. full range

GENE data in cartesian grid vs. synthetic isotropic turbulence

k (m-1) k (m-1)



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GENE and Synthetic Turbulence

Some difference

However, not certain that absolute fluctuation levels really equal

Synthetic fluctuation level may be too small

Needs full amplitude scan



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k (m-1)

Effect of Limited Radial Extent of Turbulence

Using isotropic synthetic turbulence and O mode

Gaussian envelope around =0.86

Spectral shape stays the same

More scattering volume means just overall increase

Only a problem for extremely small widths

0.02 0.06



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O Mode Doppler Reflectometry: First Results

seems to be 'less non-linear', i.e. potentially easier to analyse

knee closer to real position

spectral index very high

From TORE SUPRAand ASDEX Upgrademeasurements,larger (>7) spectral indexexpected



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Conclusions

Synthetic Doppler reflectometry for turbulence diagnostics on ASDEX Upgrade

Coupling of turbulence code GENE with fullwave code IPF-FD3D

Results

wavenumber spectrum recovered in simulations, but spectral index much steeper

knee position (turbulent drive) shifted to higher k

Explained: non-linear effects of strong fluctuations affect spectral characteristics

Big differences in X mode solvers

O mode seems to be less far in the non-linear regime

Properties of plasma turbulence vs. synthetic isotropic turbulence

Outlook

Investigation of scattering process in different solvers

Further co-moving / lab frame analysis

Application to more recent data

Acknowledgements: bwUniCluster (Ministry of Science, Research and Arts and the Universities of the State of Baden-Württemberg) and HERMIT and HELIOS supercomputers



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Ex grid points

Sources for Gaussian Beams in 2D

add E or H component to grid line

phase and amplitude according to desired wave pattern including tilt and curved phase front (focussing or diverging beam)

higher order Hermite modes

many frequencies simultaneously (ref. freq. 100 GHz, all multiples of 100 MHz need 100 GHz/100 MHz = 1000 cycles to separate at receiver) still 25 fold speed increase

radiates in both directions, need to subtract backpropagating wave from receiver signal



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Why Is The Spectral Index So Large?

Not a problem of resolution

32 vs. 48 sampling points per wave period (~4 times CPU)

w m doppler reflectometry simulations e d t r a for...

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