Doppler Reflectometry Simulations for ASDEX Upgrade

Doppler Reflectometry Simulations for ASDEX Upgrade C. Lechte IGVP University of Stuttgart Pfaffenwaldring 31, 70569 Stuttgart Germany Phone +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 Plasmaphysik Boltzmannstr. 2, 85748 Garching Germany 1

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 2

Doppler Reflectometry as a Turbulence Diagnostic Millimeter waves reflected at cutoff Backscattering on fluctuations, wavenumber resolved Pol. velocity from Doppler shift: ωd -2 kin vperp sin(θ) Scattering condition: kfluct = -2 Nkin = -2 kin sin(θ) already widely used on fusion experiments robust diagnostic for poloidal rotation for fluctuations + transport + correlations, large interest in simulations vpol from shift of fitted peak Scan θ, kin Sfluct(k) Simulate ñe(k) Sfluct(k) Sfluct from area of fitted peak [C. Tröster, PhD Thesis 2008] 3

Overall Goal for Doppler Reflectometry Simulations Experiment Information known? Simulation Plasma turbulence S(k) spectrum Turbulence code(s) S(k) spectrum Doppler wave scattering F(S(k)) Reflectometry code F(S(k)) Received Doppler spectrum (sim.) Received Doppler spectrum (exp.) Comparison at level of received signal: Synthetic Diagnostic Explore characteristics of exp. diagnostics F( ) Validate turbulence codes 4

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 E B 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 5

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 AUG lower outer quadrant fmicrowave >>> fturbulence: frozen turbulence run simulations at time points determined by turbulence time scale assemble complex, time dependent RX signal from ~1000 runs IF turbulence has rotation speed: recover Doppler spectrum ELSE: std deviation as measure of fluctuation level [E. Blanco, priv. disc.] 6

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 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 electron eq. of motion Hy dx = c dt z J colocated with E same time grid as H Hy z Hy Hz Ex Hz dx Ex y H z y Hy Hy 7

Magnetised Plasma: X Mode n, n+1 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: n+1/2 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? 8

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 9

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 11

The Typical Turbulence Spectrum: Knee And Power Law L mode [C. Tröster, PhD Thesis 2008] GENE spectrum features similar characteristics: spectral index very close knee position off by significant amount ASDEX Upgrade shot 22009ff Use same setup in fullwave simulations nature of turbulent cascade determines slope k-4 knee at k where turbulent drive is occurring 12

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 13

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 E B 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 [C. Tröster, PhD Thesis 2008] 14

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 E B 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 ) For now, treat turbulence snapshots as independent and use Experimental Doppler Spectrum: variance of signal as measure of fluctuation prominentstrength carrier [C. Tröster, PhD Thesis 2008] 15

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: 1000 100 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 10 1-1 -0.5 0 0.5 Doppler shift (MHz) 1 16

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 Experiment knee GENE knee knee to higher k in saturation Explained by nonlinear saturation of reflected power spectrum 'squished' against maximum spectral index too high 17

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 19

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 k (m-1) vs. synthetic isotropic turbulence k (m-1) 21

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 22

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 k (m-1) 23

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 SUPRA and ASDEX Upgrade measurements, larger (>7) spectral index expected 24

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 25

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 Ex grid points 26

Why Is The Spectral Index So Large? Not a problem of resolution 32 vs. 48 sampling points per wave period (~4 times CPU) 27