Numerical Simulations of Modulated Electron Cyclotron Heating Experiments

1. The CUTIE Turbulence Simulation Code Visualisation IDL programme “CutieScope” used to visualize data • Time traces of central values • Time evolution “movies” of profiles and 2D contourplots • Several representations of spectral data Overview CUTIE [1] is a global, electromagnetic, two-fluid turbulence simulation code • Periodic cylinder geometry (r, ,   z/R) with circular flux surfaces, field line curvature and line bending • Quasi-neutrality: j = 0 • Reduced Tokamak Ordering (no fast magnetosonic waves) • No trapped particle modes • All plasma properties written as sum of mean (flux surface average) and fluctuating part. • Fluctuating “fields” (*, *, n*, * and potential vorticity *) decoupled from fluctuating temperatures and solved seperately (1) • Gradient  is in the direction of the unperturbed field; nonlinear terms account for real field direction. • Fluctuation source e* includes neoclassical perpendicular transport terms [2] and turbulent diffusion terms to provide high-k cut-off. Exact transport equation for n0 averaged over angles: (2) • Feedback mechanism on particle source Sp(r,t) used to keep line averaged density fixed • Boundary conditions: Fixed edge value and zero gradient at r = 0 for average, fluctuations vanish at r = 0 and r = a • Eqn. (1) and other turbulent equations of motion solved by Fourier-transforming and radial finite-differencing • Block-tridiagonal system for coupling terms between , , n,  and  solved for fourier harmonics (m, n) using Gauss-Jordan pivoting • Two predictor-corrector iterations at each time step Example of equations: density ne As an example of the formula´s involved, the equations for the electron density will be studied in a bit more detail. The equation of motion for the non-dimensional density fluctuation, n* = ne/ne(0,t) is given by eqn. (1) Fig. 1: Contourplot of a poloidal cross-section of an RTP plasma, produced by CutieScope. The colours correspond to values of Te. CutieScope can produce time-evolution movies of these and other contours and several profiles. Future References • Develop and use Centori, a new code similar to CUTIE, but with • Full toroidal geometry • Finite  • Non-circular (i.e. shaped) plasma´s • Parallel computing possibilities (SARA / Aethelwolf-Cluster) • Studie turbulent transport in the TEC-tokamak TEXTOR (Jülich, Germany) using CUTIE / Centori [1] A. Thyagaraja, Plasma Phys. Control. Fusion 42 (2000) B255 [2] R.D. Hazeltine and J.D. Meiss Plasma Confinement (NY: Addison-Wesley) [3] P. Mantica et.al., Phys. Rev. Lett. 85 (2000) 4534 [4] P. Mantica et.al., This conference, P.II.05 [5] N.J. Lopes Cardozo et.al., Plasma Phys. Control. Fusion 39 (1997) 303 [6] P. Mantica et.al., Phys. Rev. Lett. 82 (1999) 5048 [7] G.M.D. Hogeweij et.al., Plasma Phys. Control. Fusion 42 (2000) 1137 Numerical Simulations of Modulated Electron Cyclotron Heating Experiments E. Min 1), A. Thyagaraja 2), P.J. Knight 2), G.M.D. Hogeweij 1), P. Mantica 3) 1)FOM-Instituut voor Plasmafysica “Rijnhuizen”, Associatie Euratom-FOM, Trilateral Euregio Cluster, P.O. Box 1207, 3430 BE Nieuwegein, The Netherlands 2)Euratom/UKAEA Fusion Association, Culham Science Centre, Abingdon OX14 3DB, United Kingdom 3)Istituto di Fisica del Plasma, Euratom-ENEA-CNR Association, Milan, Italy Simulation of Modulated ECH in RTP RTP Edge Cold Pulse Simulations The Experiment • RTP: R0 = 0.72 m; a = 0.165 m; strong electron heating (PECH  350 kW). • ECH modulated (cd = 0.85, dep = 0.25) to study electron heat transport [3,4]. • Maximum of 1st harmonic shifts inward with respect to ECH deposition radius (dep). This was attributed to a heat pinch component inside dep. The Experiment • In RTP: During off-axis ECH (dep = 0.25) an oblique pellet is injected, cooling the edge. [6,7] • Strong rise in Te(0) observed at a timescale of ~5 ms • Simulated in CUTIE by introducing sink inelectron energy equation for  > 0.75 during 0.4 ms (more like laser ablation) Fig. 3: Time traces of Te (top), Ti (middle) and ne (bottom). The period of the edge cooling is indicated by the dashed line. Note that the Te profile has an off-axis maximum, and thus the upper trace is not the one at  = 0.What happens around t = 62.5 ms is still under investigation. Fig. 2: Comparison of CUTIE simulations (lines) with experimental profiles (symbols). Left panel: the time-averaged Te profile. Mid panel: the amplitudes of Te at first three harmonics of the modulation frequency. Right panel: the phase difference between the MECH and the Te response. Results of CUTIE simulation • Reasonable agreement with experiment for phase difference. • Te overestimated in average profile and MECH amplitudes. • Difference with results on [4] is due to smaller ECH deposition width. • No inward shift of the maximum of the first harmonic is observed in the simulation. • Simple (turbulence “switched off”) CUTIE simulations with a heat pinch term added do reproduce the shift. • This means that, although a heat-pinch can cause a shift in the first harmonic, such a heat pinch does not follow from the CUTIE set of equations. Preliminary Results • Small but almost instantanious rise in Te(0) and Ti(0). A sharp rise in E is observed at the same time but is too transient to account for this. • A flattening of the density profile is observed. • At t = 62.5 ms a sudden rise in edge Te, Ti and ne is observed. This “shock” travels inward very fast, and is only slowed down around   0.5. The nature of this event is still under investigation.