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 Future  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 References 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 The CUTIE Turbulence Simulation Code Fig. 1: Contourplot of a poloidal cross-section of an RTP plasma, produced by CutieScope. The colours correspond to values of  T e. CutieScope can produce time-evolution movies of these and other contours and several profiles. 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  Feedback mechanism on particle source S p (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 n e 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 * =  n e /n e (0,t) is given by eqn. (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 n 0 averaged over angles: (2) (1) The Experiment  In RTP: During off-axis ECH (  dep = 0.25) an oblique pellet is injected, cooling the edge. [6,7]  Strong rise in T e (0) observed at a timescale of ~5 ms  Simulated in CUTIE by introducing sink in electron energy equation for  > 0.75 during 0.4 ms (more like laser ablation) Preliminary Results  Small but almost instantanious rise in T e (0) and T i (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 T e, T i and n e 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. Fig. 3: Time traces of T e (top), T i (middle) and n e (bottom). The period of the edge cooling is indicated by the dashed line. Note that the T e 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. RTP Edge Cold Pulse Simulations The Experiment  RTP: R 0 = 0.72 m; a = m; strong electron heating (P ECH  350 kW).  ECH modulated (c d = 0.85,  dep = 0.25) to study electron heat transport [3,4].  Maximum of 1 st harmonic shifts inward with respect to ECH deposition radius (  dep ). This was attributed to a heat pinch component inside  dep. Results of CUTIE simulation  Reasonable agreement with experiment for phase difference.  T e 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. Fig. 2: Comparison of CUTIE simulations (lines) with experimental profiles (symbols). Left panel: the time-averaged T e profile. Mid panel: the amplitudes of T e at first three harmonics of the modulation frequency. Right panel: the phase difference between the MECH and the T e response. Simulation of Modulated ECH in RTP