Mechanisms for losses during Edge Localised modes (ELMs) Abhinav Gupta Institut für Energieforschung-4, Forschungszentrum Jülich GmbH, Association FZJ-Euratom, 52425 Jülich, Germany Forschungszentrum Jülich in der Helmholtz-Gemeinschaft

Contents Motivation Energy loss during ELMs Parallel conductive heat flux Elucidation of heat flux limit from magnetic island heating experiment Convective heat flux Conclusion Forschungszentrum Jülich in der Helmholtz-Gemeinschaft

Motivation ELMs an MHD activity at the edge of tokamak plasmas, cause high impulse heat and particles fluxes on target plates which may lead to unacceptable loads under reactor conditions K.Kamiya et al, Plasma Physics, Control Fusion (2007) S43-S62 Forschungszentrum Jülich in der Helmholtz-Gemeinschaft

Model for ELMs loss mechanism Type I ELMs are generated by ballooning-peeling ideal MHD modes developing when the pressure gradient exceeds the critical level These modes produce a radial component of the magnetic field Radial inhomogeneity of plasma parameters in the ETB (edge transport barrier) results in radial particle and heat transport along such field lines This model could explain the collisionality dependence of losses during ELMs observed on diverse tokamak devices Forschungszentrum Jülich in der Helmholtz-Gemeinschaft

Energy loss Energy drop per ELM Heat flux density through separatrix Heat conduction is dominated by the contribution from light electrons α is inclination angle of perturbed field line to toroidal direction Convection heat loss with charged particles escaping from ETB during ELM Forschungszentrum Jülich in der Helmholtz-Gemeinschaft

Conductive heat loss For high collisionality Spitzer-Harm formula is applied for parallel conduction For low collisionality a free streaming heat flux has to be reduced by a factor  heat flux limit: Smooth transition between collisional and collisionless limits is described by the formulae Forschungszentrum Jülich in der Helmholtz-Gemeinschaft

Q//k at separatrix, assuming linear variation of Q//k in the barrier Q//k at separatrix, assuming linear variation of Q//k in the barrier, Qb//k=0 Q//k at separatrix, assuming linear variation of Q//k in the barrier Thus, net heat flux at separatrix Collisionality dependent, with heat flux limit becoming important at low collisionality Interpretation of experiments with laser fusion plasmas: Malone et al, PRL 34, 721 (1975); Luciani et al, PRL 51, 1664 (1983) Physical mechanism: Non-local effects reduce the perturbation in distribution function caused by ||T Forschungszentrum Jülich in der Helmholtz-Gemeinschaft

Elucidation of the heat flux limit from magnetic island heating experiment Forschungszentrum Jülich in der Helmholtz-Gemeinschaft

Magnetic Islands Magnetic islands generated by spontaneous (e.g. due to tearing modes) and externally applied magnetic field perturbations. Due to radial component of B, field lines deviate from magnetic surfaces and island chains are formed. Apart from anomalous perpendicular transport there is a contribution to radial transport due to flows along field lines qr core edge q q|| Studying transport through islands gives information about transport characteristics perpendicular to and along field lines Forschungszentrum Jülich in der Helmholtz-Gemeinschaft

Experiments on magnetic island heating Classen et al, PRL, 98, 035001 (2007) Tearing mode islands (m/n=2/1) in TEXTOR destabilized by Dynamic Ergodic Divertor and heated by Electron Cyclotron Resonance Heating Island is heated uniformly at the resonant surface. Heat transfers along and perpendicular to field lines from resonant surface to island separatrix. An analytical model can help us to determine  and ||, and thus the heat flux limit. Forschungszentrum Jülich in der Helmholtz-Gemeinschaft

“Optimal path” model for heat transfer in islands Heat deposited on resonant surface is transported first || and then  field lines, along the path with minimum ΔT Total radial heat flux Perpendicularpath part Parallel path part Total temperature change along path Main parameter Forschungszentrum Jülich in der Helmholtz-Gemeinschaft

Temperature profile at resonance surface Temperature profile at resonance surface measured by ECEI Calculated temperature 400 kW 300 kW 200 kW Dependence on  allows to determine  and || Forschungszentrum Jülich in der Helmholtz-Gemeinschaft

Determination of , // and FS 400 kW 300 kW 200 kW FS in agreement with interpretation of laser experiments! Forschungszentrum Jülich in der Helmholtz-Gemeinschaft

Calculations of convective heat losses along perturbed field lines Forschungszentrum Jülich in der Helmholtz-Gemeinschaft

The kinematic equation, ion motion equation and energy equations are solved for particles in the region inside the separatrix, to determine the parameter space (s, U, ε) of particles that come out of the ETB during ELM time. Kinematic equation Ion motion equation Ion energy equation Forschungszentrum Jülich in der Helmholtz-Gemeinschaft

The number of particles coming out during ELMs with specific initial parameters s, U, ε is determined under assumption of local maxwellian distribution By integrating over this parameter space, we calculate the net convective energy loss Forschungszentrum Jülich in der Helmholtz-Gemeinschaft

Conclusion A model for particle and energy losses during ELMs, considering both conductive and convective losses, has been developed The heat flux limit important for this has been elucidated from heat transport analysis in magnetic islands A model for convective losses during ELMs is under development As outlook, the final complete model would be tested to examine collisionality dependence of energy losses as observed in experiments Forschungszentrum Jülich in der Helmholtz-Gemeinschaft