Integrated Simulation of ELM Energy Loss Determined by Pedestal MHD and SOL Transport N. Hayashi, T. Takizuka, T. Ozeki, N. Aiba, N. Oyama JAEA Naka TH/4-2

Introduction Energy loss caused by edge localized modes (ELMs) is crucial for reducing the divertor plate lifetime and limiting the plasma confinement in tokamaks. It is necessary to clarify the physical mechanism of collisionality dependence of the ELM energy loss. Purpose of this paper We develop an integrated simulation code TOPICS-IB based on a transport code with a stability code for the peeling-ballooning modes and a scrape-off-layer (SOL) plasma model. Collisionality dependence of the ELM energy loss is investigated by artificially enhancing the collisionality in models of bootstrap current and SOL plasma. ELM energy loss was found to decrease with increasing the collisionality in multi- machine experiments. Loarte, PPCF03

TOPICS-IB : TOPICS extended to Integrated simulation for Burning plasma 1.5D core transport code ( TOPICS ) 2D Grad-Shafranov equation 1D transport & current diffusion equations ELM model : Enhance transport 2D MHD equilibrium Eigenvalue & Eigenfunction Heat & particle flows across separatrix Boundary conditions at separatrix SOL transport model (Five-point model) Integral fluid equations Exponential radial profiles with characteristic scale length Flux-tube geometry Linear MHD stability code ( MARG2D ) Applicable to wide range of mode numbers from low to high Eigenvalue problem of 2D Newcomb equation (See details at TH/P8-1)

ELM model (Ozeki, FST06) Pedestal formation : Neoclassical transport in peripheral region and anomalous in inside region (given pedestal width Δ ped ) ELM enhanced transport is maintained for a given time-interval (δt ELM ). Stabilities of n=1-30 modes are examined by MARG2D (Tokuda, PoP99) in each time step along the pedestal growth. When modes become unstable, ELM enhanced diffusivities (χ ELM ) are added on the basis of radial profiles of eigenfunctions of unstable modes. (given maximum χ ELM max, N: total number of unstable modes)

SOL model (Hayashi, PSI06) Validated by particle code Validated by fluid codes Point model based on integral fluid equations easily reproduces many static features found in experiments. (Stangeby, textbook) Dynamic version of the point model (Five-point model) has been developed for the integrated ELM modeling. Parallel heat conduction and equipartition energy depend on the collisionality. Flux-tube geometry - 2 SOL & 2 divertor regions (5 positions) - Symmetry assumed in this paper

Integrated simulation result by TOPICS-IB

Transient behavior of core-pedestal-SOL-divertor plasmas along pedestal growth and ELM crash Simulation condition : JT-60U like parameters - R=3.4 m, a=0.9 m, I p =1.5 MA, B t =3.5 T, κ~1.5, δ~0.21, Z eff = , P NB =12 MW, β N =0.8-1 TOPICS-IB successfully simulates the transient behavior of whole plasma. - ELM duration δt ELM = 200 μs, diffusivity χ ELM max =100 m 2 /s Pedestal width Δ PED = Fixed density profile, n div =1x10 20 m -3 (High recycling divertor)

Increase of SOL temperature mitigates the radial edge gradient and lowers the ELM energy loss. Electron energy loss is larger than the ion one, due to larger heat conduction parallel to the magnetic field. Energy flows into the SOL and the SOL- divertor temperatures rapidly increases. The resultant energy loss (< 10% of W ped ) is comparable with that in JT-60U.

Reduction of ELM energy loss through bootstrap current

Bootstrap current decreases with increasing the collisionality and intensifies the magnetic shear at the pedestal region. Bootstrap current reduces the area and the edge value of ELM enhanced transport. The collisionality in the bootstrap current model is artificially enhanced by C BS =100 (enhanced collisionality: ν* ped = C BS ν* ped0 = 9). The increase of magnetic shear reduces the width of eignfunctions of unstable modes.

Total ELM energy loss is about 3 times larger than that in the case with SOL model. (Importance of SOL plasma) Simulation condition : T SOL =100 eV, SOL model is not used to clear only the bootstrap current effect. fixed B.C. w/o SOL model ELM energy loss is reduced by increasing collisionality in bootstrap current. Both electron and ion energy losses are reduced in almost the same ratio.

Reduction of ELM energy loss through SOL transport

SOL electron temperature increases with the collisionality, because the parallel heat conduction is inversely proportional to the collisionality. SOL electron temperature increases with collisionality, while ion one decreases. The collisionality in SOL model is artificially enhanced by C SOL =100 (ν* ped = 9). SOL ion temperature decreases with increasing the collisionality, because the equipartition energy flows is proportional to the collisionality.

ELM energy loss is reduced by increasing collisionality in SOL transport. Total ELM energy loss is reduced according to the electron energy loss and the ion contribution is small. For higher collisionality, the SOL electron temperature increases more and the electron energy loss is reduced. On the contrary, the SOL ion temperature decreases and the ion energy loss is enhanced a little.

Dependence of ELM energy loss on the collisionality and the model parameters

Bootstrap current and SOL transport have major effect on the collisionality dependence. Collisionality in both models is enhanced by C=C BS =C SOL. When the collisionality is enhanced by C=100, the electron energy loss is reduced by about 1/3, but the ion one is reduced a little. Total energy loss is reduced about half. Model parameter dependence Standard (C=1) : δt ELM =200 μs, χ ELM max =200 m 2 /s, Δ ped = 0.05 The magnitude of ELM energy loss is changed by the model parameters, but its collisionality dependence is unchanged. CaseStandardδt ELM x2χ ELM max x2Δ ped x2 & χ ELM max x4 ΔW ELM /W ped ΔW ELM /W ped ~0.05 was measured in JT-60U plasmas with ν* ped ~0.1.

Conclusion (1/2) - An integrated simulation code TOPICS-IB based on a 1.5D transport code with a stability code for peeling- ballooning modes and a SOL model has been developed to clarify self-consistent effects of ELMs and SOL on the plasma performance. - Experimentally observed collisionality dependence of the ELM energy loss is found to be caused by both the edge bootstrap current and the SOL transport. - Bootstrap current decreases with increasing the collisionality and intensifies the magnetic shear at the pedestal region. The increase of magnetic shear reduces the width of eigenfunctions of unstable modes, which results in the reduction of the area and the edge value near the separatrix of the ELM enhanced transport.

Conclusion (2/2) - When an ELM crash occurs, the energy flows into the SOL and the SOL temperature rapidly increases. The increase of SOL temperature lowers the ELM energy loss due to the flattening of the radial edge gradient. The parallel electron heat conduction determines how the SOL temperature increases. For higher collisionality, the conduction becomes lower and the SOL electron temperature increases more. - By the above two mechanisms, the ELM energy loss decreases with increasing the collisionality. The bootstrap current and the SOL transport have the major effect on the collisionality dependence.

Future work Effect of plasma shape Model validation - Different plasma shape affects the ELM energy loss through the change of the mode structure. - Comparison not only with experiments but also with nonlinear simulations - ΔW ELM /W ped 10 % in other machines Model improvement - Density dynamics (density collapse enhances ΔW ELM by about 40 % under assumption of similar collapse to temperature.) - Increase of bootstrap current near the separatrix changes the unstable model number from medium-n to low-n (n<10), but does not change the localization of eigenfunctions near the pedestal region.

Mode characteristics in the present simulation - When the collisionality in the bootstrap current model is enhanced by C BS =100, the pressure profile does not change very much at the ELM onset. Ballooning mode is dominant rather than the peeling mode. - Increase of bootstrap current near the separatrix changes the unstable model number from medium-n to low-n (n<10), but does not change the localization of eigenfunctions near the pedestal region.