Integrated Simulation of ELM Energy Loss Determined by Pedestal MHD and SOL Transport

1. TH/4-2 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

2. 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. ELM energy loss was found to decrease with increasing the collisionality in multi-machine experiments. Loarte, PPCF03 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. Collisionality dependence of the ELM energy loss is investigated by artificially enhancing the collisionality in models of bootstrap current and SOL plasma.

3. 1.5D core transport code ( TOPICS ) SOL transport model (Five-point model) Linear MHD stability code ( MARG2D ) Heat & particle flows across separatrix Boundary conditions at separatrix 1D transport & current diffusion equations ELM model : Enhance transport 2D MHD equilibrium Eigenvalue problem of 2D Newcomb equation 2D Grad-Shafranov equation Flux-tube geometry Integral fluid equations Eigenvalue & Eigenfunction Applicable to wide range of mode numbers from low to high Exponential radial profiles with characteristic scale length (See details at TH/P8-1) TOPICS-IB : TOPICS extended to Integratedsimulation for Burning plasma

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

5. SOL model (Hayashi, PSI06) Flux-tube geometry Parallel heat conduction and equipartition energy depend on the collisionality. - 2 SOL & 2 divertor regions (5 positions) - Symmetry assumed in this paper 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.

6. Integrated simulation result by TOPICS-IB

7. Transient behavior of core-pedestal-SOL-divertor plasmas along pedestal growth and ELM crash - Fixed density profile, ndiv=1x1020 m-3 (High recycling divertor) TOPICS-IB successfully simulates the transient behavior of whole plasma. Simulation condition : JT-60U like parameters - R=3.4 m, a=0.9 m, Ip=1.5 MA, Bt=3.5 T, κ~1.5, δ~0.21, Zeff=2.3-2.8, PNB=12 MW, βN=0.8-1 - ELM duration δtELM = 200 μs, diffusivity χELMmax=100 m2/s Pedestal width ΔPED = 0.05

8. Energy flows into the SOL and the SOL-divertor temperatures rapidly increases. 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. The resultant energy loss (< 10% of Wped) is comparable with that in JT-60U.

9. Reduction of ELM energy loss through bootstrap current

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

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

12. Reduction of ELM energy loss through SOL transport

13. SOL ion temperature decreases with increasing the collisionality, because the equipartition energy flows is proportional to the collisionality. 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 CSOL=100 (ν*ped= 9).

14. ELM energy loss is reduced by increasing collisionality in SOL transport. 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. Total ELM energy loss is reduced according to the electron energy loss and the ion contribution is small.

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

16. Bootstrap current and SOL transport have major effect on the collisionality dependence. Case Model parameter dependence Standard δtELMx2 χELMmaxx2 Δpedx2 & χELMmaxx4 Total energy loss is reduced about half. The magnitude of ELM energy loss is changed by the model parameters, but its collisionality dependence is unchanged. ΔWELM/Wped 0.028 0.047 0.040 0.049 Standard (C=1) : δtELM=200 μs, χELMmax=200 m2/s, Δped = 0.05 Collisionality in both models is enhanced by C=CBS=CSOL. 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. ΔWELM/Wped~0.05 was measured in JT-60U plasmas with ν*ped~0.1.

17. 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.

18. 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 theflattening 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.

19. Future work Effect of plasma shape - ΔWELM/Wped < 10 % in JT-60U, but > 10 % in other machines - 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. - Different plasma shape affects the ELM energy loss through the change of the mode structure. Model improvement - Density dynamics (density collapse enhances ΔWELM by about 40 % under assumption of similar collapse to temperature.) Model validation - Comparison not only with experiments but also with nonlinear simulations

20. Mode characteristics in the present simulation - When the collisionality in the bootstrap current model is enhanced by CBS=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.