A mechanism for magnetic field stochastization and energy release during an edge pedestal collapse

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1 A mechanism for magnetic field stochastization and energy release during an edge pedestal collapse S. S. Kim, Hogun Jhang, T. Rhee, G. Y. Park, R. Singh National Fusion Research Institute, Korea Acknowledgements: P. H. Diamond, A. Aydemir, X. Q. Xu, T. S. Hahm 1 7 th IAEA Technical Meeting on Theory of Plasma Instabilities 4-6 March, 2015, Frascati, Rome, Italy

2 ELMs Edge localized modes (ELMs): instability occurring at edge pedestal in H-mode operation Large (Type-I) ELMs should be avoided or significantly mitigated Serious concern in ITER and beyond Understanding physics of ELM crash and ensuing energy loss has been a central issue in fusion plasma physics society for decades Present idea: Identity of Type-I ELM: destabilization of ideal Peeling-Ballooning mode [Snyder et. al., PoP 2002] and its nonlinear evolution (filaments, Wilson and Cowley, PRL, 2004) Energy release: ELM filaments carries heat flux 2

3 Is this the end of the story? Missing loss is likely to be present: A recent study shows that filament-induced energy loss is < 30% of total energy loss [Kirk et. al., Nucl. Fusion 2014] what does account for > 70% of ELM energy loss?? Many nonlinear simulations [JOREK, BOUT++, M3D] have often shown the generation of stochastic fields during a simulated edge pedestal collapse, though the degree of stochastization varies in models. how stochastic fields are generated out of initial ballooning modes? do stochastic fields affect ELM energy loss? 3 Main focus of this presentation is try to answer above three questions..

4 Outline Simulation model and conditions Magnetic field stochastization Secondary tearing mode (STM) formation from ballooning mode (BM) Tearing mode generation via nonlinear interactions bet. BM and STM Energy loss through stochastic magnetic field Conclusion and future works 4

5 Simulation model Three-field model of reduced MHD equations with a model parallel heat flow Vorticity equation U min t V E U J 2 B 0 b B P Resistivity S 0RV / 10 A 9 Ohm s law A t 0 A 2 H 4 0 A Hyper-resistivity S R / 3 12 H 0 V A H 10 Total pressure equation P t V E P 2 Q q 3 Q b0 b0 U Pi, VE, VDi, 0 b0 b0, B0 en B0 enb0 A b0 1 2 B B0 B1, B1 A b0, b0, J J 0 A B 0 0 i eb m i 0 5 Simulations are performed using BOUT++ framework

6 Simulation conditions No sources/sinks Not flux-driven simulations Computational domain: -0.6 X(normalized y) 0.2 Boundary conditions: Dirichlet (U), Neumann (P), zero-laplacian (A ) Normalized pressure profile: a=-2 0 q 2 R 0 (dp 0 /dr)/b 2 =3.87 at r=r max Unstable to peeling-ballooning mode (a c =2.75) Initiate from a single unstable mode with n = n 0 <P> evolution Pressure contour evolution 6 X

7 Strong stochastization of field lines Field line tracing shows a strong stochastization of magnetic field lines during pedestal collapse. Stochastization front propagates into core and saturates at t 75 Chirikov parameter evolution X X 7 Z Z Saturation

8 Secondary tearing mode formation before full stochastization Magnetic island grows in the middle of two rational flux surfaces where the initial BMs are unstable Secondary Tearing Modes (STM) with n=2n 0 (n 0 : toroidal mode number of unstable primary BMs) Total field line trace Field line trace for n=2n 0 STM is nonlinearly driven and grows even when D STM <0 Perturbed flux for n=2n 0 n = 2n 0 Secondary 8 X

9 Even parity modes generated from odd parity BMs Even parity modes start to grow rapidly at t ~ 60, saturates for 70 t 85, and reduces to a steady state (SS) value at t ~ 105. Equipartition of magnetic energy at SS, STM growth rate (g 2+ ) is twice of PBM growth rate (g 0- ) STM is generated by a coherent nonlinear interaction between PBMs during the growth phase. n = n 0 n = n 0 PTM acceleration n = 2n 0 Tearing mode with n=n 0 grows rapidly after t 60t A Primary Tearing Mode (PTM) 9

10 Nonlinear TM generation occurs in stages Sudden increase of PTM growth rate is synchronized to the drop of STM growth rate, which signifies the weakening of STM growth due to the growth of PTM. strong nonlinear interaction between STM and PTM Initial stochastization is due to STM, while the full stochastization is realized by PTM via nonlinear interaction with STM. PTM acceleration 10

11 Nonlinear energy transfer rate to PTM: Energetics PTM 2Re J, y V PTM PBM * STM dv In the early stages of nonlinear interactions, energy transfer occurs from PBM to STM. PTM grows by extracting kinetic energy of PBM via STM! 10 ) 7 Energy transfer from PBM to PTM via STM Energy transfer from PBM to STM STM plays a role of mediator transferring kinetic energy of PBM to magnetic energy of PTM! PBM PTM 11 t t A ) STM

12 Energy loss through stochastic fields Total pressure equation: P t V To find an appropriate model for Q, collisionless parallel energy loss process should be considered (rather than oft-quoted Braginskii model). (Lyapunov length)/(collisional m.f.p) = L c /l ~ 0.01 (Stochastization time)/e-i collision time ~ 0.07 E P Use Rechester-Rosenbluth model, given the lack of exact ion fluid closure model in presence of stochastic fields. Q 2 Q q 3 f K : kinetic factor to account for reduction of thermal transport [G. Y. Park et. al, PoP, 2010] f K = 0.1 suggested by Park et. al. 12 f K variation does not change main features of this work!

13 Q is dominant over filamentary convective loss!! When f K =0.1, convective loss (Q cv ) dominant in the early stage of crash (t<80), while Q becomes dominant eventually, accounting ~75% of total energy loss can be a candidate for missing energy loss in ELM crash. f K =1 f K =1 f K =0.1 f K =0.1 13

14 Conclusions Three-dimensional nonlinear, reduced MHD simulations show two important dynamical processes are involved in edge pedestal collapse. Nonlinearly driven TM generation from BM and stochastization of field lines due to island overlap Parallel energy loss through the stochastic field lines A mechanism for ELM crash is proposed: STM generation through a nonlinear energy transfer from PBM PTM generation by extracting energy from PBM via STM Island overlap and field line stochastization Large energy loss through the stochastic field lines 14

15 Implications and future works Implications: Indicates the possible presence of a precursor period during which STMs develop from PBMs. Expects strong magnetic activities prior to an ELM crash with high toroidal mode number (twice that of BMs) STM can be a candidate for the precursor mode observed in experiments On-going and future works: Improvement of parallel closure in presence of stochastic fields RMP effects on ELM crash hindering the growth of STMs?? Flux-driven simulations for repetitive ELMs 15

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