An Overview of LH Transition and Future Perspectives

1. An Overview of LH Transition and Future Perspectives HogunJhang WCI Center for Fusion Theory, NFRI, Korea Asia-Pacific Transport Working Group (APTWG 2012), May 15, South-Western Institute of Physics (SWIP), Chengdu, China

2. Outline • Introduction to H-mode: A reminder • LH transition as a phase transition • ExB shear suppression of turbulence: a paradigm • LH transition: bifurcation • LH transition as 1st order phase transition III. Barrier dynamics & beyond • Simple sandpile model • Predator-prey paradigm [mostly covered by Pat, yesterday] • Other possibilities: ETL, SOL turbulence • PLH roll-over in density IV. Self-consistent simulations of LH transition: can we learn from ITB simulations? V. Conclusions

3. I. Introduction to H-mode: A reminder II. LH transition as a phase transition • ExB shear suppression of turbulence: a paradigm • LH transition: bifurcation • LH transition as 1st order phase transition III. Barrier dynamics & beyond • Simple sandpile model • Predator-prey paradigm [mostly covered by Pat, yesterday] • Other possibilities: ETL, SOL turbulence • PLH roll-over in density IV. Self-consistent simulations of LH transition: can we learn from ITB simulations? V. Conclusions

4. H-mode • H-mode: sudden enhancement of plasma confinement (in all channels) manifested by appearance of transport barriers at edge (edge pedestal) when applied power exceeds some threshold value. • Why H-mode? • Practical reason: reduction of reactor size • Neoclassical  Reactor size ~ JET • ITER design evolution • Profile resilience requires to have ETB to obtain high fusion performance

5. A brief survey of phenomenology • First discovered at ASDEX, 1982  Ubiquitous (independent of magnetic configuration and magnetic topology)  Suggest to develop a general theory regardless of confinement topology • Existence of power threshold • PLH/S= C<n> BT F (other physics) • Other physics: B direction w.r.t X-pt., Isotope effects, Wall conditioning and recycling … • Role over of PLH/S in density • Common signature at LH transition • Er shear layer formation (preceded by Er oscillations: Estrada, G. S. Xu, ..) • Fluctuation decrease • Formation of transport barriers  occurs in same region in space (2-3 cm inside LCFS) • Local phenomena (local conditions) – local bifurcation • Sawtooth driven H-mode, noisy heat flux driven H-mode,.. • But, 1D consideration  turbulence spreading • LH transition theory should explain • Sudden fluctuation suppression • Flow generation • Physics of transition and transition condition (e.g. PLH …)

6. I. Introduction to H-mode: A reminder II. LH transition as a phase transition • ExB shear suppression of turbulence: a paradigm • LH transition: bifurcation • LH transition as 1st order phase transition III. Barrier dynamics & beyond • Simple sandpile model • Predator-prey paradigm [mostly covered by Pat, yesterday] • Other possibilities: ETL, SOL turbulence • PLH roll-over in density IV. Self-consistent simulations of LH transition: can we learn from ITB simulations? V. Conclusions

7. ExB flow shear suppression of turbulence: a paradigm for transport reduction • Turbulence suppression when [Biglari, Diamond, Terry, PoF B, 1990]  BDT Criteria [Biglari, Diamond, Terry, PoF B, 1990]  Hahm-Burrell formula in general toroidal geometry [Hahm & Burrell, PoP, 1995]  not only Er but also dq/dr is important. Waltz rule (gyrofluid simulations) : [Waltz et. al., PoP, 1994]  reduction factor

8. LH transition as transport bifurcation • Early idea [Itoh, PPCF, 1994]: Poloidal torque balance and Er bifurcation Itoh and Itoh, PRL, 1988 Shaing, PRL, 1989

9. LH transition as bifurcation: Transition rule and hysteresis • 1 field barrier dynamics: Turbulence suppression by ExB shear and subsequent positive feedback by mean field [Hinton, PoF B, 91] • Exhibits S-curve like confinement bifurcation • 1st order phase transition with maximum hysteresis • Spatio-temporal structure for slowly evolving barriers [Diamond et. al., PRL 1997, Lebedev, Diamond, PoP, 1997] • Flux landscape for spatially varying • Transition location: Maxwell rule • Barrier width:  P. Diamond [Plenary talk, this conference]

10. LH transition as bifurcation: 2 field model • Barrier occurs both in density and temperature  2 field of n and P [Hinton & Stabler, NF, 1997; Malkov & Diamond, PoP, 2007] • Role of pressure curvature: • P’’ defines the location of a barrier • Forward transition  Maxwell criteria • Back transition  Minimum flux • Hysteresis strength: • ~1/2 of maximum rule •  Analytic solution

11. Role of intrinsic rotation and external torque? • Motivated by recent gyrofluidITB simulations [Kim et. al., NF, 2011] •  Two field model of P and Vf including external and intrinsic torque [Jhang, PoP, 2012] •  Analytic bifurcation relation: Intrinsic rotation only: bifurcation depends on pre-transition turbulence With external torque: intrinsic-external torque interaction governs bifurcation

12. I. Introduction to H-mode: A reminder II. LH transition as a phase transition • ExB shear suppression of turbulence: a paradigm • LH transition: bifurcation • LH transition as 1st order phase transition III. Barrier dynamics & beyond • Simple sandpile model • Predator-prey paradigm [mostly covered by Pat, yesterday] • Other possibilities: ETL, SOL turbulence • PLH roll-over in density • PLH vs. BB drift direction, etc. IV. Self-consistent simulations of LH transition: can we learn from ITB simulations? V. Conclusions

13. LH transition in a simple model • Advent of SOC paradigm for turbulent transport [Diamond & Hahm, PoP, 1995]  “running sandpile” model [Newman et. al., PoP 1996] • Diffusive bistablesandpile model as the simplest model to study LH transition and barrier dynamics [Gruzinov et. al., PRL, 2002; PoP, 2003]  Great simplicity for complicated phenomena!  bistable toppling rule + hard boundary at edge  Transition happens but no hysteresis without diffusion (i.e. residual pedestal transport)  Applied to pedestal perturbation effects on ELM [T. Rhee et. al., PoP, 2012; in this conf.] Hysteresis when sufficient diffusion No hysteresis when insufficient diffusion T. Rhee et. al., in this conference

14. Predator-Prey paradigm (mostly covered by Pat’s talk) • Mean field predator-prey model [PD et. al., PRL, 1994; Carreras et. al., PoP, 1994] PD et. al., PRL 1994 Carreras et. al., PoP 1994 • Zonal flow (Pat’s plenary talk) as a new player in plasma turbulence  paradigm shift [PD, Itohs, Hahm, PPCF, 2005] •  A natural predator in the feedback loop •  ZF can not sustain barrier but triggers transition •  Multi predator (ZF and mean flow) - prey model [Kim & PD, PRL, 2003] •  Expansion of 0D to 1D model done [Miki, in this conference] • Transport equations for densityand pressure • Evolution equations for turbulence intensity, ZF energy and poloidal rotation •  include all the efforts for the past 20 years (except for orbit loss, nonlinear viscosity, V||dynamics )!!!

15. Other models • Edge Turbulence Layer (ETL) [Ossipenko & Tsaun] • Four-field model of electrostatic potential, density, ion and electron temperatures  Lorentz-like set of equations describing nonlinear convective cells • Implemented in transport code (ASTRA – ETL) • SOL Turbulence: FM3 [Fundamenski et. al., NF, 2012] • LH transition happens when  Strong coupling of drift and Alfven waves  Enhance inverse cascade and ZF(?) • Still speculative and underlying physics unclear but.. • Suggests LH transition may be affected by outside (i.e. SOL)  boundary condition? • Revisit “seesaw” model?? [Itoh, JPFR • 2009]

16. Transition characteristics change by pre-transition turbulence? • Roll-over of PLH in density observed in many tokamaks • Pre-transition turbulence mode can affect bifurcation [Jhang et. al., PoP, 2012] in ITB. Possibility in H-mode transition? • TEM  ITG cross-over story is applicable in this case? • Roll-over density is close to LOC  SOC transition, more or less (within 1~2 times smaller than LOCSOC transition density) • He discharge at JET [McDonald, 2012] shows increase in roll-over density  Support the role of electron channel in low density branch? • Non-local transport in low density branch?

17. I. Introduction to H-mode: A reminder II. LH transition as a phase transition • ExB shear suppression of turbulence: a paradigm • LH transition: bifurcation • LH transition as 1st order phase transition III. Barrier dynamics & beyond • Simple sandpile model • Predator-prey paradigm [mostly covered by Pat, yesterday] • Other possibilities: ETL, SOL turbulence • PLH roll-over in density IV. Self-consistent simulations of LH transition: can we learn from ITB simulations? V. Conclusions

18. Large scale first principle simulations… • Large scale gyrokineticsimulations have contributed a lot in elucidating physics of turbulent transport •  ZF shearing and turbulent regulation [Lin et. al., Science, 1998], …. •  Transition from Bohm to gyro-Bohm[Lin et. al., PRL, 2002, GTC] •  Predator-Prey paradigm, Turbulence spreading and size scaling [GYRO] •  Formation of self-organized structure [G. Dif-Pradalier et.al., PRE, 2009;GYSELA] •  Physics of turbulence-driven intrinsic rotation [Ku et.al., NF, 2012;XGC1, GYSELA], ….. • BUT… • Neither LH transition nor internal transport barrier formation (except for some signature of ITB) • have been produced in gyrokinetic simulations!!

19. Gyrofluid simulations of ITB dynamics • Internal transport barrier (ITB) formation shares main physics features with LH transition: • ExB flow shear suppression of turbulence • Positive feedback by mean flow shear • Transport bifurcation • Recent gyrofluid simulations using revised TRB code reveal ITB dynamics [Kim, et. al., NF, 2011] •  Whole process of formation, sustainment and back transition studied •  Formation of Ti and V|| barriers •  Existence of open loop hysteresis (DQc∝ Nu) •  Role of intrinsic and external torque in barrier dynamics

20. Some interesting lessons from ITB simulations • ZF at ITB head triggers ITB formation and mean flow causes positive feedback at ITB foot  two predators may be in different place! • g▽V||is important in formation and sustainment of ITB  cancellation of intrinsic rotation yields ITB collapse (in contrast to H-mode)  Cancellation experiments in QH-mode? • Back transition triggered by large momentum burst  cause negative feedback at ITB foot •  large heat flux from pedestal may cause trigger H-L back transition! Condition? •  RSB in QH mode with strong Vfshear?

21. Lesson cntd.: Nonlocal interactions of fluctuations via ZFs • ITB is robust for dynamic changes of gE after formation. Near t=t5, the ITB is rather strengthened in spite of the reduction of gE . • Stronger fluctuations at r=0.63 suppress weaker fluctuations at r=0.6, via induction of ZFs: seesaw mechanism [Itoh et.al. JPFR, 2009]Ti increases in spite of gE reduction!!  Role of SOL turbulence in enhancing ZF at edge?

22. Towards self-consistent simulations of LH transition… • First principle simulations  long way to go (in spite of big investment, useful for detailed snap shot analysis) • 1D transport simulations  lack of self-consistency (legacy of 20th century, useful for operational purpose, but not in physics research) • Core-edge coupled gyrofluid simulations as a possible solution! • Retain relevant physics self-consistently • Computationally cheap  flux-driven core-edge global simulation • Framework has been developed (e.g. BOUT++, Xu et. al.) •  easy to implement • Confidence grows (reproduce main features in barrier dynamics) • Near & mid-term issues : • Refine closure: “exact” parallel closure & physics interpretation, FLR and trapped particle, etc.… • Obtain ITB in presence of (1) non-resonant modes (2) electromagnetic fluctuations • Core-edge coupling and LH transition!

23. I. Introduction to H-mode: A reminder II. LH transition as a phase transition • ExB shear suppression of turbulence: a paradigm • LH transition: bifurcation • LH transition as 1st order phase transition III. Barrier dynamics & beyond • Simple sandpile model • Predator-prey paradigm [mostly covered by Pat, yesterday] • Other possibilities: ETL, SOL turbulence • PLH roll-over in density • PLH vs. BB drift direction IV. Self-consistent simulations of LH transition: can we learn from ITB simulations? V. Conclusions

24. Conclusions • Big progress has been made in the physics of LH transition (or transport barrier formation, in general) for the last ~25 years. • Concepts: transport bifurcation, shear flow suppression of turbulence, ZF and Predator prey paradigm… • A simple 1D model developed capturing knowledge/concepts for the past years  Knowledge Reservoir • Converging picture: LH transition triggered by ZF and positive feedback by mean flow  supported by recent experiments [Estrada et. al., PRL, 2011; Xu, et. al., PRL, 2011, Schmitz, …] • First principle based simulations have contributed in elucidating basic physics of turbulent transport, but not that much in the physics transport barrier formation… •  Self-consistent gyrofluid simulations would be a good solution bridging the gap • between “traditional” 1D transport code and gyrokinetic simulations. • Some remaining and interesting issues: • Effects of pre-transition turbulence mode in transition dynamics? • Nonlocal effects in transport bifurcation? • Transition dynamics to decoupled barrier formation (e.g. I-mode, QH-mode)?