1 An Overview of LH Transition and Future Perspectives Hogun Jhang 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 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 1 st order phase transition III. Barrier dynamics & beyond Simple sandpile model Predator-prey paradigm [mostly covered by Pat, yesterday] Other possibilities: ETL, SOL turbulence P LH 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 1 st order phase transition III. Barrier dynamics & beyond Simple sandpile model Predator-prey paradigm [mostly covered by Pat, yesterday] Other possibilities: ETL, SOL turbulence P LH 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 P LH /S = C B T F (other physics) Other physics:  B direction w.r.t X-pt., Isotope effects, Wall conditioning and recycling … Role over of P LH /S in density Common signature at LH transition E r shear layer formation (preceded by E r 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. P LH …)

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 1 st order phase transition III. Barrier dynamics & beyond Simple sandpile model Predator-prey paradigm [mostly covered by Pat, yesterday] Other possibilities: ETL, SOL turbulence P LH 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 E r 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 E r bifurcation Itoh and Itoh, PRL, 1988Shaing, PRL, 1989

9 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  1 st 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] LH transition as bifurcation: Transition rule and hysteresis

10 Barrier occurs both in density and temperature  2 field of n and P [Hinton & Stabler, NF, 1997; Malkov & Diamond, PoP, 2007] LH transition as bifurcation: 2 field model 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?  Analytic bifurcation relation: Intrinsic rotation only: bifurcation depends on pre-transition turbulence Motivated by recent gyrofluid ITB simulations [Kim et. al., NF, 2011]  Two field model of P and V  including external and intrinsic torque [Jhang, PoP, 2012] 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 1 st order phase transition III. Barrier dynamics & beyond Simple sandpile model Predator-prey paradigm [mostly covered by Pat, yesterday] Other possibilities: ETL, SOL turbulence P LH roll-over in density P LH 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 bistable sandpile 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.] T. Rhee et. al., in this conference No hysteresis when insufficient diffusion Hysteresis when sufficient diffusion

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 1994Carreras 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 density and 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 P LH 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 1 st order phase transition III. Barrier dynamics & beyond Simple sandpile model Predator-prey paradigm [mostly covered by Pat, yesterday] Other possibilities: ETL, SOL turbulence P LH 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 gyrokinetic simulations 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 T i and V || barriers  Existence of open loop hysteresis (  Q c ∝ 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!  ▽ 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 V  shear?

21 Lesson cntd.: Nonlocal interactions of fluctuations via ZFs ITB is robust for dynamic changes of   after formation. Near t=t 5, the ITB is rather strengthened in spite of the reduction of  . Stronger fluctuations at r=0.63 suppress weaker fluctuations at r=0.6, via induction of ZFs: seesaw mechanism [Itoh et.al. JPFR, 2009]   T i increases in spite of   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 20 th 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 1 st order phase transition III. Barrier dynamics & beyond Simple sandpile model Predator-prey paradigm [mostly covered by Pat, yesterday] Other possibilities: ETL, SOL turbulence P LH roll-over in density P LH 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)?