1 an overview of lh transition and future perspectives hogun jhang wci center for fusion theory,...

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An Overview of LH Transition and Future Perspec-

tives

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

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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 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 sim-ulations?

V. Conclusions

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V. Conclusions

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H-mode H-mode: sudden enhancement of plasma confinement (in all channels) manifested by appear-

ance 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

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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 recy-

cling … 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 …)

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V. Conclusions

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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

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LH transition as transport bifurcation

Early idea [Itoh, PPCF, 1994]: Poloidal torque balance and Er bifurcation

Itoh and Itoh, PRL, 1988 Shaing, PRL, 1989

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1 field barrier dynamics: Turbulence suppression by ExB shear and subsequent posi-

tive 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]

neoturbc DDQ /~

r

rP

rnreBr

v

r

P

rvQ

rSrQrrt

P

E

E

)(

)(

11 ,

/1

),()(1

21

0

LH transition as bifurcation: Transition rule and hysteresis

)(1 r

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

curvature pressurecdiamagneti: EV

Hysteresis strength:

~1/2 of maximum rule Analytic solution

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Role of intrinsic rotation and external torque?

)(1

1

)(1

1

21

0

21

0

rMr

Vrrrt

V

rSr

Prrrt

P

resE

E

Analytic bifurcation relation:

r

V

qr

rP

r

rn

eBnr

vEE

)()(12

21

1 EEres

)(ˆ)21(1

)1()(

22

22

rQg

gggF

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 Vf including external and intrinsic torque [Jhang, PoP, 2012]

With external torque: intrinsic-external torque

interaction governs bifurcation

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• PLH vs. BB drift direction, etc.


V. Conclusions

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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 dif-fusion

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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 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 )!!!

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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 af-fected by outside (i.e. SOL) boundary condition?

Revisit “seesaw” model?? [Itoh, JPFR

2009]

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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 LOCSOC 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?

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V. Conclusions

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Large scale first principle simulations…

Large scale gyrokinetic simulations have contributed a lot in elucidating physics of turbulent trans-port

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!!

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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

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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 Vf shear?

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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?

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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!

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• PLH vs. BB drift direction


V. Conclusions

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Conclusions

Big progress has been made in the physics of LH transition (or transport barrier forma-tion, 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 sup-

ported 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)?

1 an overview of lh transition and future perspectives hogun jhang wci center for fusion theory,...

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