Hysteresis in the L-H-L transition, D C McDonald, ITPA, Princeton 20091/22 Hysterics in the L-H transition D C McDonald

Hysteresis in the L-H-L transition, D C McDonald, ITPA, Princeton 2009 1/22

Hysterics in the L-H transition

D C McDonald


Hysteresis in the L↔H transition

D C McDonald

Thanks to: Amanda Hubbard, Jack Connor, Punit Gohil, Stan Kaye, George McKee, Carlos Hidalgo,

Yves Martin


Structure of talk

• Introduction

• Theory basis

• Experimental evidence

• Points for discussion


Introduction

• The L-H transition is a bifurcation in both global and edge conditions

• Study of it largely focuses on the L→H transition

• To understand a bifurcating process, we should study both directions

• Certainly has been much good work on hysteresis, although ITPA involvement has been minor. Should be stimulated further


Theory basis


Types of ‘phase transitions’

-T

-Tc

T

L-TB

TB-L

L-TB

TB-L

L

TB

-T

-Tc

T

-Tc

r

L-TB

First Order Transition Second order Transition


Bifurcation diagrams: topologies


Poloidal force balance bifurcations

na anom lc bv RS neo neo cx0 re i i i i i e i

E

e t( )

• Some contributions are functions of

-

• Can produce bifurcation in Er

K Itoh et al Transport & Structural Formation in Plasmas 1999 IoP p 239

na(anom) lc 2e-i n i rΓ λ - X ;Γ exp -X ;X E

rE

n 1 n dn dr


L-H transition model: ion orbit loss

• Orbit loss can lead to Er bifurcation• Associated reduction in transport can cause L-

H transitionS-I Itoh & K Itoh Phys Rev Lett 60 2276 (1988)K C Shaing & E C Crume Phys Rev Lett 3 2369 (1989)


Turbulent viscosity bifurcation

• Increasing flow increases ωE

• Increasing ωE leads to reduction in turbulent ITG viscosity

• Reduction in viscosity produces transition in flow G M Staebler & R R Dominguez

Nucl Fus 33 77 (1993)


Transport bifurcation diagram• Flow shear ωE depends on radial

plasma gradients, g

• Model diffusivity

Bifurcation in flux and confinement transition:

L-H or ITB

jr pol torj j tor j pol

j j

dp1E v B v B

n e dr

0

2

E s

DD

1

F L Hinton & G M Staebler, Phys Fluids B 4 319 (1993)


Experimental evidence


Nature of L-H-L hysteresis

Snipes PPCF 2000

C-Mod• Hysteresis in threshold power is a common feature of ramp-up/ramp-down studies

• Not common to all studies: many experiments show no hysteresis

• Phase of H-mode (eg Type I/III) may effect existence/non-existence of hysteresis

•NB: Snipes 2000 is only ITPA paper that addresses hysteresis and it does so briefly.


Global v local parameters

Thomas PPCF 1998

DIII-D

• When hysteresis is seen in power it is not seen in Te,knee

• Certainly is seen in edge gradients


Global v local parameters

Andrew PPCF 2008

JET

• JET 2008 study saw a mix of hysteresis and not in power, but Te,knee does not show it

• Similarly for Ti,knee


Local parameters during L-H-L cycle

Hubbard PPCF 2002

C-Mod

• First systematic edge parameter study by Hubbard 2002 on C-Mod

• S-curve shown in several key edge gradient parameters

NSTXNSTX

H-Mode Workshop 17Sept. 30 – Oct. 2, 2009

L-H/H-L Power Thresholds in Pure Helium and Deuterium L-H/H-L Power Thresholds in Pure Helium and Deuterium Plasmas Were Explored in NSTXPlasmas Were Explored in NSTX

• High Harmonic Fast Waves (HHFW) were used to heat pure helium and deuterium plasmas

• Continuous ramping of HHFW power allowed for “fine” determination of PLH and PHL

• “Perturbation technique” used to determine HHFW electron heating efficiency (<0.16>0.1)• Ion heating efficiency similar

• In what follows, PRF is taken to be PRF,e

Forward or back transitions not always

Obvious in D signal even for D-plasmas.

- No D indication in He-plasmas

Use change in edge profiles as an

Indication of both L-H and H-L transition

NSTXNSTX


L-H Transition Powers Linearly Dependent on Density;L-H Transition Powers Linearly Dependent on Density;Not True for H-L TransitionsNot True for H-L Transitions

L-H

H-L

NSTXNSTX


L-H Power Thresholds for He and D SimilarL-H Power Thresholds for He and D Similar

H-L power thresholds lower, indicating somehysteresis

Normalize PRF + POH by density for comparison

Large error bars due to uncertainty in heating efficiency!

Carlos Hidalgo H-mode workshop, 200920

Stellarators: 3 - D devicesGoal of C Hidalgo’s H-mode WS 2009 talk:

Stellarator results as guideline for further developments in the physics of plasma bifurcations

L-H transition general to stellarators, spherical tokamaks


Summary

• L-H threshold is a bifurcation and more information on it can be obtained by studying the complete L-H-L cycle.– Currently, the focus is more on the L-H threshold alone

• Tokamak studies often, but not always, see first order hysteresis in power and edge gradients

• The H-mode phase (eg Type I/III) may effect the existence or otherwise of hysteresis, but has not been systematically studied

• No observations of hysteresis in Tknee: a strange result, but is it informative?

• S-curve analyses of transition performed on some machines, but should be more widely performed

• Hysteresis is a fundamental physics issue common to many types of machines and should be studied widely

• Theory: most models predict bifurcation in edge parameters. Can we test them against the observed data? The existence/non-existence and fixed Tknee would be too strong results to test.


Possible further work

• Analysis– Study of existing experimental results in s-curve form

– Collation of L-H-L studies by all machines. Clarification of which machines see hysteresis, when and in what

– Review of theories in terms of their predictions for hysteresis

• Experiments– Study of L-H-L using turbulence diagnostics

– Combining H-L study explicitly into TC-2

– General encouragement of L-H-L studies across a variety of machines

– Don’t see a definitive hysteresis experiment

Documents

Hysteresis in the L-H-L transition, D C McDonald, ITPA, Princeton 20091/22 Hysterics in the L-H transition D C McDonald