Hysterics in the l h transition
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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.

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Hysterics in the l h transition

Hysterics in the L-H transition

D C McDonald

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


Hysteresis in the l h transition

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

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


Structure of talk

Structure of talk

  • Introduction

  • Theory basis

  • Experimental evidence

  • Points for discussion

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


Introduction

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

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


Hysterics in the l h transition

Theory basis

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


Types of phase transitions

Types of ‘phase transitions’

Second order Transition

First Order Transition

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


Bifurcation diagrams topologies

Bifurcation diagrams: topologies

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


Poloidal force balance bifurcations

Poloidal force balance bifurcations

  • Some contributions are functions of

    -

  • Can produce bifurcation in Er

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

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


L h transition model ion orbit loss

L-H transition model: ion orbit loss

  • Orbit loss can lead to Er bifurcation

  • Associated reduction in transport can cause L-H transition

    S-I Itoh & K Itoh Phys Rev Lett 60 2276 (1988)

    K C Shaing & E C Crume Phys Rev Lett 3 2369 (1989)

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


Turbulent viscosity bifurcation

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)

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


Transport bifurcation diagram

Transport bifurcation diagram

  • Flow shear ωE depends on radial plasma gradients, g

  • Model diffusivity

  •  Bifurcation in flux and confinement transition:

    L-H or ITB

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

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


Hysterics in the l h transition

Experimental evidence

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


Nature of l h l hysteresis

Nature of L-H-L hysteresis

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.

Snipes PPCF 2000

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


Global v local parameters

Global v local parameters

DIII-D

Thomas PPCF 1998

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

  • Certainly is seen in edge gradients

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


Global v local parameters1

Global v local parameters

JET

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

  • Similarly for Ti,knee

Andrew PPCF 2008

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


Local parameters during l h l cycle

Local parameters during L-H-L cycle

C-Mod

Hubbard PPCF 2002

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

  • S-curve shown in several key edge gradient parameters

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


L h h l power thresholds in pure helium and deuterium plasmas were explored in nstx

L-H/H-L Power Thresholds in Pure Helium and Deuterium Plasmas 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

Use change in edge profiles as an

Indication of both L-H and H-L transition

Forward or back transitions not always

Obvious in Da signal even for D-plasmas.

- No Da indication in He-plasmas


L h transition powers linearly dependent on density not true for h l transitions

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

L-H

H-L


L h power thresholds for he and d similar

L-H Power Thresholds for He and D Similar

H-L power thresholds lower, indicating some

hysteresis

Normalize PRF + POH by density for comparison

Large error bars due to uncertainty in heating efficiency!


Hysterics in the l h transition

L-H transition general to stellarators, spherical tokamaks

Stellarators: 3 - D devices

Goal of C Hidalgo’s H-mode WS 2009 talk:

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

H-mode workshop, 2009


Summary

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.

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


Possible further work

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

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


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