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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

slide5
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

slide12
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 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!

slide20

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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