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Hysterics in the L-H transition

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

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

  2. 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

  3. Structure of talk • Introduction • Theory basis • Experimental evidence • Points for discussion Hysteresis in the L-H-L transition, D C McDonald, ITPA, Princeton 2009

  4. 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

  5. Theory basis Hysteresis in the L-H-L transition, D C McDonald, ITPA, Princeton 2009

  6. Types of ‘phase transitions’ Second order Transition First Order Transition Hysteresis in the L-H-L transition, D C McDonald, ITPA, Princeton 2009

  7. Bifurcation diagrams: topologies Hysteresis in the L-H-L transition, D C McDonald, ITPA, Princeton 2009

  8. 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

  9. 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

  10. 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

  11. 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

  12. Experimental evidence Hysteresis in the L-H-L transition, D C McDonald, ITPA, Princeton 2009

  13. 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

  14. 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

  15. 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

  16. 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

  17. 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

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

  19. 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!

  20. 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

  21. 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

  22. 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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