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

2. Hysteresis in the L-H-L transition, D C McDonald, ITPA, Princeton 20092/22 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

3. Hysteresis in the L-H-L transition, D C McDonald, ITPA, Princeton 20093/22 Structure of talk Introduction Theory basis Experimental evidence Points for discussion

4. Hysteresis in the L-H-L transition, D C McDonald, ITPA, Princeton 20094/22 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

5. Hysteresis in the L-H-L transition, D C McDonald, ITPA, Princeton 20095/22 Theory basis

6. Hysteresis in the L-H-L transition, D C McDonald, ITPA, Princeton 20096/22 Types of ‘phase transitions’ First Order Transition Second order Transition

7. Hysteresis in the L-H-L transition, D C McDonald, ITPA, Princeton 20097/22 Bifurcation diagrams: topologies

8. Hysteresis in the L-H-L transition, D C McDonald, ITPA, Princeton 20098/22 Poloidal force balance bifurcations Some contributions are functions of - Can produce bifurcation in E r K Itoh et al Transport & Structural Formation in Plasmas 1999 IoP p 239

9. Hysteresis in the L-H-L transition, D C McDonald, ITPA, Princeton 20099/22 L-H transition model: ion orbit loss Orbit loss can lead to E r 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)

10. Hysteresis in the L-H-L transition, D C McDonald, ITPA, Princeton 200910/22 Turbulent viscosity bifurcation Increasing flow increases ω E Increasing ω E 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)

11. Hysteresis in the L-H-L transition, D C McDonald, ITPA, Princeton 200911/22 Transport bifurcation diagram Flow shear ω E 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)

12. Hysteresis in the L-H-L transition, D C McDonald, ITPA, Princeton 200912/22 Experimental evidence

13. Hysteresis in the L-H-L transition, D C McDonald, ITPA, Princeton 200913/22 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.

14. Hysteresis in the L-H-L transition, D C McDonald, ITPA, Princeton 200914/22 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

15. Hysteresis in the L-H-L transition, D C McDonald, ITPA, Princeton 200915/22 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

16. Hysteresis in the L-H-L transition, D C McDonald, ITPA, Princeton 200916/22 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

17. NSTX H-Mode WorkshopSept. 30 – Oct. 2, 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 P LH and P HL “Perturbation technique” used to determine HHFW electron heating efficiency (  0.1) Ion heating efficiency similar In what follows, P RF is taken to be P RF,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

18. NSTX H-Mode WorkshopSept. 30 – Oct. 2, 2009 18 L-H Transition Powers Linearly Dependent on Density; Not True for H-L Transitions L-H H-L

19. NSTX H-Mode WorkshopSept. 30 – Oct. 2, 2009 19 L-H Power Thresholds for He and D Similar H-L power thresholds lower, indicating some hysteresis Normalize P RF + P OH by density for comparison Large error bars due to uncertainty in heating efficiency!

20. 20 Carlos HidalgoH-mode workshop, 2009 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 L-H transition general to stellarators, spherical tokamaks

21. Hysteresis in the L-H-L transition, D C McDonald, ITPA, Princeton 200921/22 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.

22. Hysteresis in the L-H-L transition, D C McDonald, ITPA, Princeton 200922/22 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