Towards a Model of the L-H Power Threshold Scaling. Mikhail Malkov. Collaborators: P. Diamond and K. Miki UCSD 1 / 18

Transcription

1 Towards a Model of the L-H Power Threshold Scaling Mikhail Malkov UCSD Collaborators: P. Diamond and K. Miki 1 / 18

2 Outline 1 Basic physics of LH transition 2 Recent Incentive Experiments and Shortcomings of Available Models 3 Available Physical Models and their Retrotting to Studies of P th Minimum 4 Model Equations 5 Results and analysis 6 Conclusions 2 / 18

3 Mechanism and occurrence of LH transition originates via coupling of turbulence to low frequency shear ows by Reynolds work causes collapse of turbulence and turbulent transport growth of diamagnetic electric eld associated with P LH transition occur via a protracted I-phase or in a single burst of shear ow 3 / 18

4 Objectives of this work (ongoing) establish link between microscopics and macroscopics in power threshold scaling reproduce and understand observed threshold P th (n) minimum explore P th in terms of other parameters, such as e-i thermal coupling eciency, noise... investigate the role of heating prole in LH transition e-i heating split ratio mean shear in locking-in of the transition 4 / 18

5 Observations of power threshold minimum Ryter et al 2013 ion heat ux plays a dominant role in LH transition electron channel is ignorable But: in low-density regimes with dominant EC heating electrons must transfer energy to ions electron description must be separated from that of ions temperature and density dependence of collision rate need to be included (average values do not suce) 5 / 18

6 Preceding models: Advantages of 0-D E,U,N time (M & Diamond 2009) similar Predator-Prey dynamics in 0D+1D-k-space (M, Diamond & Rosenbluth 2001) N E U 0-D KD2003 model captures pre-transition limit-cycle oscillations (Kim & Diamond 2003) reproduces NL period growth (L. Schmitz, this meeting) allows simple dynamical system interpretation of L-I-H transition as Hopf bifurcation from unstable xed point to LC 6 / 18

7 0-D model prospective to another unstable (hyperbolic) FP (H-mode) nally to stable xed point QH 0.5 L E T N H QH M & Diamond / 18

8 New 1-D Numerical Model Based on 1-D numerical 5-eld model (Miki & Diamond 2012,13+) signicantly extends KD D model MD 2012 captures transition layer evolution but is incapable of separating species modify MD 2012 by adding separate electron heat transport equation include e-i thermal coupling depending on locally evolving temperatures and density include these parameters in ZF damping description include trapped electron growth 8 / 18

9 Predator-Prey Model Equations Heat transport i,e: [ ] P i,e + 1 t r r rγ(p) = ± 2m (r a) 2 i,e Mτ (P e P i ) + Q exp 2 r 2 Density χ, D t = Γ = (χ neo + χ t ) P r [ ] n t + 1 a r (a r) 2 r r rγ(n) = Γ a L 2 exp 2L 2 dep dep Γ (n) = (D neo + D t ) n r τ c C 2 s I 1 + α t V E, 2 V E ( = ρ i C s L 1 p L 1 p ) L 1 n Vϑ 9 / 18

10 Equations cont'd DW turbulence ( ) I t = γ L ωi α 0 E 0 α V V E 2 I +χ N r I I r, χ N ω C 2 s γ L = γ 0i C s R ZF energy R L p R L n E 0 t ( ) L R crit + γ 0e C s ( L 1 T e α 0 E 0 I = 1 + ζ 0 V ϑ γ 2 dampe 0 mean ow shear ( ) V ϑ = α 5 γ 0i C 2 a R s R L t R L p L n R µ neo ν ( ) ii q 2 R 2 V ϑ 1.17C s ρ i L 1 T crit ) + L 1 n I r 10 / 18

11 Transition dynamics, transition criterion take half-way to clean pedestal cross-check with DW,ZF,MF channels need transition criterion to scan P th ( n, He,i, L dep,... ) 11 / 18

12 Spatio-temporal dynamics of transition I-phase persists before transition clearly spatio-temporal behavior beyond 0-D model ZF signicantly advances into the core before transition 12 / 18

13 Spatio-temporal dynamics of transition slight temperature attening in the core due to enhanced turbulent transport I-phase in density 13 / 18

14 Accurate transition identication 0.50 <n> x-aver density n_scale=1.00_q= dat many transitions are poorly resolved select only well resolved transitions for density and power scans Qth <n> 0.7 n_scale=1.50_q= dat Shallow P th (n,....) minimum requires accurate determination of transition point Qth / 18

15 Identifying transitions, P th density scans <n> <n> n_scale=1.00_q[= ].dat n_scale=1.00_q[= ].dat L dep =0 0.8 L dep =0.4 <n> Q(t) Q(t) n_scale=1.00_q[= ].dat scan.pdw L dep = Q(t) Qth n_h 15 / 18

16 P th scans PL-H sharp rise to 0.02 very bottom of the curve is not robust in density scans (work ongoing) considerably more robust in other representations (such as e-i heating ratio) H spl=h i/(h i+h e) Power threshold minimum recovered P L-H <N> pre-trans / 18

17 Analysis threshold power increase for o-axis electron heat deposition (reduced electron-ion coupling) minimum power is predicted for heating mix scan as well as for density scan possibility of a global minimum in multi-parameter space no clear threshold minimum for pure ion heat deposition Ongoing work is concerned with quantifying the strength of hysteresis in terms of multiple macroscopic parameters and with relating this to observed back-transition shear ow and turbulence dynamics 17 / 18

18 Conclusions an extended 6-eld 1-D PDE model is developed (P e, P i, n, DW, ZF, Mean Flow) link between microscopics (e-i collisional heat exchange, turbulence) and macroscopics (transport barrier, P-n proles) in power threshold scaling is established threshold P th (n) minimum is reproduced and understood using a simple model of e-i heat transfer P th ( n, Ldep,.... ) is explored in terms of its dependence on other parameters, such as e-i thermal coupling eciency the role of heating prole in LH transition is investigated the role of e-i heating split ratio is studied, minimum of P th predicted role of mean shear in locking-in of transition is signicant 18 / 18