Infernal modes and physical interpreta3on of the edge harmonic oscilla3ons in tokamak QH mode discharges

Infernal modes and physical interpreta3on of the edge harmonic oscilla3ons in tokamak QH mode discharges Linjin Zheng, M. Kotschenreuther, and P. Valanju Ins3tute for Fusion Studies University of Texas at Aus3n, TX 78712 1

Outline I. Mo%va%ons: Experimental observa3ons of edge harmonic oscilla3on (EHO) The differences between ELMs and EHO Infernal (or low magne3c shear) modes vs EHO II. Equilibrium with bootstrap current III. Edge instabili%es without FLR IV. Edge instabili%es with FLR V. Discussion and conclusions 2

Observa%on of EHOs at DIII- 3 Burrell et al., Phys. of Plasmas 12, 056121 (2005) 4

Observa%on of OMs (EHOs) at JET E.R. Solano, IAEA FEC, 2010 5

Exis%ng peeling ballooning theory Snyder et al. Nucl. Fusion 44 (2004) 320 6

Internal (EHOs) versus external (ELMs) modes Instabili3es ELMs EHOs: Infernal modes ELMs: Nonlinear coupling of the SOL current, etc. Burrell et al., Phys. of Plasmas 12, 056121 (2005) 7

Infernal modes at ITB and pedestal Internal transport barrier: Pedestal: q maximum q minimum 1. No ELMs- like modes at ITB 2. The snake modes observed both at ITB and at QH mode pedestal 8

Tokamak edge features 1. There is a current jump between plasma edge & SOL 2. Excessive charges: Plasma edge: nega3ve Divertor sheets: posi3ve 3. SOL current excita3on In addi3on to External modes more unstable - - - peeling mode 9

ELM physics Peeling off modes (Zheng and Furukawa, PoP 2014): 1. Peel off the hot edge plasma to SOL. 2. Leads to the charge recombina3on nega3ve charge at plasma edge and posi3ve charge at divertor sheets Consequently, the SOL current bursts. Posi3ve feed back (Zheng, et al, PRL 08): 1. The SOL current burst enhances field line reconnec3on => ELMs 2. The hoop force drives the magne3c island to move outwardly => blob transport 10

EHO/OMs are not peeling ballooning modes Experimental observations: 1. Modes resonate at the pedestal top 2. Mode frequencies are n-multiple of rotation frequency at pedestal n=3 n=2 top n=1 Peeling mode has resonance in the vacuum region and therefore does not fit the frequency of experimentally observed modes. 11

Ideal MHD is inapplicable at pedestal for n > 3 ω * > ω 3 Diamagne%c frequency at pedestal Peak at pedestal Diamagne3c drik frequency profile: Directly propor3onal to pressure gradient Inversely propor3onal to density 12

Equilibrium: Reduced magne%c shear profile due to the bootstrap current Equilibrium pressure and safety factor profiles computed by VMEC. Rota%on and density have same profiles as pressure Five cases: q_plateau = 4.1, 4.05, 4., 3.96, 3.92 14

Current and safety factor reconstruc3on C.E. Kessel et al., Nucl. Fusion 47 (2007) 1274 There is a safety factor maximum q max (or reduced magnetic shear) near plasma edge 15

MHD stability computed by AEGIS code The case with q- plateau > 4 is more unstable, because higher pressure gradient meets with low magne3c shear. 16

Outline I. Mo%va%ons: Experimental observa3ons of edge harmonic oscilla3on (EHO)/ outer modes (OMs) The differences between ELMs and EHO Infernal (or low magne3c shear) modes vs EHO II. Equilibrium with bootstrap current III. Edge instabili%es without FLR IV. Edge instabili%es with FLR V. Discussion and conclusions 17

MHD eigen modes: n = 1 Infernal mode harmonic: m = 4 18

Stability diagram with rota%on n = 1, q_s > 4 Infernal mode features: Frequency is independent of wall posi3on Growthrate is independent of rota3on frequency Mode frequency is close to the rota3on frequency at pedestal top - - - agree with exp. observa3ons 19

Stability diagram with rota%on n = 1, q_s < 4 It is not as typical of infernal mode as the q_p = 4.1 case, due to peeling mode coupling - - - q=4 surface is close to the plasma- vacuum interface. Infernal mode is s3ll predominant: Frequency is independent of wall posi3on Growthrate is independent of rota3on frequency Mode frequency/growthrate drops 20

Stability diagram with rota%on n = 1, 2, 3 q_s > 4 ω = nω rule: agree with experimental observa3ons q_s < 4 21

Basic set of equa%ons and the AEGIS code Basic set of equa3ons: where Generalized energy principle where 23

FLR stabiliza3on and q- plateau FLR stabiliza3on effect are much stronger when the q- plateau is closer or lower than an integer This is because the infernal harmonic shiks to the edge, where the diamagne3c frequency is bigger. Without FLR With FLR 24

EHO- like frequency mul3plying rule EHO- like frequency mul3plying rule: ω = nω is s3ll preserved with FLR effects. FLR or diamagne3c drik effects are important for not very high n modes Without FLR With FLR 25

Rota3on direc3on effects Co- rota3on is more effec3ve for stabiliza3on 26

Discussion: ELMs 1. There is a current jump between the edge plasma inside the last closed flux surface and SOL. 2. The peeling- ballooning modes can readily convert to the tearing modes - - - the peeling- off modes. 3. The H- mode edge confinement is worse than the conven3onal kink/ballooning es3mate. But, this may be good for avoiding the global disrup3on. 28

Global and edge- localized relaxa3ons Disrup%on Halo current Low n, global kink => tearing ELMs SOL current Edge localized, kink => tearing 29 Some illustra3on figs are loaded from web

Conclusions: EHOs I. Bootstrap current reduce the local magne3c shear, so that infernal modes develop II. Infernal modes reproduce EHO/OMs features observed experimentally: the ω = nω rule the n=1 mode frequency is close to the rota3on frequency at pedestal top III. Peeling or kink modes are not easy to explain the frequency features of EHO/OMs. 30

Infernal modes at ITB and pedestal ITB q minimum Ohmic current Snake type modes ω = nω Transport barrier Pedestal q maximum Bootstrap current Snake type modes ω = nω Transport barrier 31