Heat flux transported by fast electrons in front of lower hybrid wave antenna on EAST tokamak Nong Xiang 1, 2 In collaboration with Zhongzheng Men 1, 2, Jing Ou 1, 2,Xueyi Wang 3, Chunyun Gan 1, 2 1 Ins&tute of Plasma Physics, Chinese Academy of Sciences, Hefei 230031, China 2 Center for Magne&c Fusion Theory, Chinese Academy of Sciences, China 3 Physics Department, 206 Allison Laboratory, Auburn University, USA 8 th IAEA Technique Mee0ng Theory of Plasma instabili0es, June.12-14, 2017 Vienna, Austria
Outline Background and mo0va0on Par0cle-in-cell simula0on model 1) fast electrons 2) Secondary electrom emission Simula0on results Summary & discussions 2
Steady state scenarios are strongly desired by Tokamak reactors for which rf wave hea8ng and current drive is very important Ø ITER will have the first plasma in 2025. CFETR has been finished with conceptual design and begun engineering tests. Ø Steady state discharge is one of the main opera0on scenarios for ITER and CFETR. Lower hybrid current drive is a promising method sustaining plasma current and controlling current profile. ITER 3
EAST primary goal in 5 years: 400s steady state opera8on with 50% Boot strap current Ø Long pulse SS (>400s) H mode discharges with more than 50% boot strap current will be achieved on EAST in next 5 years. Steady state opera0ons on EAST are ozen stopped by accumula0on of impuri0es and lose of density control. Hot spots ozen observed in LHCD with high input power becomes the bo\leneck for realizing long pulse SS discharges on EAST! 4
Hot spots observed during LHCD experiments have seriously degraded EAST discharges Hotspots related to LHW launcher are generally observed. As P(f=4.6Ghz) >2MW, hot spots are observed 1) LH antenna guard limters are damaged badly 2) A lot of impuri0es are generated which degrade opera0ons Hot spots during LHCD are observed also on JET, Tore Supra, TdeV, ASDEX etc..
Mechanism for hot spot produc8ons: fast electron effects Ø Hot spots are caused by strong heat fluxes flowing to walls. Ø Why are strong heat fluxes produced during lower hybrid current drive? Fast electrons are responsible for the strong heat flux! (Rantamaki et al.nf 2000; Li et al. POP 15, Gunn et al. NF 2016) 6
Fast electrons generated by interac8ons of electrons and high n // modes Ø Electrons in the SOL interact with high-n // LH modes Ø The resonances can overlap as the input power is sufficiently high, resul0ng in forma0on of quasi-linear plateau Ø A frac0on of energy absorbed is deposited into limiters carried by fast electrons, giving rise to a large heat flux and cause the hot spots (only fast electrons ma\er!). (Rantamaki et al.nf 2000; Li, POP2015) (Rantamaki et al.nf 2000) 7
What is missed in the previous studies? Ø Sheaths natured formed in front of the limiter walls are neglected in es0ma0ng the heat flux to the walls. Sheaths are important! Why? 1) A sheath can distribute the heat flux carried by electrons and ions to walls 2) Presence of fast electrons can affect sheath structure, which in turn changes the heat fluxes of electrons and ions. It is a mul0-scale issues (fast electrons, background electrons, ions)! 8
Simula8on model (I) A PIC code GCPIC is developed to calculate the heat flux to the limiter, which includes sheaths. Plasma is confined between two limiters at x=0 and x=l. Parameters: L=0.2m (5396λD ) n0 = 1018m-3 Te= 25ev Model includes: 1. Fast electrons produced by resonant electron-wave interac0ons. 2. Secondary electron emissions at the limiter surfaces. 9
Simula8on model (II) Ø Fast electron model due to lower hybrid wave (Fisch 1978) f (u) = n 0 e 0.5u 2, u < u 1 or u > u 2 2π v te C 0 e wdw 1+Dw 3, u 1 < u < u 2 Ø Secondary electron emission yield δ(e 0 ) = δ m E 0 E m exp(2 2 E 0 E m ). δ m =0.7 (C), 0.9(W), E m = 350eV (C), 600eV(W) 10
Heat flux to limiters without fast electrons (theory) Ø The sheath expels electrons and accelerates ions, Ø For Maxwellian electrons & ions, floa0ng poten0al between the sheath edge and walls ϕ f 2.5T e Electrons wall Heat flux to walls: q e q i 0.2n 0 C s T e For n 0 =10 18 m 3,T e = 25ev, q e 0.5MW / m 2 ions Without fast electrons the heat flux to the limiter is small! 11
Results without fast electrons agree with sheath theory Ø Floa0ng poten0al and heat flux agree with theore0cal result. Electron and ion densities (top), and potential (bottom) as a function of the normalized distance for maxwellian electrons and ions. The sheath edge is indicated by the vertical line. Electron (a), ion velocity distribution function (b) and heat flux at x = 5394λ D. 12
Physical insight of fast electron effects Ø A sheath is formed to balance the par0cle fluxes. The sheath poten0al should be increased to reduce the fast electron flux. J e + J f = J i J e n 0 exp( eφ f / T e ), J f αn 0 exp( eφ f / T f ), T f >> T e J i n 0 C s. (Stangeby PPCF 95) Ø The ion heat flux is significantly increased. Ion energy at the wall, E i = T e φ f, eφ f >> T e, q i eγ i φ f >> q i,0 (without fast electrons, proportional to density) Fast electron energy at the wall, E f = T f +φ f q f eγ i E f < q i 13
Results in the presence of fast electrons but without SEE(I) Ø Loading the electrons with a quasi-linear plateau giving driven current J ~ 40KA/m 2 in the plasma Electron VDF in plasma region Ø Sheath poten0al is enhanced by nearly one order higher. 14
Results in the presence of fast electrons but without SEE(II) Ø Background electrons are repelled from sheath, but fast electrons can penetrate, giving a slow decay density profile. Electron VDF near the limiter surface Ø Ion heat flux is enhanced and exceed the electron heat flux. Total heat flux is increased by one order higher! Consistent with analysis 15
Effects of secondary electron emissions (I) Ø Secondary electrons emission (SEE) reduces the fast electron current, thus reduce sheath poten0al too. J e + J f = J i J e n 0 (1 δ e )exp( eφ f / T e ), J f αn 0 (1 δ f )exp( eφ f / T f ), T f >> T e J i n 0 C s. Ø SEE strongly depends on materials. Consider C and W Electron energy distribu0on at wall 16
Effects of secondary electron emissions (II) Ø Sheath poten0als are reduced with SEE. Ø Sheath width decreases with SEE. Ø Ion heat flux is comparable to electron s Total heat flux is about 8MW/m2 which may cause hot spot! 17
Summary & Discussions Ø The sheath is important in the calcula0on of electron and ion heat fluxes. The presence of fast electrons can significantly increase the sheath poten0al. The resul0ng sheath field can significantly accelerate ions which causes enhancement of ion and electron heat fluxes and make the ion heat flux comparable to the electron s. For typical LHCD parameters on EAST, the total heat flux > 8MW/m 2, responsible for hot spots observed. In addi0on, the energe0c ions may produce heavily spu\ering and damage the walls. Ø The secondary electron emission can reduce sheath poten0al, increasing the electron heat flux. The total heat flux to the limiter walls remains nearly the same. 18