G. Kawamura

L.W. Yan

M. Ueno

N. Ohno

Y. Tomita

Y.D. Pan

Z.H. Huang

National Institute for Fusion Science (NIFS-Repository)

-0.02-0.015-0.01-0.00500.00500.050.10.150.20 0.2 0.4 0.6 0.8 1Ti / Tec(Ew2 - E w2 _Ti=0) / Ew2_Ti=0Teh / Tec = 3.020.011.522.530123456E w2  / (nse Tec / ε 0)Λ  jwΛ iw|Ti=0Λ ew(a)02468101205101520250 0.05 0.1 0.15 0.2neh / nseE w2  / (nse Tec / ε 0)Λ  jwΛ iw|Ti=0Λ ew(b) The electric field Ew at a plasma-facing wall (PFW) for a two-temperature Maxwellian distribution of electrons at the sheath entrance (TTED) is obtained from the Poisson equation:  Ew2 ≡Ew2nseTec / ε0=Λiw−Λew , Λ jw ≡−2 q jnseTecdφn j (φ)0φw∫ .  (1) Here nse and Tec are the electron density at the sheath entrance and electron temperature of the cold component. The electron contribution Λew is expressed by using the wall potential drop φw:  Λew =2nseTecnekTek{1− eeφw /Tek 11+ erf ( −eφw / Tek )k=c,h∑        −2 −eφw / Tekπ[1+ erf ( −eφw / Tek )]eeφw /Tek } (2) The contribution from ions Λiw with a shifted Maxwellian distribution at the sheath entrance is expressed as follows:       Λiw =8νese2 TiZiTec[1+ erf (νese )]νeseπ        dξ  ξ  ( ξ2 +αese −ξ) exp[−νese2 (ξ−1)2]0∞∫ , (3) where  νese ≡cs,DETυthi=12(ZiλesTecTi+ γi ),        αese ≡−Zieφwνese2 Ti=−2ZieφwZiλesTec + γiTi,        and  λes ≡ nse / (nesc + neshTecTeh) . (4) When the ion temperature Ti approaches to zero, the ion part, Eq. (3), approaches a value of       Λiw Ti=0= 2λes[ 1−2λeseφw(Ti = 0)Tec−1] . (5) Here φw(Ti = 0) is the potential drop in the case of Ti = 0 and the TTED. In the case where the effect of the ion temperature is neglected, the normalized wall electric field, which depends on the hot electron component, is shown in Fig.1,for the cases of (a) a lower electron temperature of the hot electron component (LET), Teh/Tec = 3.0, and (b) a higher one (HET), Teh/Tec = 20.0. The much larger wall drop gives us an approximate form of the electron component Λew ,       Λew ~ 2(nec/nse) + 2(neh/nse)(Teh/Tec)          = 2 + 2 [(Teh/Tec) – 1] (neh/nse), (6) which comes from the first terms of the cold and hot components in Eq. (2). In this case, the terms including the wall potential drop are neglected. This approximate form is proportional to neh/nse and has the dependences shown in Fig. 1 (a) and (b). The ion part Λiw|Ti=0, where Ti = 0, represents the dependence of the wall potential drop. In the case of HET, the maximum of the electric field occurs at higher (nec/nse), which is a result of the functional dependence on neh/nse, i.e.  Λew ∝ (neh / nse ) [Eq.(5)]   and  Λiw ∝ −φw(Ti = 0) ∝ ln(neh / nse )  at the higher nec/nse.  The normalized changes of the electric field due to the effect of finite ion temperature are shown in Fig. 2, where neh/nse is 0.1, Ti/Tec < 1.0 for (a) LET, Teh/Tec = 3.0, and (b) HET, Teh/Tec = 20.0. The normalized square of electric field at Ti = 0 are 2.012 and 11.67 for the case LET and HET, respectively. The changes are complex because the effect of the finite ion temperature changes the wall potential drop, Eq. (3), as well as the ion contribution to Ew. The normalized change of LET, however, is smaller than 2 %. In the case of HET, it is as large as 20 %.                     Fig.1 Normalized electric field at PFW. (a) LET,  Teh/Tec = 3.0, and (b) HET, Teh/Tec = 20.0.            Fig.2 Normalized changes of electric field at PFW.  Teh/Tec = 3.0, and Teh/Tec = 20.0, where neh/nse is 0.1. 362§21. Electric Field at a Plasma-Facing Wall for a Two-Temperature Electron DistributionTomita, Y., Kawamura, G.,  Ueno, M., Ohno, N. (Nagoya Univ.),  Huang, Z.H., Pan, Y.D., Yan, L.W. (Southwestern Institute of Physics)

Electric Field at a Plasma-Facing Wall for a Two-Temperature Electron Distribution

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