H. "Saleem

K. Watanabe

T." Sato

National Institute for Fusion Science (NIFS-Repository)

§ 1 3. Thermoelectric Effect on Magnetic Field Generation H.Saleem, K.Watanabe and T.Sato For a long time, it has been commonly be-lieved that unfavorable pressure gradient can give rise to very strong magnetic fields in unmagne-tized nonuniform plasmas [1]. These investiga-tions usually take into account the electron dy-namics only, which can be collionless or colli-sional. Several authors have discussed surface wave-like magnetic electron drift vortex (MEDV) modes [2] in the limit Wpi < < w < < Wpe (where w · w are ion and electron plasma oscillation P'' pe frequencies, respectively). The so-called thermo-electric term Vno x VTt (where no is the unper-turbed density and Tt is the perturbed electron temperature) is considered to be the main source of magnetic fluctuations in such plasmas. Recently [3] it has been shown that the mag-netic fluctuations can be generated on an ion time scale in the limit w < < Wpe. The curl of the elec-tron equation of motion in unmagnetized plasmas does not give e 1 atv X Vt = --\1 X Et + --\lno X VTt, (2) m mno where e is the charge amd m is the mass of an electron. The subscripts naught and one denote the equilibrium and perturbed quantities, respec-tively. We elaborate this point in detail in the following. The curl of Eq.(l) gives m(Vno x 8tVt +no \1 x 8tvl) = -e(no \1 x Et +\!no x El), 236 (3) If one takes the cross product of Vno with Eq.(l) and then subsitutes the tenn Vno x E1 in Eq. (3), one can obtain Eq.(2). Si1nilarly, if one first divides Eq.(l) with no and then takes the curl of the same, it would yield Eq.(2). This is what the previous authors have done to obtain Eq. (2). But, in our opinion, the appearance of the thermoelectric term is due to inappropriate order-ing of the terms involved. To elaborate this point, another way to reach Eq.(2) through Eq.(3) has been presented here. By ignoring ion dynamics ' 1 1 and displacement current, one drops ( 6.5 ) or ( 7. 7 ) compared to 1 in the calculations for H or D-D plasmas. On the other hand, the second term on right-hand side (RHS) of Eq.(3) is ~- times smaller than the first (where K;1 is the density scale length and k is the wave vector). The local approximation requires !f- < < 1. If ( rv ~ is the smallness parameter' then ( rv ¥- seems natural to be assumed. We notice that on the one hand terms of order t are ignored and on the other hand the thermoelectric term is retained which is also of the same order of magnitude. This work shows that the thermoelectric tenn does not seem to be the 1nain source of magnetic field fluctuations linearly. Furthermore the order of magnitude of the magnetic field estimated by including ion motion [3] turns out to be the same as has been observed experimentally. REFERENCES 1. J.A.Starnper et al. Rev.Lett. 26, 1012 (1971). 2. R.D.Jones, Phys.Rev.Lett. 51, 1269 (1983). 3. H.Saleem, Phys. Rev. E 54, 4469 (1996). 

Thermoelectric Effect on Magnetic Field Generation

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