Changes between Version 9 and Version 10 of AstroBearProjects/resistiveMHD
- Timestamp:
- 08/11/11 17:26:05 (13 years ago)
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AstroBearProjects/resistiveMHD
v9 v10 42 42 43 43 where [[latex($\sigma$)]] is the material conductivity which depends on the electron-ion collision rate [[latex($\nu_{ei}$)]] which in term depends on the electron temperature [[latex($T^{-3/2}$)]]. [[BR]] 44 The diffusivity can thus be expressed as function of electron temperature[[BR]]44 The cross field diffusivity can thus be expressed as function of electron temperature[[BR]] 45 45 46 [[latex($\eta = 0.14 m_{e}^{1/2} c^2 \ln \Lambda F(Z_{eff})(k_B T_{e}^{3/2})$)]]46 [[latex($\eta = 0.14 m_{e}^{1/2} c^2 Z \ln \Lambda (k_B T_{e}^{3/2})$)]] 47 47 48 48 where [[latex($\ln \Lambda$)]] is the Coulomb logarithm:[[BR]] 49 49 50 [[latex($\ln \Lambda = 16.3+1.5 \ln T - 0.5\ln n$, (for $T < 4.2 \times 10^{5}$ K))]]50 [[latex($\ln \Lambda = 16.3+1.5 \ln T - 0.5\ln n$, (for $T < 4.2 \times 10^{5}$ K)\\$\ln \Lambda =$$22.8+1.5 \ln T - 0.5\ln n$, (for $T > 4.2 \times 10^{5}$ K) )]] 51 51 52 [[latex( $22.8+1.5 \ln T - 0.5\ln n$, (for $T > 4.2 \times 10^{5}$ K))]] 52 The parallel diffusivity however, is dependent on[[BR]] 53 54 [[latex($F(Z) = \frac{1+1.198Z+0.222Z^2}{1+2.996Z+0.753Z^2}$)]] 55 56 For [[latex($Z = 1$)]] case, parallel diffusivity is about half of cross field diffusivity.[[BR]] 53 57 54 58 = ======================================= =
