Changes between Version 4 and Version 5 of AstroBearProjects/multiphysics
- Timestamp:
- 02/14/12 15:21:44 (13 years ago)
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AstroBearProjects/multiphysics
v4 v5 190 190 where T is the electron temperature in eV, Zeff is the effective ion charge. The Coulomb logarithm is given by: [[BR]] 191 191 192 [[ 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))]][[BR]][[BR]]192 [[Image(coulomblog.png 60%)]][[BR]][[BR]] 193 193 194 194 THe Coulomb logarithm for interested number density is plotted below: [[BR]] … … 200 200 201 201 [[latex($F(Z) = \frac{1+1.198Z+0.222Z^2}{1+2.996Z+0.753Z^2}$)]][[BR]][[BR]] 202 203 Since the electron's maxwellian will be distorted when there is a strong outer magnetic field applied, the realistic resistivity can depend on the local field orientation. [[BR]] 204 The anisotropicity is around 2 for the parallel and cross field resistivity. This requires the electron mean free path to be much longer than the gyroradius under such a field: [[BR]] 205 [[latex($R_B << \lambda_{mfp}$)]][[BR]][[BR]] 206 or, the gyro frequency to be much greater than the mean electron ion collision frequency. [[BR]] 207 This effect is not considered currently. [[BR]][[BR]] 202 208 203 209 '''Resistivity Interface''' … … 220 226 221 227 The anisotropic thermal conduction is determined by the following equations: [[BR]][[BR]] 222 228 [[latex($\kappa_{align} = 5.6 \times 10^{-7} T^{5/2}$)]][[BR]] 229 [[latex($\kappa_{perp} = 3.3 \times 10^{-16} \frac{n^2}{T^{1/2}B^2}$)]][[BR]][[BR]] 230 The ratio between the cross and parallel diffusion can be written as: [[BR]][[BR]] 231 [[latex($r = 1.7 \times 10^{-3} \frac{n \beta}{T^4}$)]][[BR]][[BR]] 232 where T is in per 100 Kelvin, n is in per cubic centimeter.[[BR]] 223 233 224 234 Another user controlled isotropic thermal diffusion is added to make the code stubborn. There are . The microphysical thermal conduction is also flux limited, heat flow at each cell face [[BR]] 225 centers cannot surpass a fraction of electron mean thermal speed (Cowie, Mckee 1977): 235 centers cannot surpass a fraction of electron mean thermal speed (Cowie, Mckee 1977):[[BR]] 236 237 [[latex($q_{sat} = 5\phi \rho c_s^3$)]][[BR]][[BR]] 226 238 227 239 … … 232 244 First, the heat flux at each cell centers are calculated: on x interfaces, qx are directly obtained, qy is obtained by averaging the adjacent 4 qy, Same for y interfaces.[[BR]] 233 245 We do projections of heat flux twice: first onto the field direction, then to the face normal.[[BR]][[BR]] 234 235 236 We also calculate the saturation flux and project to the face normal. Remember, the saturation flux is always aligned with the field.[[BR]][[BR]] 237 238 246 [[Image(thermalconddiagram.png 60%)]][[BR]][[BR]] 247 248 We also calculate the saturation flux and project to the face normal. Remember, the saturation flux is always aligned with the field.[[BR]] 239 249 Both the projected heat flux and saturation flux are feed into the saturation function to calculate the final flux. The saturation starts at a "saturation point", which is controllable. [[BR]] 240 250 Below the saturation point, there is no saturation so there is no additional modification to the original heat flux. Above the saturation point, the flux gets saturated and gradually reach [[BR]] 241 251 the saturation flux. [[BR]][[BR]] 242 252 243 253 [[Image(saturationflux.png 60%)]][[BR]][[BR]] 244 254 245 255 '''Thermal Conduction Interface''' [[BR]]
