Changes between Version 3 and Version 4 of ResistiveMhd


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Timestamp:
01/04/21 13:58:42 (4 years ago)
Author:
Jonathan
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  • ResistiveMhd

    v3 v4  
    135135
    136136
     137The Hall frequency is given by $\omega_H=\frac{e  B}{m_i c}$ and the corresponding length scale $L_H = \frac{v_{A}}{\omega_H}$
     138
     139
     140Comparing the advective and the Hall terms, we can calculate the length scale for magnetic gradients below which the Hall term becomes larger than the advective term.
     141
     142$L = \frac{B}{n e v}$
     143
     144For the lab experiments, $B = 5 T$, $v = 60 \mbox{km/s}$, $n=1\times 10^{18} \mbox{cm}^{-3}$ which works out to give
     145
     146$L = \frac{5\times 10^4 G}{\sqrt{4\pi} \left ( 1\times 10^{18}\right) \left( 6 \times 10^6 \right) \left ( 5.67956774 \times 10^{-20}  \right )} \frac{\mbox{g}^{1/2} \mbox{cm}^{-1/2} \mbox{s}^{-1}}{\mbox{cm}^{-3} \mbox{cm}^1 \mbox{s}^{-1} \mbox{g}^{1/2} \mbox{cm}^{1/2} } = .04 \mbox{cm}$
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    137150
    138151== Discretization ==