Resistive timescale: Difference between revisions

Jump to navigation Jump to search
no edit summary
No edit summary
No edit summary
Line 1: Line 1:
The resistive timescale is the typical time for the diffusion of a magnetic field into a resistive plasma.
The resistive timescale is the typical time for the diffusion of a magnetic field into a resistive plasma.
Based on Faraday's Law,
Based on Faraday's Law,
:<math>\frac{d\vec B}{dt} = \vec \nabla \times \vec E,</math>
:<math>\frac{\partial \vec B}{\partial t} = -\vec \nabla \times \vec E,</math>
Ohm's Law,
Ohm's Law,
:<math>\vec E = \eta \vec j,</math>
:<math>\vec E = \eta \vec j,</math>
Line 7: Line 7:
:<math> \vec \nabla \times \vec B = \mu_0 \vec j,</math>
:<math> \vec \nabla \times \vec B = \mu_0 \vec j,</math>
one immediately derives a diffusion type equation for the magnetic field:
one immediately derives a diffusion type equation for the magnetic field:
:<math>\frac{d\vec B}{dt} = \frac{\eta}{\mu_0} \vec \nabla \times \vec \nabla \times \vec B = - \frac{\eta}{\mu_0} \nabla^2 \vec B,</math>
:<math>\frac{\partial \vec B}{\partial t} = -\frac{\eta}{\mu_0} \vec \nabla \times \vec \nabla \times \vec B = \frac{\eta}{\mu_0} \nabla^2 \vec B,</math>
since  
since  
: <math>\vec \nabla \cdot \vec B = 0.</math>
: <math>\vec \nabla \cdot \vec B = 0.</math>

Navigation menu