Induction Equation Diffusion term Advection term

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Presentation transcript:

Induction Equation Clare E Parnell School of Mathematics and Statistics

Induction Equation Diffusion term Advection term  If Rm >> 1 then magnetic field advected:  If Rm << 1 then magnetic field diffuses:

Diffusion Equation Consider what happens to the following magnetic field after diffusion

Diffusion Equation Solution for magnetic field: Solution for current density:

Diffusion - Evolution of the magnetic field lines

Diffusion - Evolution of Bz versus x

Diffusion - Evolution of jy versus x

Advection Equation Consider what happens to the following magnetic field B moved by the flow v

Advection Equation Solution for magnetic field: Solution for current density:

Advection - Evolution of the magnetic field lines

Advection - Evolution of Bz versus x

Advection - Evolution of jy versus x

Importance On Sun vast majority of plasma is advected except where small length scales are created, e.g., in current sheets. Combination of advection and diffusion known as magnetic reconnection

Importance Magnetic reconnection important in: Powering solar flares Heating solar corona Driving solar wind Triggering CMEs