An Etymological Dictionary of Astronomy and Astrophysics

In magnetohydrodynamics, an equation that describes the transport of plasma and magnetic field lines over time:
∂B/∂t = ∇ x (v x B) + η∇²B,

where B is the → magnetic induction, v is the plasma velocity, and η = (μσ)^-1 the → magnetic diffusivity. The first term on the right side represents → magnetic advection and the second term → magnetic diffusion.
The induction equation can also be expressed as:
∂B/∂t = -(v.∇)B + (B.∇)v - B(∇.v),

where the terms of the right-hand side stand for advection, stretching, and compression, respectively. Among these terms, net increase of the field can be done only through the stretching and compression.

See also: → induction; → equation.