Generating a magnetic field by a rotating plasma

Abstract

In this paper we show, via an analytical study, new results for a rotating plasma generating a magnetic field. We study infinitely long cylindrical shells containing plasma. For a plasma of infinite conductivity we show that the existence of a magnetic field is compatible with the dynamics of two coaxial cylinders rotating at different uniform angular velocities, along with a single uniformly accelerated cylinder. In the case of finite conductivity, we show that under a series of constraints on the fluid characteristics and the dynamic fields, such as pressure and external force, the generation of a magnetic field is compatible with the dynamics of the cylindrical shells starting from null initial conditions of all the related fields. Finally, we show that the magnetic field generally is not parallel to the fluid velocity for both infinite and finite conductivity.

Analytical estimation of the Earth's magnetic field scale

“…In a previous work [6] the authors showed that a magnetic field can be generated in the laminar region of a fluid velocity under the condition ρ = ησµ, but such a condition is far from the usual condition of the celestial body and, more important, its magnitude would be of the order of B ∼ ΩR √ ρµ 0 where Ω is the rotational velocity, R is the radius of the outer core, and ρ is the density of the fluid in the outer core of Earth [7]. Inserting Earth's parameters would imply an intensity field of B ∼ 10 5 gauss that is very far from Earth's actual magnetic field value.…”