Paul Lorrain

Electrostatic charges in v*B fields: the Faraday disk and the rotating sphere

When a conductor moves in a magnetic field, v*B acts like a distributed source. If the divergence of this vector is not zero, then the divergence of E is not zero either and the conductor carries electrostatic charges whose fields are as important as v*B. The Faraday disk and a conducting sphere rotating in a uniform magnetic field serve as examples. This little known effect plays a fundamental role in magnetohydrodynamic phenomena.

Two dynamical models for solar spicules

Solar spicules are luminous jets that erupt up to 10 000 km from the surface of the Sun and have diameters, all along their length, of only about 150–200 km. We first review some recent observations made at the Hα wavelength. According to our models, a solar spicule is a self-channelled proton beam emitted by a magnetic element and surrounded by a cold sheath. The beam originates in a self-excited dynamo that exploits a v × B field and that could be situated either below or above the element, where v is the local plasma velocity and B is the local magnetic flux density. In falling back, the sheath provides a return current of protons that cancels the outgoing current. We discuss the channelling of charged-particle beams of very large cross-section and propose velocity channelling, which is apparently a new concept. We assume a steady state and a hydrogen plasma.

Magnetic fields in moving conductors: four simple examples

Assuming given externally applied magnetic fields and given velocities, we calculate the currents induced in moving conductors of arbitrary conductivity, and the net magnetic field. Three of the four conductors are solid, and the fourth is fluid. We find that, in these examples, the net magnetic field is either unaffected by the moving conductor, or distorted downstream, or distorted upstream. In all cases the net magnetic field is static.

Electrostatic charges in v × B fields

Professor D?V?Redzic corrects an error that appeared in my 1990 paper on electrostatic space charges in v ? B fields. These charges are almost invariably disregarded, despite the fact that they play a crucial role throughout magnetohydrodynamics.

Chromospheric heating by electric currents induced by fluctuating magnetic elements

We refer to two papers by Goodman (1995, 1996) on the heating of the chromosphere by large-scale electric currents, and to our paper (Lorrain and Koutchmy, 1993) on magnetic elements. Goodman assumes that the dynamo that runs a magnetic element stops operating at t = 0. From then on, the magnetic field decays exponentially, and the induced currents heat the chromosphere. The time constants calculated by Goodman disagree with the observed values, possibly because he disregards the driving dynamo. Also, he assumes static conditions, but his magnetic force density appears suddenly when the dynamo stops, and it is about equal to the gravitational force density. The magnetic force acts downward and fluctuations in the current flowing through the magnetic element should induce vertical oscillations at the photosphere. This point should be investigated further.

The Cowling 'limiting-points' proof of his anti-dynamo theorem

According to the Cowling antidynamo theorem, a self-excited steady-state dynamo in a conducting fluid cannot be axisymmetric. One of his proofs, which is based on the impossibility of the existence of limiting points, was referred to by I. Alexeff (ibid., vol.17, pp.282-283, Apr. 1989) who showed that it is not valid in diffuse plasmas. It is here shown that Cowlings limiting-points proof, which implicitly applies to closed systems, rests on an unrealistic assumption. Cowlings proof is shown not to apply to one particular type of open system. >

The disk-dynamo model for natural dynamos

We analyze the kinematic and the dynamic self-excited disk dynamo models for natural dynamos. In the kinematic model (given disk angular velocity), the magnetic field can either increase or decrease exponentially with time, or it can be constant if the angular velocity has a specific value that is a function of the geometry and of the resistance of the circuit. With the dynamic disk dynamo (given mechanical power input), there are both transient and steady-state solutions, and the steady-state magnetic flux density is proportional to the square root of the power input. The polarity of the induced magnetic field in either dynamo is the same as the seed field, and erratic polarity reversals can be expected if the power input is erratic.