Dusty Plasma - Dynamics

Dynamics

Interest in the dynamics of charged dust in plasmas was amplified by the detection of spokes in the rings of Saturn. The motion of solid particles in a plasma follows the following equation:

where terms are for the Lorentz force, the graviational forces, forces due to radiation pressure, the drag forces and the thermophoretic force respectively.

The Lorentz force, the contributions from the electric and magnetic force, is given by:

where E is the electric field, v is the velocity and B is the magnetic field.

is the sum of all gravitational forces acting on the dust particle, whether it be from planets, satellites or other particles and is the force contribution from radiation pressure. This is given as:

The direction of the force vector, is that of the incident radation of photon flux . The radius of the dust particle is .

For the drag force there are two major components of interest, those from positive ions-dust particle interactions, and neutral-dust particle interactions. Ion-dust interactions are further divided into three different interactions, through regular collisions, through Debye sheath modifications, and through coulomb collisions.

The thermophoretic force is the force that arises from the net temperature gradient that may be present in a plasma, and the subsequent pressure imbalance; causing more net momentum to be imparted from collisions from a specific direction.

Then depending in the size of the particle, there are four categories:

1. Very small particles, where dominates over .
2. Small grains, where q/m ≈ √G, and plasma still plays a major role in the dynamics.
3. Large grains, where the electromagnetic term is negligible, and the particles are referred to as grains. Their motion is determined by gravity and viscosity.
4. Large solid bodies. In centimeter and meter-sized bodies, viscosity may cause significant perturbations that can change an orbit. In kilometer-sized (or more) bodies, gravity and inertia dominate the motion.