Topology of magnetodynamic flows: Kinetic and internal energy of a one-fluid plasma

A mathematical formalism describing the relation between the structure of a one-fluid, collisionless plasma and the topological features of the vector lines of the magnetic, velocity and electric fields is suggested and a rigorous approach to the problem of determining the local features of the plasma from the properties of the velocity field v, observed at a chosen point of space, is developed. The limits to drawing conclusions from the observational data (such as encountered in magnetospheric physics) are outlined in Section 2.Energization of a plasma during a stationary convection is an example of a process characterized by the properties of the tensor $\text{V}\text{= grad}\text{v}$. In particular, if the plasma density and the velocity and pressure components in a volume element of the plasma are known, then the time rates of change of the kinetic and internal energies are described by stretchings of the element and by its shearing in the surface defined by the vectors of magnetic field and perpendicular velocity. Criteria according to which plasma gains or loses kinetic and internal energies are derived.