Mathematics – Logic
Scientific paper
Jul 1982
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1982p%26ss...30..701h&link_type=abstract
Planetary and Space Science, vol. 30, July 1982, p. 701-709.
Mathematics
Logic
4
Collisionless Plasmas, Magnetohydrodynamic Flow, Plasma Dynamics, Internal Energy, Kinetic Energy, Topology
Scientific paper
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. Energization of a plasma during a stationary convection is an example of a process characterized by the properties of tensor V = grad 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.
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