Plasma
Filamentation, the striations or "stringy things" seen in a "plasma ball", the aurora, lightning, electric arcs, and nebulae. They are caused by larger current densities, and are also called magnetic ropes or plasma cables.
Double layers, localised charge separation regions that have a large potential difference across the layer, and a vanishing electric field on either side. Double layers are found between adjacent plasmas regions with different physical characteristics, and can accelerate ions and produce synchrotron radiation (such as x-rays and gamma rays).
Birkeland currents, a magnetic-field-aligned electric current, first observed in the Earth's aurora, and also found in plasma filaments.
Circuits. Birkeland currents imply electric circuits, that follow Kirchhoff's circuit laws. Circuits have a resistance and inductance, and the behaviour of the plasma depends on the entire circuit. Such circuits also store inductive energy, and should the circuit be disrupted, for example, by a plasma instability, the inductive energy will be released in the plasma.
Cellular structure. Plasma double layers may separate regions with different properties such as magnetization, density, and temperature, resulting in cell-like regions. Examples include the magnetosphere, heliosphere, and heliospheric current sheet.
Critical ionization velocity in which the relative velocity between an ionized plasma and a neutral gas, may cause further ionization of the gas, resulting in a greater influence of electomagnetic forces.
Ultracold plasmas
It is also possible to create ultracold plasmas, by using lasers to trap and cool neutral atoms to temperatures of 1 mK or lower. Another laser then ionizes the atoms by giving each of the outermost electrons just enough energy to escape the electrical attraction of its parent ion.
The key point about ultracold plasmas is that by manipulating the atoms with lasers, the kinetic energy of the liberated electrons can be controlled. Using standard pulsed lasers, the electron energy can be made to correspond to a temperature of as low as 0.1 K a limit set by the frequency bandwidth of the laser pulse. The ions, however, retain the millikelvin temperatures of the neutral atoms. This type of non-equilibrium ultracold plasma evolves rapidly, and many fundamental questions about its behaviour remain unanswered. Experiments conducted so far have revealed surprising dynamics and recombination behaviour that are pushing the limits of our knowledge of plasma physics.
Mathematical descriptions
Plasmas may be usefully described with various levels of detail. However the plasma itself is described, if electric or magnetic fields are present, then Maxwell's equations will be needed to describe them. The coupling of the description of a conductive fluid to electromagnetic fields is known generally as magnetohydrodynamics, or simply MHD.
Fluid
The simplest possibility is to treat the plasma as a single fluid governed by the Navier Stokes Equations. A more general description is the two-fluid picture, where the ions and electrons are considered to be distinct.
Kinetic
For some cases the fluid description is not sufficient. Kinetic models include information on distortions of the velocity distribution functions with respect to a Maxwell-Boltzmann distribution. This may be important when currents flow, when waves are involved, or when gradients are very steep.
Particle-in-cell
Particle-in-cell (PIC) models include kinetic information by following the trajectories of a large number of individual particles. Charge and current densities are determined by summing the particles in cells which are small compared to the problem at hand but still contain many particles. The electric and magnetic fields are found from the charge and current densities with appropriate boundary conditions. PIC codes for plasma applications were developed at Los Alamos National Laboratory in the 1950's. Although often more calculationally intensive than alternative models, they are relatively easy to understand and program and can be very general.
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