The most typical plasma configurations are fibers through which an electric current circulates (pinch). We find them in the channels within lightnings, in solar protuberances and in distant nebulae and in the nuclei of galaxies. As spherical structures are characteristic for gravitational interactions (stars, globules, and planets) so are cylindrical structures characteristic for plasmas. The axial current generates an azimuthal magnetic field. This field compresses the pinch due to the gradient of magnetic pressure pm = B2/2μ and against it reacts the gradient of material pressure and radiation (in the stars the pressure gradient of radiation and matter react against gravity). The presence of fibrous structures in the Universe regularly signifies the presence of ionized matter and magnetic fields.
Plasma fibers – pinch
In the plasma there can be manifestations of a great diversity of waves and oscillations. The richness of these phenomena is given by the response of plasma to electric and magnetic fields. This response is lacking in normal fluids and the waves that propagate in gases and liquids do not reach even one tenth the wave modes that propagate in the plasma. Roughly speaking the waves can be classified into two sets:
The typical motion of the charged particles is in the form of circles or helices around the magnetic field lines. This motion is called Larmor rotation (gyration, cyclotron motion). The motion frequency is called cyclotron frequency (ω = QB/m) and the radius of orbit is the Larmor radius (RL = mv/QB). If there is in the plasma present some other field (for example, electric), which slowly changes in time and space in comparison with the period and radius of the Larmor rotation, then a drift is manifested. It is about a motion of charged particles which is rolling sideward perpendicularly to both the electric field (or other field) and the magnetic field. Such curves we call trochoids (a special example is the cycloid). The velocity of the sideward motion (drift) is vD = F×B/QB2. For the electric field F = QE, the magnitude of this velocity is vD = E/B. It is a well known fact that the ratio of the electric to the magnetic field is the typical velocity within a given system. In electromagnetic waves, for example, E/B = c. In the plasma it is the typical drift velocity of the particles.
The charged particles are expelled from the strongest zone of the magnetic field by force F = −μ grad B. This force produces for example the phenomenon know as magnetic mirror, where the particles are reflected in the zones with higher density of magnetic force lines to the zones of lower density of the same lines. It also acts on charged particles which rotate along the magnetic field force-lines of the Earth, which were captured from the solar wind. In the polar zones, where the field is stronger (force lines are denser) the particles are reflected and travel back along the force lines. In the places where particles are reflected appears a synchrotron or bremsstrahlung radiation.
The plasma is like a sack of fleas. In the laboratory it always escapes there where we do not want it to. The culprit of this can be different types of instabilities in the plasma, which in the Universe can develop into very interesting structures. We refer to instability, whenever small events (random fluctuations, disturbs product of external influences, etc.) lead to a complete change in the plasma configuration. Let us show just a few of them:
Instability “neck lace beads” [also known as ‘sausage’ or m = 0 (N. of T.)]: If a plasma fiber with axial current, strangles itself, then the induced magnetic field will deepen that strangling until the fiber disintegrates into smaller zones or “neck lace beads”. This instability is strongly supressed in helical pinches, where the current and the magnetic field have both axial components and azimuthal (around a circumference) components creating a spiral of fibers.
Kink instability: In the case that the plasma fiber has axial current and randomly bends, then the induced magnetic field will deepen that bending. Even this instability is partially supressed in helical pinches.
Diocotron instability: If for some reason a separation of electric charg in the radial direction of the pinch occures, there appears a non-zero electric field which, together with the axial magnetic field Bz produces a drift of the azimuthal velocity vφ. The entire pinch then begins to rotate with differential rotation (the zones at different distances from the axis rotate with different velocity). In the surface of the pinch two zones, with different velocity, become neighbors (the pinch which rotates and its surrounding media) and can lead into an instability known from observations in fluids. We call this diocotron instability. The typical consequence is a modification of the pinch surface into a vortex structure.
Translation: Arturo Ortiz Tapia, 2005