In this page you will find:
item     Pinching
item     Oscillations and wawes
item     Drifts
item     Grad B force
item     Instability
Chapter 4



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

The pinch in terrestrial laboratories:

Medium European devices (1 MA, 3×5 μs)

  • University of Ferrara (Italy)
  • IPPLM Varszaw (Poland)

Big European devices (1 MA, 200×400 ns)

  • Imperial College London (England)
  • Ecole Polytechnique Paris (France)
  • Universität Düsseldorf (Germany)

The biggest world devices

  • Troitsk (3 MA, 10 ns)
  • S-300 (3,5 MA, 150 ns), Russian Research Center Kurchatov, Moscow
  • Saturn (10 MA, 20 ns), Sandia National Laboratories, USA
  • Jupiter (20 MA, 100 ns), Sandia National Laboratories, USA


The Saturn


Oscillations and waves

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:

  • Low-frequency waves: It is about waves with frequency near the plasma frequency of ions ωpi = (ne2/miε0)1/2. This frequency is the natural oscillation of the ions. We call the waves with similar frequency magnetoacoustic. It is about an analogy with acoustic waves in normal matter, only that in this occasion they are influenced by a magnetic field. The sound propagates in this case anisotropically and in various wave modes.
  • High-frequency waves: It is about waves with a similar frequency as the plasma frequency of electrons ωpe = (ne2/meε0)1/2. This frequency is the natural one for oscillations of the electrons. There exists a great quantity of different types of electromagnetic waves that propagate in the plasma.

Some wave modes:


  • AW – Alfvén Wave
  • S – Slow Magnetoacoustic Wave
  • F – Fast Magnetoacoustic Wave


  • O – Ordinary Wave
  • X – eXtraordinary Wave
  • R – Right-winding wave
  • L – Left-winding wave
  • Whistles
  • Lower Hybrid Frequency
  • Upper Hybrid Frequency



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 best known drifts:

  • E×B drift (transversal to the electro and magnetic fields, electric force)
  • Gravitational drift (transversal to the gravitational and magnetic fields, gravitational force)
  • Grad B drift (product of the change in density of the magnetic force lines, force gradient of B)
  • Curvature Drift (result of the curvature of the magnetic force field lines, centrifugal force)
  • Polarization Drift (result of the slow change of the electric field in time, induced force)

Magnetic dipole

Magnetic dipole.

A particle in a magnetic dipole performs three motions:

  1. Larmor rotation.
  2. Motion along the force lines with reflection in the polar zones. The reflection is given in the dense parts of the magnetic field by the influence of the force grad B (magnetic mirror effect).
  3. Drift transversal to the force-lines by effect of the centrifugal force generated from motion 2. The velocity of this drift is perpendicular to both the magnetic field and this centrifugal force.


Grad B Force

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.

Typical configurations of magnetic mirrors:

Magnetic mirrors

Magnetic mirror (left), azimuthal mirror (right).



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.

Sausage instability Sausage instability

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.

Kink instability

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.

Diocotronová nestabilita

Transversal section of the developed diocotron instability


Polar lights [also known as ‘aurora borealis’ or ‘northern lights’ N. of T.] observed above Alaska 31.1.1973


Translation: Arturo Ortiz Tapia, 2005