In this page you will find
item      Types of plasma fibers
item      Examples
item     Comparison of pinches with stars
item      Electromagnetic collapse
Chapter 4


Types of plasma fibers

Pinch: The pinch or plasma current fiber probable belongs to the most common plasma formations. In the simplest situations the current propagates along the pinch axis (in axial direction) and round the pinch a magnetic field is created (in azimuthal direction). This field exerts a Lorentz force in the plasma fiber achieving its contraction. After a while equilibrium is reached between the plasma gradient of pressures, which tries to disperse the gas, and the Lorentz force, which compresses the pinch. This equilibrium is unstable and this kind of pinch disintegrates rapidly.

Helical pinch: It is enough, however, that the magnetic lines are twisted in a kind of magnetic string, so that the pinch becomes relatively stable. The current density and the magnetic field have both axial and azimuthal components. The axial component of the current generates an azimuthal field and the azimuthal component generates an axial field. In this case we are talking about the so-called helical pinch (spiral). If the pinch had enough time, it would deform into a spiral structure with the least possible energy. The current is guided along the twists of the spiral, the lines of magnetic force. This aligned current is called Birkeland current. The density of the Lorentz force j × B generated by the Birkeland currents is zero. Hence, this magnetic field and current configuration is known as force free configuration. The pinch with Birkeland current is always helical.

Helical pinch

Double spiral: Frequently are observed current fibers which are mutually entangled (double spirals). This is the result of two spiral pinches with currents that match in orientation attract each other from a long distance (much in the same way as two parallel conductors would attract when having currents that match each other). However, at short distances a repulsion is achieved, product of the azimuthal component of the current. In this way it is possible to create an energetic couple – double spiral.

Double spiral

Toroidal pinch: In the laboratory it is distinguished yet another configuration – the plasma which is bounded to a toroidal geometry in the tokamaks [From the Russian “toroidalnaja kamera magnitnaja katuska” – toroidal chamber of magnetic confinement. N. of the T.]. In fact, it is about pinches so twisted until they get the shape of an automobile pneumatic. Instead of the axial field here is more common to talk about a toroidal field, and instead of an azimuthal field, we talk about a poloidal field.

Current wall: Excepting the most well known cylindrical structures, the pinch can be shaped into a layer of current or laminated pinch kept together by its own magnetic field. In such a wall flows a laminated current, which generates a neighboring magnetic field. This own field takes the azimuthal component of the field into a normal pinch and blocks the widening of the wall and its disintegration. The most typical examples of the wall of current are the polar lights. Here the laminated currents flow along the bipolar field of the planets and therefore it is a typical Birkeland current.

Plasma focus: The plasma focus is a very interesting laboratory arrangement. It was built for the first time around the end of the 1950’s. No one suspected that nature itself produces similar effects in Jupiter’s moon Io. It is about a coaxial plasma accelerator – between two cylindrical electrodes the plasma is accelerated by its own magnetic field. Once the plasma leaves the electrodes, it is transformed into a characteristic magnetic structure, with the shape of an umbrella, within which still propagates the electric current. This current generates a magnetic field, which compresses the plasma “handle” into a very dense, lineal formation, called plasma focus. The plasma focus is nothing else but a very dense pinch. It was in the plasma focus, where the first attempts of thermonuclear synthesis were done and nowadays, together with modern laser technology we are going back to this principle.

Plasma focus



The best known conducting walls are the polar lights. In the auroral zone appear conducting walls or laminae, located around the 70° of latitude south and north of our planet. The thickness of this wall is some tens of kilometers. Linearly their dimensions are something about a thousand kilometers. The wall is orientated along the lines of the Earth magnetic field, which corresponds to the axial component of the cylindrical pinch. In the lamina take place electric discharges with a current density of ~ 30 μA/m2 which generate their own magnetic field with guiding effects. The first observation in detail of a laminar pinch on Earth was done with the satellite TRIAD in the year 1976. The first detection, however, was done already in the year 1966 (with the navigation satellite 1963-38C). The polar lights are nowadays very well studied plasma effects not only on the Earth. In the figure it can be appreciated the polar lights on Saturn, at the beginning of 1998.

Polar lights on the Saturn

Polar lights on Saturn as a result of Birkeland currents that influence the laminar pinch in the auroral zone. HST, camera STIS, 7. January 1998.

Just after that date, when the satellites Voyager 1 and Voyager 2 photographed in Io’s surface active volcanoes, Gold proposed (1979) that the volcanic gases could be ionized and in the mouth of the volcano could occur the electric discharge, which is analogous to the discharge in a coaxial accelerator. Nowadays we have already concrete data. Jupiter’s magnetic field around Io’s orbit has a value of 1 900 nT. The electromotive force induced as a result of the moon’s motion transversal to the lines of force is 400 kV and the Birkeland current detected is around 1 MA. The liberated power then is ~0.4 TW! If this power was distributed among some of the biggest volcanoes, it is still enough to keep up the plasma discharge and create plasma focus. Compare the photograph of the volcanoes with the current lazer in a laboratory plasma focus.

Prometeo Prometeo

Volcano Prometeo on the moon Io. Voyager 2, 1979. The second take is the profile of the volcano Prometeo from the satellite Galileo, 28. 6. 1997. Is it natural plasma focus in the Universe?

Plasma focus

The fibrous structures are present in almost all nebulae. They are witnesses of ionized matter and of the presence of magnetic fields. In those fibers an electric current flows, which creates a magnetic field around the fiber.

Cygnus loop

NGC 6960/95 (The Cygnus Loop). Remnant of a supernova with the typical fibrous structure. Age 5 000 years. Hubble Space Telescope, 1996.


Comparison of the pinch with the stars

Let us try to formulate the basic differences of the equilibrium configurations of the gravitational interaction (stars) and the electromagnetic interaction (pinch):

  • The objects which are the result of gravity have a spherical geometry; objects based on electromagnetism have a cylindrical geometry.
  • Objects based on gravity do not need the interaction with the world around them; pinches need a circulating current, which in the laboratories has to be created with an external circuit and in the Universe with an external field.
  • Both configurations can have striking differences in size. This is given by the difference in magnitue of the electromagnetic and the gravitational interactions. For example, the ratio between the gravitational and electrostatic force for two protons is Fe/Fg ~ 1036. Thanks to this fact we can create a small pinch in laboratory conditions, (millimeters, centimeters), inside which we can observe matter with parameters comparable with stellar nuclei!
  • The equilibrium configuration of the stars is stable for an ample scale of parameters; the equilibrium configuration of a pinch shows an entire range of instabilities: for example, in the place on a random contraction of the pinch it is created a stronger magnetic field (because of the radius reduction) and a stronger magnetic pressure in the pinch compresses that section even more than the rest, until the pinch divides or even disintegrates into several parts – like a pearl necklace or a chain of sausages (sausage instability). In the place where the pinch warps, a stronger magnetic field and a pressure is created in the interior face of the warping, hence, the initial warping will increase. Because the pinches are structures fundamentally unstable, their long-time preservation is given in the case of helical magnetic fields.


Electromagnetic collapse

A plasma fiber is found in equilibrium, if the Lorentz force is balanced with the gradient of pressures. This condition is valid for configurations in equilibrium in a sort of general way, hence it is valid not only for a pinch and from here it is inferred that during the equilibrium the lines of current and the lines of force of the magnetic field are found within layers of constant pressure. W. H. Bennett deduced for the first time, for a cylindrical geometry, the equilibrium conditions under the assumption of a constant current density in the pinch. In the pinch, let us say, in the laboratory, it is reached a very strong Joule heating due to the circulating current. The heat produced in this way would increase the pressure in the pinch, stopping the emergence of the equilibrium in the pinch. Since the pinches are observed as relatively stable formations, the pinch’s heat must be expelled from itself. R. S. Pease and S. Braginskij proposed that in the equilibrium the Joule heat production is plenty compensated by the loss of radiation. The radiation of the pinches is probably due to the most important mechanism of liberation of energy from a pinch, which impedes the heating of the pinch.

R. S. Pease and S. Braginskij deduced independently in the year 1957 the theoretical possibility of the electromagnetic collapse of the pinch. The circulating current in the pinch liberates the calorific energy through Ohm’s (Joule’s) mechanism, which otherwise would heat the pinch. This energy is radiated outwards. The power of the radiation increases with the temperature. At high current values, and therefore at high temperatures, so much energy is radiated, that this breaks up the equilibrium of the pinch, the external magnetic pressure supersedes the material pressure and the plasma fiber commences to collapse inwardly. The temperature is not only steady and not rising, but it can even decrease thanks to the radiated energy. This collapse can stop in a degenerated gas of electrons or neutrons (quantum effects of superdense matter). The electromagnetic collapse scenario reminds a lot of the final stages in the explosion of a star – the gravitational collapse into a white dwarf or a neutron star (including the final cooling). The electromagnetic collapse should be reached at currents greater than the value IPB ~ 1 MA deduced by Pease and Braginskij. This quantity does not depend on the shape or size of the pinch. It is a universal constant composed of other basic constants (vacuum permeability, Boltzmann’s constant, Stefan-Boltzmann’s constant ...).

This theoretical assumption is markedly problematic, because the assumptions deduced from Pease-Braginskij are never accomplished in a precise way. The deduction was carried out for optically diffuse plasmas which radiate only through recombinatory processes; it was considered only the conductivity of normal collisions in the plasma; the guided current can be, in extreme conditions, influenced by diverse anomalous effects; the energy conduction can be exhausted through mechanisms distinct from radiation (for example, the fast electrons in the tail of Maxwell’s distribution). The basic problem is that before the pinch reaches Pease-Braginskij’s minimal current, the pinch usually disintegrates as a consequence of the onset of instabilities or is divided into smaller pinches. The possibility of electromagnetic collapse is therefore, an open question as yet.


Translation: Arturo Ortiz Tapia, 2005