In the previous episode we covered Hannes Alfven general properties and mechanism
in a double layer. In this episode we will continue to explore his paper and
focus on what experiments have revealed about the properties of double layers.
At the beginning of the 20th-century geophysicists began to be interested in electrical discharges,
because it seemed possible that the aurora was an electrical discharge.
Anyone who is familiar with electrical discharges in the laboratory and observes a really beautiful
aurora cannot avoid noting the similarity between the mutli-coloured flickering light in the sky
and in the laboratory. Birkeland was the most prominent pioneer.
He made his famous terrella experiment in order to investigate this possibility.
Based on his experiments, and on extensive observations of aurora in the auroral region
he proposed a current system which is basically the same as is generally accepted today.
At the time the theory of electrical discharge was still in a very primitive state.
When Syndey Chapman began his investigations on magnetic storms and aurora one or two decades
later, he proposed a current system which was located entirely in the ionosphere.
His most important argument against Birkeland’s current system was that above the atmosphere
there was a vacuum, and hence there could be no electrons or ions which could carry any currents.
The interest in double layers made a great leap forward when Langmuir began his investigations.
He introduced the term plasma in his paper ‘Oscillations in Ionised Gases’ in 1928. Why
he chose this term is not made clear but was probably borrowed from medical terminology.
All he stated was ‘We shall use the name ‘plasma’ to describe this region containing balanced
charges of ions and electrons. Langmuir also made the first detailed analyses of double layers.
Towards the end of the nineteenth century, electrical discharges in gases began to attract
increasing attention. They were studied in Germany and in England. As there were few international
conferences, the Germans and the English made the same discoveries independently. Langmuir’s
curiosity was all-embracing, his enthusiasm indiscriminate. He would examine whatever took
his interest no matter where it took him. This could be anything from electrical discharges and
plasmas to biological and geophysical phenomena. Science as fun was one of his cardinal tenets.
From this, you might get the impression that he was very superficial. This is absolutely
not correct. He got the Nobel prize in chemistry because he was recognised as the father of surface
chemistry. He knew enough about biology to borrow the term plasma from this science,
and the mechanism of double layers from surface chemistry. Langmuir’s probes were of decisive
value for the early exploration of plasma and double layers, and they are still used today.
Today 90 years after Langmuir’s work
most astrophysicists still have no knowledge of his work.
In Sweden, the waterpower is located in the north and the industry in the south. The transfer of
power between these regions over a distance of about 1000km was first done with AC. When it was
realised that DC transmission would be cheaper and that it also could be used in underwater cables,
mercury rectifiers were deployed. It turned out that such a system normally worked well,
but it happened now and then that the rectifiers produced enormous overvoltages,
so that fat electric sparks filled the rectifying station and did considerable damage.
In order to get rid of this, a collaboration started between the rectifier constructors
and some plasma physicists at the Royal Institue of Technology in Stockholm.
An arc rectifier must have a very low pressure of mercury vapour in order to stand the high back
voltages during half of the AC cycle. On the other hand, it must be able to carry large currents
during the other half cycle. It turned out that these two requirements were conflicting because
at a very low pressure the plasma could not carry enough current. If the current density is too
high, an exploding double layer can form. This means that in the plasma an evacuated region is
produced. The plasma refuses to carry any current at all. At the sudden interruption, some 100 or
1000km inductance produces enormous over-voltages, which can ultimately be very destructive.
In order to understand this better a series of laboratory experiments were carried out
while at the same time developing a theoretical model of the same phenomena.
At low current densities, a drift motion Vd is superimposed on the thermal velocity Vt
of the electrons in the plasma. At this stage, drift motion is less than the terminal velocity.
If the current density increases so that the drift velocity becomes
large than the thermal velocity the motion becomes similar to a beam, and an instability sets in
which is related to the two-stream instability. This produces a double later which may be
relatively stable. If the voltage over the tube is increased in order to increase the current,
the higher voltage is taken up by the double layer and the current is not increased.
However, under certain conditions, the double layer may explode.
A simple mechanism of the explosion is as follows:
The double-layer can be considered as a diode for electrons combined with a reverse diode for ions,
limited by a slab of plasma on the cathode side and another slab on the anode side.
Electrons starting from the cathode get accelerated in the diode and impinge
upon the anode slab with a considerable momentum which they transfer to the plasma.
Similarly, accelerated ions transfer momentum to the cathode slab
When more energy is supplied from the outer circuit
the result is that the anode and cathode plasma columns are pushed away from each other
When the distance between the electrons in the diode becomes larger the drop in
voltage increases. This run-away phenomenon leads to an explosion.
Nowadays the mercury arc rectifiers have been replaced by semiconductors,
but this work led Hannes Alfven to an interesting spin-off in cosmic physics.
In 1964 Jacobsen and Carlquist suggested that the violent explosion of solar flares were produced
by the same basic mechanism as was observed by the exploding rectifiers. It drew the attention
to the fact that every indicative circuit carrying a current is intrinsically explosive.
Further consequences were: The obvious connection between laboratory
and space plasma led to a long series of plasma experiments planned to clarify cosmic phenomena
It inspired Carlqvist to work out a detailed theory of solar flares, and later to develop a
theory of relativistic double layers It inspired Bostrom to develop
a theory of magnetic substorms, which in important respects is similar to Akasofu’s
In most of the double layers in the magnetospheres and those studied so far in the laboratory,
the electrons and ions have such low energies that relativistic effects are usually not very
important. In flares with voltages of 10^9V or more, it is possible to reach the energies
requires. In galactic phenomena, we have voltages which are several orders of magnitude larger.
Carlqvist found that in a relativistic double layer the distribution of charges
can be divided into three regions. Two density spikes near the electrodes and one
intermediate region with almost constant charge density. In a later paper, Carlqvist gives
examples of possible galactic double-layer voltage differences of 10^14V. This by
straightforward exploration from our knowledge of our cosmic neighbourhood, means that we can
derive an acceleration mechanism which brings us up to the energy region of cosmic radiation.
A double layer that release power must be part of a circuit in which a current flows. If we
examine a simple circuit containing a double layer which is depicted by a D and L written together
with the L pointing in the direction of the current. Besides the double later the circuit
contains an inductance in which energy is stored according to the following formula.
Where Bi is the magnetic field produced by the current I and dt is the volume element.
If a magnetised plasma with a field Bo moves with velocity v in relation to the circuit
it produces an emf in the circuit given by this equation
Where ds is a line element in the direction of I
If the emf is greater than zero we have a generator transferring
plasma power into the circuit. If the emf is less than zero we have
a motor transferring circuit energy into kinetic energy of the plasma.
Finally, the circuit may contain a resistance R which dissipates power into heat.
A normal circuit consists essentially of metal wires. Is it realistic to use this for cosmic
plasma? Probably not. There are obviously no metal wires in space and most of the
circuit elements we are interested in will be distributed across cosmic distances. There have
been many detailed studies made concerning the relations between kinetic energy of a plasma
and currents, which give a deeper understanding of these processes than a circuit approach.
However, the purpose is not to study the detailed problems
but to get a general survey of energy transport in cosmical physics.
In this respect, the circuit approach may be useful as a first approximation of these problems.
A map of a city is useful despite the fact that it does not show all the houses.
In space, charged particle move more easily parallel to the magnetic field
rather than perpendicular, and parallel currents are often pinched to filaments.
A wire is not too bad an approximation to a pinched filament. Also, the generators/motors
as well as the double layers are often confined to a relatively small volume.
The circuit representation could and must be developed in many respects. One
important observation is that a theory of certain phenomena need not necessarily be expressed in the
traditional language of differential equations. It could also be expressed as an equivalent circuit.
The pioneer in this field was Bostrom who summarised his theory of magnetic substorms
in the following circuit. If this method is developed further it is quite possible
that it will be recognised as the best way to represent energy transfer in cosmic plasmas.
Every circuit which contains an inductance is intrinsically explosive. The inductive energy
can be trapped at any point of the circuit. If we try to interrupt the current the inductance
tends to supply its energy to the point of interruption, where the power is delivered.
This means that most of the circuit energy may be released in a double layer and if large it
can cause an explosion of the double layer. In a laboratory plasma, this occurs due to a region of
negative resistance in the current-voltage characteristics of the double layer.
Consider a long homogenously magnetised uniform plasma. It is confined laterally
by a tube wall or by a magnetic field. It carries not longitudinal current.
Information/energy is transmitted in a time T from one end to the other by sound waves
or hydromagnetic waves or by diffusion. Phenomena with a time constant much smaller than T
can be treated by local theories as one end does not know what happens in the other.
If a longitudinal current flows through the plasma and returns through an outer wire or
circuit the situation is different. Except for rapid transients, the current must be the same in
the whole tube and in the wire. If the current is modulated in one end this information is rapidly
transferred to the other end and to the wire. The current may produce double layers which accelerate
electrons and ions. It may pinch the plasma producing filaments. These effects also produce a
coupling between the two ends of the plasma column and reduce the coupling to its local environment.
Electrons accelerated in a double layer in the plasma column
may travel very rapidly from one end of the plasma column to the other. Therefore is there
is current through a plasma we must use global theories, taking into account all the regions
through which the current through the plasma column flows. Local theories are not valid.
A global theory must also be used to describe the influence of a double layer
on the motions of the plasma column.
The theoretical treatment of a current-carrying plasma must start with locating the whole region
in which the current flows. It is convenient to draw the circuit to determine the resistance,
the inductances, and the generators and double layers. These elements are
usually distributed and non-linear, and the circuit theory may be rather complicated.
The return current need not flow through a wire.
It could very well flow through another plasma column.