Auroral Codes


The Abisko Version




Christer Jurén

Swedish Institute of Space Phycics

Alfvén waves



There are two ways of describing Alfvén waves.  First, we have a wave in a bath of mercury containing magnetic fields:


 If you jump into a bath of mercury in a strong magnetic field and follow its motions, you will not experience an electric field.  The electric field is always zero in the frame moving with the fluid. But seen from a stationary observer the electric field will vary according to relativity and depend directly on the speed of the fluid. A varying electric field will always be accompanied by a varying magnetic field – even in this case. The magnetic field will carry energy but the electric field will not. The moving mercury will also carry energy.


We have a space and time varying magnetic and electric field together with electric currents and fluid flow. Maxwell’s equations, relativity and Newton’s law, “Force = mass * acceleration”, will give a wave equation.


Our model, the chain hanging from the ceiling, will illustrate an Alfvén wave. It has moving masses and it bends. The tension corresponds to the original magnetic field and the bending corresponds to the magnetic field in the wave.  In both cases the wave velocity will be the same:


   Wave velocity = SQRT (tension/mass).


Next we have a wave in space consisting of ions together with electrons all feeling a magnetic field. In this case we don’t have a fluid but a lot of independent charged particles which feel a static and strong magnetic field, weaker magnetic fields which have been produced by the particles themselves and an electric field generated by the static magnetic field through a relativistic effect.


The actors are the masses and currents from the particles together with the static magnetic field B and the electric field e.


B, e, b, j, v and m are the actors.


 (j is current, m is mass and v is velocity)


 m is the total mass density, no matter what charges the different particles have. All contribute equally.


b,t = - e,x ; b,x = µ0*j ; e= B*v ; j*B = M*v,t



b,t = - e,x

b,x = 1/(B2/(µ0*M)) *e,t


This would be the same as Maxwell’s equations for electromagnetic waves in a vacuum if the constant (B2/(µ0*m)) were  c2.


SQRT(B2/(µ0*m)) is the Alfvén velocity.


It is the magnetic field and the moving masses, that vibrate.



The Sun has a very active inner life. High temperature plasma with embedded magnetic field move around in the corona. Spontaneous ejections of plasma (mass) happen now and then and some of these are called Corona Mass Ejections (CMEs). This name is applied to a particular kind of ejection. There are a lot of other phenomena such as flares, but CME is the most important.


A CME consists of a sudden, out-flowing plasma cloud which carries with it a magnetic field - an Alfvén type of phenomenon. When the cloud leaves the Sun it can be as closed loops, like smoke rings, with a diameter as big as the Sun. It moves out from the Sun with a velocity of about 1000 km/s and, if it is moving in the direction towards the Earth, it will reach it within 40 hours, about 2 days.


When the CME reaches the Earth it has grown bigger in size. The magnetic field is the most interesting component, which penetrates our magnetosphere and disturbs it so that the trapped particles inside have to change their well established routes and start to interact with each other. Some get higher energy, some lower! Some particles reach the ionosphere with high energy so they can excite atoms in the upper atmosphere. The excited atoms send out photons. This is the Aurora.


The CME has trigger our magnetosphere, “little tuft overturns a big load of hay”. Littleness and bigness in space have to be considered carefully.


A CME can be so big that it smashes the magneto­sphere and causes a very brilliant Aurora, of the type that reaches all the way down to Skåne.


Cold Electron Plasma


One electron can’t make a plasma! One electron and one proton can’t make a plasma.


One molecule can make up a gas, a “Knutson” gas, but it has to move around vigorously.


Several electrons can make up a plasma if they are sufficiently many and are in a positively charged background. How many? It depends on the temperature, a plasma has a temperature. But we don’t say more!


What does a cold electron plasma mean? Intuitively it means electrons are equally distributed in a positively charged space and moving equally in each small volume element. We can think of such a collection of equally moving electrons as one particle. When one such particle moves away, it will feel a restoring force and like a pendulum start to swing or vibrate. The frequency will be the plasma frequency, which depends on the electron density. The vibration has energy.


A local vibration in a cold plasma stays local!


Electron plasmas are very common in our ionosphere and are responsible for reflection (not scattering) of “short wave” radio waves.


Warm Electron Plasma


Think of a cold electron plasma and imagine that you warm it up. The particles which consisted of equally moving electrons will instead consist of individually agitated electrons and in this way start to come in contact with their neighbours. We can imagine the particles as pieces of a string supported by several threads. They will not be free swinging pendulums but instead pieces of a vibrating string, but they have a common “plasma” frequency equal to the frequency of the pendulums, which are formed by the supporting threads.


If we disturb the string it makes a wave, a plasma wave. Such a wave can’t have a lower frequency than the supported pieces of string would have as free pendulums. It can’t have too high frequency either, because the wavelength would be too small and interfere with the individual agitations of the electrons.


The wave velocity for the plasma wave will be much higher than the agitation velocities for the electrons. But if, in addition, there should be a beam of electrons which moved with a velocity close to the velocity of the wave, there would be an interaction between the beam and the wave.


Such mechanisms are common in auroral physics.


Colour in the Aurora



Newton and Goethe both had theories for colours and how we see them. Goethe had the best one, if we want to talk about colours in Aurora.


Newton knew that one could separate different colours from white light, as happens in the rainbow. But his wider ideas are uninteresting. He, for example, tried to organise the colours he knew of after a tone scale, do - re - me -far - so - la - ti - do.  He based his idea on the Pythagorean mathematical relationship between musical tones and didn’t think of more than that.


Goethe on the other hand had more advanced ideas. He thought about light-light and dark-light. He had two rainbows, one for light-light, the normal one, and one for the dark-light. The normal has no purple, but the other one has purple, but on the other hand it has no green. Green and purple are complements to each other. Aurora can have both purple and green.


Goethe’s idea of complements, white against dark is a very nice idea. Normal Aurora has a complement in Dark-Aurora.


One needs only four types of colour to describe the colours in Aurora.


1.      Green from Oxygen atoms 557.7 nM  -  0.7s

2.      Blue from Nitrogen-ion       427.8 nM -  <0.001 s

3.      Red from Oxygen                  630.0 nM -  200 s

4.      Red from Nitrogen-ion         669.0 nM -  <0.001 s


The values are for wavelengths in nanometres (10-9 metre)

  and for lifetime in seconds for the lightemissions.


Electrons moving in the Magneto­sphere


Around the Earth there is a magnetic field. Individual electrons move in that field. They circulate around the field lines with a frequency which depends on the field strength – the frequency is about 1 MHz close to the ground.  An electron with a velocity of 1/300 times the velocity of the light will move one metre during one circulation. This is a very small orbit in space and we can think of a new object, a gyrating electron, which moves along the field lines. They will move back and forth along the field lines between the northern and southern hemispheres. It will take some seconds for the round-trip, back and forth. We can further think of the “back and forth” track as a new object and look how it behaves. It will circulate around the Earth, from west to east. It will take several hours to drift round the whole Earth!


So we have found a way to describe the 3-dimensional electron motion with three “objects”. The objects don’t behave exactly as we have described, but almost. We could refine the situation, introducing sub-objects, but we can’t go the whole way to an exact description using these ‘objects’.


A corollary: in the old days when they thought that the planets moved round the Earth, a similar procedure was used to describe the motion of the planets. “Epicycles” were used, and with those an exact description of the planetary motion could be reached.


In the case of the moving electrons one can’t reach exactness, but the “objects” give an approximate description in an intuitive and practical way. 


In the case of the planets, the description in terms of epicycles reached exactness, but in an unpractical way.

Plasma, what’s that?


A new Professor in plasma physics started to buy new books and periodicals suitable for his subject. He found one with the title “Plasma”, for him a new periodical. He ordered it. When the first issue came he could read all the latest news about blood.


There are as many plasmas as there are theoretical plasma physicists. So we don’t define plasma, instead we give some examples.


One could think of a small road during the night with cars driving in both directions and the cars interacting with their lights as a plasma. Life on the road is unstable and as such it is a plasma, the famous Night Traffic Plasma! (O. Buneman, a famous plasma physicist, suggested that one could organize plasmas after the instabilities they had).


Another plasma is a school of Gyrinides, which are very nice water beetles.  The Gyrinides have a two dimensional sex-life. They live on water surfaces on ponds deep in the forest. The males and females are equal in number and they communicate through water waves. Thus, they have two qualities needed to be named a plasma, Gyrined Plasma. Females and males are equal in number and communicate over large distances.


Plasma has been called  the fourth state of matter, but this leads to a large misconception. One should not start to look at a plasma from the point of view of matter; one should start from the parts and proceed to the whole. The parts in a plasma have long-range interactions with each other and one must look at the qualities of the parts to understand the whole.


If you look around you will find many plasmas! They are 99% in the universe.


The Spatial Perspective of the Aurora.


The auroral light comes from atoms, molecules and ions in the atmosphere. They are high up, in the ionosphere, 90 km and higher. It means that we do not have objects to relate to the perspective of what we see. Long ago, no one knew how high the aurora was and Kristian. Birkeland and his colleagues built an observatory on a mountain 3000 m high, to try to get close. What they found was the same as from the ground.


The aurora can be very mobile, with distinct rays, and from common experiences of moving objects in our close environment, we can be fooled in several ways.


We can see the aurora in front of mountains. We can see it very close to us, only meters away and sometimes only half a meter. We see it moving towards and away from us!


If we want to get an idea of how far away the Aurora really is we have to triangulate with a base line of around 50 km.


If we want to take a stereoscopic picture of the Aurora, we have to use two cameras 6 km apart!


A corollary: a zebra has lines on its body. On the neck, they are vertical. A lion can get confused when using its well developed stereoscopic viewing.  The auroral rays are vertical!


The Sun


The Sun is a large ball, 100 times bigger than the Earth, and the distance from the Earth to the Sun is 100 times the Sun’s diameter.

The temperature of the different parts of the Sun varies, but for the surface we see, it is about 50000 K.  We see the temperature as the colour white - there is a relationship between temperature and colour!


The Sun consists of three regions, a fusion reactor (hydrogen bomb), a corona and a chromo sphere.


Of course there are far more regions but for now we won’t worry about the others.


The fusion reactor is just in the centre with a diameter of one fourth of the Sun’s diameter.


The corona is the rest up to the surface. The corona consists of plasma in a very turbulent magnetic field. The chromosphere surrounds the Sun and during solar eclipses, one can see it as a handsome structure of loops of lines.


One more thing, the Sun rotates. The equator rotates one turn every 25 days!








Whistlers were first noticed during the First World War in the middle of Europe. Sometimes a whistling sound could be heard in telephones connected to very long lines. No one could work out what it was. Nowadays we know that lightning in one hemisphere can excite an electromagnetic pulse, which can follow a magnetic field line to the other hemisphere. It can go all the way down to the ground and induce a current in a telephone line, or be reflected and go back again.


Whistlers are very interesting waves out in space, where they interact with charged particles. They are important for the aurora.


A whistler can be thought of as two waves, wave1 and wave2, living close together.


In one aspect they are like Alfvén waves, i.e. the time variation of the electric field has no meaning, however of its own!


There is one big difference, the particle mass is not important, so long as it is small enough.  In addition, a plasma consisting of particles with equal masses but different charges can’t have whistlers. In the magnetosphere, the plasma consists of light electrons, which move with the wave, and heavy protons, which do not.


The electric field in wave1 is connected with the current of wave2, and vice versa. The original magnetic field is important for that connection.




e1, b1, j1   e2, b2, j2     together with B and q, charge.

q/B * e1 = - j2 ;   (1)

q/B * e2 =   j1 ;    (2)   


e1,x  = - b1,t ;        (3)

b1,x = µ0* j1 ;       (4)


e2,x  = - b2,t ;         (5)

b2,x = µ0* j2 ;        (6)


(3) => b1,t  = B/q * j2,x = B/(µ0*q)* b2,xx

(5) => b2,t  = -B/q * j1,x = B/(µ0*q)* b1,xx


(3) and (5) are so strongly coupled that we can have them as one equation for a complex field!


Let us call that field Ψ = b1+ib2.


            i Ψ,t    = - B/(µ0*q)* Ψ,xx   


It looks like the Schrödinger equation for a free particle! A free particle with higher energy moves faster than one with a lower energy. Energy is related to frequency so a whistler wave with higher frequency moves faster than one with lower frequency. That’s why a whistling sound will be heard when an electro/ magnetic pulse from one hemisphere finally arrives at a telephone line in the other.


We have a spring, which sounds like a whistler if you pluck it. A wave starts and goes along the spring thread as a bending of the thread. The equation for such a wave is also similar to the Schrödinger equation. Similar mechanisms apply for waves across ice on lakes and along thick telephone wires. They sound similar!


The spring, when it acts as such, will rotate the thread.


When you whistle at the Aurora it comes closer!




   As a little boy around 8 years old, Martin Johnsson, nowadays a retired professor in parapsychology, made his first scientific experiment. He had been told “if you whistle at the aurora it will come close to you and catch you, so don’t do it!” He placed himself on the outer porch just in front of the house, but had seen to it that the main door behind him was open, as well as the adjoining internal doors. He looked at the aurora and whistled, but the aurora stayed where it was. He made the experiment in Malå, in the south of Lappland, the northern part of Sweden.


It is a very common mode of expression that the aurora will be disturbed by whistling at it. Very often such sayings have realities behind them, but for a modern scientist the saying about whistling at the aurora has certainly no deep truth behind it, certainly no truth at all.


But I would recommend everyone to do the experiment Martin did. The aurora should be a distinct aurora and it should be cold outside, but there is no need to have a hiding place to run to. Perhaps the experimenter will be astonished! Perhaps the aurora will come close to him, very close indeed.


With a distinct aurora I mean an aurora with gently connected arcs with clear rays, moving not too fast.


Once when I lectured on the aurora in Jokkmokk, in the middle of Lappland, a woman in the audience commented: “My children came home a little bit late the other day and when I asked them where they had been, they answered: “There was an aurora and it was so close that we didn’t dare go through it.” She then asked me if that could be the case, that the aurora could be that close.


There is an explanation. When it is cold outside, our breath condenses to form small water drops and ice crystals. These can line up in some structure when we whistle. Our eyes constitute a very sophisticated system and they will focus on the structure without our noticing it, particularly so for a child. When our eyes do this, it can happen that the left eye will notice an auroral structure with a similar form as the right eye will notice, but in a different direction. The eyes will together create the appearance of an aurora in the same region as the ice-crystals from our breath. The younger the child, the better the eyes will create such appearances - it has to do with the binocular learning process.


Professor Martin Johnsson had bad luck when he made his first scientific experiment as an eight year old boy, or?


Personal conversation with Prof. Martin Johnsson.