Auroral Codes
The Mountain Version
xxxx-xx-xx
Christer Jurén
Swedish Institute of Space Phycics
http://www.irf.se/~christer/norrskenslandet/abisko/norrskenetsKoderAbisko.html
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
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.
CME
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
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
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
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.
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
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
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
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
If we want to take a
stereoscopic picture of the
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
Whistlers were first noticed
during the First World War in the middle of
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
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
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.
