Re: Problems understanding irrational q values in Tokamaks

Paul M Koloc wrote:

Oliver Keating wrote:
> Hi,

[snip]

There are really bad problems with the tokamak, and it doesn't have so
much to do with the physics, as the engineering.

> A Tokamak has a toroidal magnetic field which follows round the torus
> (doughnut). This confines the plasma.

It is important to realize that the toroidal component of field that
infiltrates the plasma torus, is generated by toroidal field coils, and
so that field does not "confine" the plasma, rather it confines
(compresses) the coils since a magnetic field acts against the currents
that either form the field or neutralized the field.  This is important
to understand, since the Toroidal plasma current also produces a field
but that acts to compress the plasma.  There is an interesting dynamic
interaction between the fields and their currents.  Since the current
coils are rigid held, the give and take are in the plasma field and its
current.

> However, it isn't perfect because the magnetic field is stronger on the
> inside bit of the torous than on the outside - i.e. there is a magnetic
> field gradient. This causes charge separation through a plasma physics
> phenonmenon.  

> This isn't desirable, so we put in a *poloidal* magnetic field too, 
> which is
> circular in the plane of the cross section of the torus.

Well, if there were no plasma toroidal current then the device would be
more Stellarator like, and that is where this charge separation problem
was fixed by either twisting the torus into a figure "8" or by also
adding external coils that went the long way around the torus.

> This means that the actual magnetic field looks rather like a helix
> travelling around the torus.  

Yes, that's correct, and helical fields and currents work well in the
plasma torus, and if they were freely flowing, then the device would be
a Spheromak, which is ideally MHD stable.  Unfortunately the toroidal
field is "fixed" by the generating rigid coils, so the helical field is
not as helpful and stable as it could be.

> At this point it is useful to define something called a "q" value, which
> refers to the number of times the magnetic field goes around 
> poloidally for each toriodal turn.

If the flux travels around several times before nearly reconnecting,
then instabilities have a tougher time developing, because a growing
wave gets mixed as it comes around and so does not reinforce its growth,
and tends to be damped.  That's a good thing.  The Spheromak is better
at this sort of thing, since its helicity varies with radius from the
minor toroidal axis.  This is called shear and it is useful against a
wider set of instabilities, for example those due to banana type orbits.

[snip]

> My problem is that with an irrational q number, the magnetic field line
> spins around the torus forever - it never manages to reconnect back on
> itself as it spirals around.

Remember that magnetic flux gets eaten by plasma resistivity.  So don't
worry about the forever stuff.  The one time when tokamak currents do
seem to last (forever) for a long time, is when a tokamak is started
with lower than optimum plasma density.  What happens is that the mean
free electron path is long enough for the driving flux to accelerate
them to higher velocities.  As the electrons currents are pulled out
into velocity space their effective mean free path gets even longer, and
so the plasma gets a higher effective conductivity.  This reduces
magnetic diffusion and particle diffusion.  The down side is that the
plasma does not heat sufficiently to obtain anything near a fusion
ignition. When such a "electron hot" plasma is stopped, there is usually
a burst of X-rays due to the energetic electrons.  Also there is a
situation where only the external edge of the plasma is able to have and
trap energetic electrons.  This cuts the radial energy transport at the
edge, so the bulk of the plasma cross-section becomes a bit hotter and
radially flatter in temperature.  Consequently, the main cross-section
carries more uniform thermal electron currents. Maybe this is
responsible for Super H mode or some such non-sense.

> > I don't understand this at all. I thought one of the consequences of
> > "divB=0" is that all magnetic field lines must connect back on 
> > themselves?

The flux lines will eventually reconnect as long as excessive
resistivity is not present.  Look at it this way:  The magnetic field
"lines of force" _B_ encircles surfaces of a flowing circulation of an
information field we call "_A_".  As long as _A_ is circulating, it is
stored (potential) energy.  The other place we run into _A_ is when it
is flowing in discrete pulses/unit time from a positively information
charging particle across a short time to an electron, the negatively
(anti-charging information operator).  In this case the presence of the
_A_ flow is quantized by Q a specific amount of information that is
transferred in each time frame.  So when we turn the _A_ circulation
into "electric" or chunks of annihilated information that quantum of
information is taken out of the circular flow and skimmed off into
"termination flow", where it is taken out of existence.
The work it does relates to maintenance of current by an inductive
electromotive force. So... .

> Additionally, how can you have an infinite number of field lines but a
> finite magnetic field?

The line density represents the density of the _A_ flow, and that
remains constant or at least proportional to the current.  Lines are
convenient for some aspects of visualization.  But, don't depend on them
to much unless you suffer from narcolepsy.  :-)

> As yet no one has managed to provide a answer that I understand!

BTW I did not explain the neat dynamic stuff that takes place between
the stiff toroidal field and the sloshing poloidal field.  I works like
this.  The plasma current starts out toroidally, and follows the flux
imposed by the coils.  BUT it generates poloidal field that not only
confine it, but also add helicity to the plasma's field.  For this new
situation, the plasma toroidal current tries to follow the more helical
field lines.  BUT (2) that converts some of its toroidal current into a
poloidal component of current that adds to the toroidal field.  During
this event the toroidal current drops.   That causes less helicity, so
the plasma current again becomes more toroidal, .. which .. ..

The toroidal current then appears to have a "saw tooth" component riding
along on top of its normal value.  That is because the plasma is elastic
and the currents and field sort of "snap" around.  The great benefit is
that this causes the production of a twisting slosh, which like clothes 
being
cleaned in a washing machine sort of tumbles the radial plasma around,
allowing it to mix.  This in turn smooth out the radial temperature 
gradient.  With
a flatter radial temperature, the effective conductivity is smoother and
the effective current cross-section is wider, which makes it more stable
against "kinking", which if unchecked causes disruptions.

> I did not have time to re-read this stuff for obvious idiocy.
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