Virtual Tokamak Exercises
The calculation used to compute the
score for the Virtural Tokamak is really quite complex.
In fact, fusion scientists actually use a full-fledged (with more
adjustable controls) version when they want a quick idea of how
well a tokamak reactor design would work.
At the same time, this calculation is based on real fusion experiments.
With these exercises, you can use the Virtual Tokamak to unearth that
underlying fusion physics.
Had enough yet? If not, you might as well go ahead and read
- Investigate the density limit:
We'd like to tell you more about the density limit, but frankly we
just don't really know what causes it!
- Keeping the magnetic field and auxiliary power the same,
raise the plasma density in small steps until the plasma disrupts
(a score of 0.00 is given). Make a note of the slider values for the
highest density you reach before the disruption.
- Change one of the magnetic field or auxiliary power
sliders and again determine the maximum density.
- Repeat this exercise until you understand how the maximum
density depends on the values of the other two sliders.
- Test your theory by estimating the maximum density
for values of the magnetic field and auxiliary power which you
haven't tried yet. Then, try them and see if your prediction
- Be careful while you're doing this not to get to
temperatures which are too high, otherwise the limit on the
temperature will come into play, making it more difficult for you
to single out the density limit. This is the way real physics works!
- Having understood the density limit, you can examine temperature
limit. Strictly speaking, it is a limit on the plasma pressure, which is
the product of the plasma density and temperature. In practice, though,
it's usually the temperature that increases too much, producing a plasma
too hot for the magnetic field to confine in a stable manner.
- At this limit, the ratio of the plasma pressure to the
pressure of the magnetic field has a certain value which has been
determined by experiments and theoretical calculations.
The way the Virtual Tokamak is designed, this critical ratio is
always the same.
- First, try to find a point where the plasma disrupts
at this pressure limit. Hold the magnetic field and plasma density
fixed and slowly raise the auxiliary heating power until you
get a score = 0.00. Make a note of the density, temperature,
and magnetic field for the auxiliary power value just below
the pressure limit.
- How do you know this is not the density limit?
- Now, repeat this exercise at one or two other values for
the magnetic field. How did the maximum possible plasma pressure
(density times temperature) change?
- The relationship between the maximum plasma pressure
and the magnetic field is complicated by the contribution to the
plasma pressure made by the high energy helium nuclei which are
produced by the fusion reactions. In this case, the pressure which
is compared with the limiting value is significantly larger than
you will compute just by multiplying the plasma density and
- Low Temperature Limit. The defining characteristic of a tokamak
is the toroidal plasma current, which along with the magnetic field
produced by the external magnetic field coils provides the confining
and stabilizing forces. As this current runs through the plasma,
it generates heat just like electricity does when it runs through a
circuit. In this exercise, we first set the auxiliary power slider to 0.00.
- Then, hold the magnetic field constant, and change the density
in small steps. Make a note of the temperature values at each density. What
happens to the temperature values as the density is raised?
- Now, do the same at a different magnetic field. Considering
only the lowest densities you tried at each magnetic field, see if you
can determine the relationship between the magnetic field and the
temperature in this ohmic heating limit.
- Test your theory by first selecting another magnetic field,
predicting the temperature (at low density), and then running the
Virtual Tokamak to see he well you did.