Tokamak Reactor Help:
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Tips For A Better Score
Exercises For Further Study
These represent the most important controls in a magnetic fusion reactor.
- Plasma Density
- Measures how close together particles are. If the plasma particles are closer (higher density values), they are more likely to collide and fuse.
- Auxiliary Heating Power
- Power must be put into the plasma to make the charged particles (ions) move faster (a scientist would say the power raised the temperature of the plasma). If two ions collide at a high enough speed, they can overcome their natural repulsion and fuse.
- Magnetic Field
- If the plasma particles strike the surrounding walls, they slow down again. So, a tokamak uses magnetic fields to keep the plasma away from the walls (we say that the magnetic field confines the plasma).
ScoreOnce you've picked values for the 3 sliders and pushed the START button, a short program computes the fusion power that would be produced in your reactor. Your score depends not only on the amount of fusion power, but also how much auxiliary power you had to use.
Several people have asked what the score really means. Reactor designers focus on a quantity they call Q, defined as the fusion power divided by the sum of the auxiliary and ohmic heating power. The ohmic heating power is the resistive heat generated by the tokamak's toroidal current and amounts to a few megawatts in this case. The problem with Q is that it can be very large (say, 1000) near ignition. Yet, values of 1 (breakeven) or 5 (plasma heating by alpha particles = external heating power) are interesting. Reactor designs with Q = 10 have been considered. To convey this fact to the user without going through all of the above explanation, we came up with the "score" = 100 ( Q / 100) 0.3, so that a score of 25 corresponds to Q = 1 and a score of 100 to Q = 100. Of course, scores greater than 100 are possible.
The picture in the middle represents a cut-away view of our Virtual Tokamak so we can see the plasma inside. Just for fun, this plasma changes color with your score according to the color scale at the bottom. A real fusion plasma wouldn't do this; it would always appear to be a sort of pink or red color.
TemperatureWhen the program is computing the fusion power for your reactor and your score , it also determines the temperature of the plasma. The temperature is just the way a scientist measures how fast the electrons and ions in the plasma are moving around.
For comparison, the temperature in the center of the Sun is 15 million degrees Celsius! Tokamak plasma temperatures need to be hotter than those in the Sun since tokamak plasma densities are much lower than the Sun's.
Tips For A Better ScoreAn easy way to do better is to change just one slider at a time in small steps. When you can't do better with that one, try then moving a second one in the same way.
Show the Graph or Table to keep track of how your previous tries have turned out.
You probably guessed from the slider descriptions that you should be able to get a better score by just setting all of the sliders to their largest values. But that didn't happen, did it?
That's because the program has built-in limits on the plasma density and temperature. When you exceed one of the limits, you lose control of the plasma (fusion scientists say the plasma disrupts ) and no fusion power is produced. The program returns a big fat zero for a score.
The limiting density and temperature values vary with the magnetic field (among other things) in ways which have been determined by experience with actual tokamak experiments. Your highest scores will generally be obtained just below these limits. If you want to know more, try the exercises.
One of the 3 sliders has a much bigger effect on the score than the other two. See if you can figure out which one and then use that knowledge to get a better score.
The score is related to the amount of fusion power divided by the auxiliary heating power (which you set with the slider!). So, the best scores are actually made with a low auxiliary heating power.
Exercises For Further Study
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.
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 was correct.
- 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.
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.
- 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 temperature.
- 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.