Dr. Octavious said:
Yes all the units are fine (it was a painful process to check all my equations). Well here is my thought process. The ITER has an ion and electron combined temperature of 16.8 keV. At this temperature the pressure is 269108 Pa. Now I know there are limitations regarding the achievable beta but if tokamaks want a beta close to one (that is 100%) then why do they apply such huge magnetic fields? The bigger the magnetic field the lower the beta.. Unless instabilities require big magnetic fields to stabilize them.
You're putting the cart before the horse.
One way to design a reactor is to start by considering plasma physics. When you do so you will learn that things like equilibrium, stability, and transport will set the maximum beta that your configuration can achieve. The next step, once you know the max beta, is then to calculate the strength of the magnetic field needed to support a given pressure. One you know the strength of the magnetic field, you can then design the magnets and calculate the current you need.
Another way to design a experiment is to start with a coil configuration. Then use plasma physics to calculate the maximum beta. Then use these two pieces of information to calculate the maximum pressure your experiment can achieve.
However your design ignores all plasma physics. You picked a pressure. You picked a magnetic field. Then you calculated beta. You found that your beta is way too large! What this should tell you is that your design is not physical. In real life if you tried to operate this experiment, the plasma would disrupt long before you reached your target pressure.
It might help to think of the design of an airplane. An airplane with a given shape and particular set of jet engines will have a maximum lift. Once we know what that lift is we can proceed in two ways. This lift is set by the physics of aerodynamics.
One way to operate the plane is to fill it full of cargo. This is analogous to what you're doing. Once the plane is packed full of cargo we then taxi to the runway and hope it can fly. But if the weight exceeds the maximum lift then the plane we never take off. Oops. The reason why the plane won't take off is simple. You've over loaded the plane.
Or instead, once we know the lift of the plane, we weigh cargo. Then we load the plane up to the maximum weight (with safety margins) that it can carry. This way when we taxi to the runway, we know that the plane will takeoff.
Alternatively, we could start with the goal of designing a plane that can carry a specific cargo weight. To do this we will have modify the shape of the plane, the set of engines, etc until we've met our design goals.
In sense by asserting that you experiment with reach a certain pressure you've overloaded it. The fact that beta is greater than one means that your "plane will never take."
