Flux surface average for a tokamak

In summary, the flux surface average of cos(m*theta+n*phi) at a given flux surface in a tokamak is the integral of the expression over the entire surface, which is equal to 1/A times the double integral of cos(m*theta+n*phi) with respect to the poloidal and toroidal angles, where A is the area of the flux surface and dθdφ is the differential area element.
  • #1
say_cheese
41
1
I am trying to figure out the flux surface average of a 3D perturbation in a tokamak. For example what is the flux surface average of cos(m*theta+n*phi) at a given flux surface. (Theta and phi being poloidal and toroidal angles respectively?
 
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  • #2
The flux surface average of cos(m*theta+n*phi) at a given flux surface is simply the integral of the expression over the entire surface: ∫cos(m*theta+n*phi)dA = 1/A ∫∫cos(m*theta+n*phi)dθdφ where A is the area of the flux surface, and dθdφ is the differential area element.
 

Related to Flux surface average for a tokamak

1. What is a flux surface average for a tokamak?

A flux surface average for a tokamak is a way to measure the average magnetic field strength and shape within a tokamak reactor. It takes into account the variation of the magnetic field along the toroidal (donut-shaped) direction, as well as the poloidal (vertical) direction.

2. How is the flux surface average calculated?

The flux surface average is calculated by dividing the total magnetic flux within the tokamak by the area of the flux surface. This gives an average value of the magnetic field strength within the tokamak at a particular radial distance from the center.

3. Why is flux surface average important in tokamak design?

Flux surface average is an important parameter in tokamak design because it affects the stability and efficiency of plasma confinement. A higher flux surface average leads to better plasma confinement and a more stable reactor.

4. How does the flux surface average change during plasma operation?

During plasma operation, the flux surface average can change due to variations in plasma density and temperature, as well as changes in the magnetic field strength. These changes can affect the stability and performance of the tokamak reactor.

5. Can the flux surface average be controlled in a tokamak reactor?

Yes, the flux surface average can be controlled to some extent by adjusting the magnetic field strength and shape within the tokamak. However, other factors such as plasma density and temperature also play a role in determining the flux surface average.

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