Beta (plasma physics)

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The beta of a plasma, symbolized by β, is the ratio of the plasma pressure (p = n k_B T) to the magnetic pressure (p_mag = B²/2μ₀).

$\beta = \frac{p}{p_{mag}} = \frac{n k_B T}{(B^2/2\mu_0)}$ ^[1]

Beta is a parameter indicating the relative importance of kinetic to electromagnetic phenomena. In fusion power applications, beta can be thought of as an economic figure of merit. The magnetic field in a fusion device has technological limits such as the critical field of practical superconductors. The fusion power density, which determines the power output of a reactor, scales with the square of the plasma pressure. Therefore the output of a reactor can be said to scale with the square of the average beta. In a tokamak, for example, there is a fairly firm limit on the value beta can have before destructive instabilities occur.

Beta can also be thought of (very approximately) as an economic indicator of reactor efficiency. Since temperature (and therefore thermonuclear fusion power) scale like pressure, we can say that the numerator is roughly a measure of electricity generated. The costs of large magnets roughly scales like $B 1 / 2$ . Therefore Beta can be thought of as a ratio of money in to money out for a reactor.