A circular tokamak has major radius

PHYSICS · Subjective · Fermi University Physics · Plasma Physics · Fluid and magnetohydrodynamic description · Fluid and magnetohydrodynamic description

Plasma Physics, Ch Holding a plasma still: pinches, flux surfaces and the Grad-Shafranov equation

Problem

A circular tokamak has major radius R0=1.65 mR_0 = 1.65\,\mathrm{m}, minor radius a=0.5 ma = 0.5\,\mathrm{m} and plasma current Ip=1.0 MAI_p = 1.0\,\mathrm{MA}. Its poloidal beta is βp=0.50\beta_p = 0.50 and its normalised internal inductance is ℓi=1.0\ell_i = 1.0. Using the vertical-field formula Bv=μ0Ip4πR0[ln⁡ ⁣(8R0a)+βp+ℓi2−32],B_v = \frac{\mu_0I_p}{4\pi R_0}\left[\ln\!\left(\frac{8R_0}{a}\right) + \beta_p + \frac{\ell_i}{2} - \frac{3}{2}\right], find the vertical field needed to hold the ring in radial equilibrium.

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