A circular tokamak has major radius

PHYSICS · Multi-part · 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=1.5 mR_0 = 1.5\,\mathrm{m}, minor radius a=0.5 ma = 0.5\,\mathrm{m}, edge poloidal field Bθ(a)=0.30 TB_\theta(a) = 0.30\,\mathrm{T}, volume-averaged pressure ⟨p⟩=5.0×104 Pa\langle p\rangle = 5.0\times10^4\,\mathrm{Pa} and normalised internal inductance ℓi=0.90\ell_i = 0.90. ((a)) Find the poloidal beta βp=2μ0⟨p⟩/Bθ(a)2\beta_p = 2\mu_0\langle p\rangle/B_\theta(a)^2. ((b)) Using the large-aspect-ratio estimate Δ≈a22R0(βp+ℓi2),\Delta \approx \frac{a^2}{2R_0}\left(\beta_p + \frac{\ell_i}{2}\right), find the outward shift of the magnetic axis, and express it as a fraction of aa.

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