A tokamak (circular cross-section

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 tokamak (circular cross-section, large aspect ratio) has major radius R0=1.65 mR_0 = 1.65\,\mathrm{m}, minor radius a=0.5 ma = 0.5\,\mathrm{m}, toroidal field B0=2.5 TB_0 = 2.5\,\mathrm{T} and plasma current Ip=1.0 MAI_p = 1.0\,\mathrm{MA}. Take its safety factor to rise monotonically from q0=1.0q_0 = 1.0 on the axis as q(r)=q0+(qa−q0)(r/a)2q(r) = q_0 + (q_a - q_0)(r/a)^2. ((a)) Compute the cylindrical estimate of the edge safety factor, qa=2πa2B0/(μ0R0Ip)q_a = 2\pi a^2B_0/(\mu_0R_0I_p). ((b)) Say whether a q=2q=2 surface exists inside the plasma, and find the radius of the q=3/2q=3/2 surface. ((c)) Find the shear s=(r/q) dq/drs = (r/q)\,\mathrm{d}q/\mathrm{d}r on the q=3/2q=3/2 surface.

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