In a tokamak with major radius and toroidal field

PHYSICS · Multi-part · Fermi University Physics · Plasma Physics · The plasma state and single-particle motion · Fusion plasmas

Plasma Physics, Ch Slow changes and what survives them: adiabatic invariants, mirrors and trapped orbits

Problem

In a tokamak with major radius R0=2.96 mR_0 = 2.96\,\mathrm{m} and toroidal field B0=3.4 TB_0 = 3.4\,\mathrm{T}, deuterons (mD=3.34×10−27 kgm_D = 3.34\times10^{-27}\,\mathrm{kg}) have thermal energy Ti=5.0 keVT_i = 5.0\,\mathrm{keV} at minor radius r=0.50 mr = 0.50\,\mathrm{m}, where q=1.5q = 1.5. ((a)) Find the inverse aspect ratio ϵ=r/R0\epsilon = r/R_0. ((b)) Find the deuteron Larmor radius, using the thermal speed v=Ti/mDv = \sqrt{T_i/m_D} and the local field B0B_0. ((c)) Find the outboard-midplane trapped fraction, using Rmir=(1+ϵ)/(1−ϵ)R_{\rm mir} = (1+\epsilon)/(1-\epsilon) and the loss-cone formula. ((d)) Find the banana width Δb≈qrLi/ϵ\Delta_b \approx qr_{Li}/\sqrt\epsilon.

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