On a toroidal flux surface with radius of curvature

PHYSICS · Multi-part · Fermi University Physics · Plasma Physics · Fluid and magnetohydrodynamic description · Fluid and magnetohydrodynamic description

Plasma Physics, Ch Whether it stays held: the energy principle, interchange, kink and tearing

Problem

On a toroidal flux surface with radius of curvature Rc=1.2 mR_c = 1.2\,\mathrm m, deuterium ions (mi=2mpm_i = 2m_p) have temperature Ti=2.0 keVT_i = 2.0\,\mathrm{keV}, and the pressure profile falls toward the plasma edge with scale length Lp=0.30 mL_p = 0.30\,\mathrm m. ((a)) Using the interchange criterion ∇p⋅κ>0\nabla p\cdot\boldsymbol\kappa > 0 for instability, predict whether the outboard side of the torus (bad curvature) or the inboard side (good curvature) is subject to the interchange instability. ((b)) For the unstable side, estimate the growth rate γ≈(Ti/mi)1/2/(RcLp)1/2\gamma \approx (T_i/m_i)^{1/2}/(R_cL_p)^{1/2} and the e-folding time 1/γ1/\gamma.

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