A tokamak discharge has major radius

PHYSICS · Multi-part · Fermi University Physics · Plasma Physics · Kinetic theory, collisions and transport · Kinetic theory, collisions and transport

Plasma Physics, Ch Transport across and along the field: ambipolar, classical, neoclassical and anomalous

Problem

A tokamak discharge has major radius R0=1.67 mR_0 = 1.67\,\mathrm{m}, and at a chosen flux surface the minor radius is r=0.33 mr = 0.33\,\mathrm{m}, the safety factor is q=3.0q = 3.0, the field is B=2.0 TB = 2.0\,\mathrm{T}, the electron density is n=5.0×1019 m−3n = 5.0\times10^{19}\,\mathrm{m^{-3}}, and Te=Ti=1.5 keVT_e = T_i = 1.5\,\mathrm{keV} (Z=1Z=1, ln⁡Λ=15\ln\Lambda = 15). The ions are deuterons, mi=3.34×10−27 kgm_i = 3.34\times10^{-27}\,\mathrm{kg}. ((a)) Find the electron Larmor radius rLer_{Le} and Braginskii's electron collision time τe\tau_e. ((b)) Find (Ωeτe)2(\Omega_e\tau_e)^2 and state what it implies about the temperature on this flux surface. ((c)) Using Chapter 14's relation τi/τe≈2 (mi/me)1/2(Ti/Te)3/2\tau_i/\tau_e \approx \sqrt2\,(m_i/m_e)^{1/2}(T_i/T_e)^{3/2} for Z=1Z=1, estimate the classical ion heat diffusivity χi≈rLi2/τi\chi_i \approx r_{Li}^2/\tau_i. ((d)) Find the inverse aspect ratio ϵ=r/R0\epsilon = r/R_0 and the neoclassical collisionality νe∗=νei qR0/(ϵ3/2vte)\nu_e^{*} = \nu_{ei}\,qR_0/(\epsilon^{3/2}v_{te}), and confirm the plasma is in the banana regime (νe∗<1\nu_e^{*} < 1). ((e)) Estimate the neoclassical ion heat diffusivity χineo≈q2ϵ−3/2χi\chi_i^{\rm neo} \approx q^2\epsilon^{-3/2}\chi_i.

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