A medium-sized tokamak has deuterium ions with

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 medium-sized tokamak has deuterium ions with Te=Ti=1.0 keVT_e = T_i = 1.0\,\mathrm{keV}, toroidal field B=2.5 TB = 2.5\,\mathrm{T}, and a density gradient scale length near the edge of Ln=0.20 mL_n = 0.20\,\mathrm{m}. ((a)) Estimate the ion sound Larmor radius ρs=cs/Ωi\rho_s = c_s/\Omega_i, with the sound speed cs=(Te/mi)1/2c_s = (T_e/m_i)^{1/2} and Ωi=eB/mi\Omega_i = eB/m_i, taking the deuteron mass mi=3.34×10−27 kgm_i = 3.34\times10^{-27}\,\mathrm{kg}. ((b)) Use the mixing-length estimate χgB∼ρs2cs/Ln\chi_{\rm gB} \sim \rho_s^2c_s/L_n to estimate the gyro-Bohm heat diffusivity. ((c)) Compute the Bohm diffusion coefficient DB=Te/(16eB)D_B = T_e/(16eB) and compare the gyro-Bohm estimate, the Bohm value, and a typical measured heat diffusivity of order 1 m2 s−11\,\mathrm{m^2\,s^{-1}}.

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