Direct Measurements of Nonlocal Heat Fux by Thomson Scattering*

In diverse fields of plasma physics including astrophysics, inertial confinement fusion, and magnetohydrodynamics, classical thermal transport provides the foundation for calculating heat flux. The classical theories of thermal transport [e.g., Spitzer–Härm (SH) and Braginskii] break down in the presence of large temperature gradients, turbulence, or return current instabilities: they do not include nonlocal effects where energetic electrons travel distances comparable with the temperature scale length (L_T) before colliding. Nonlocal theories have improved upon and established the limits of classical transport (λ_ei/L_T∼10^-2) by accounting for the velocity dependence of the mean free path (λ_ei). These limits were confirmed by a novel Thomson-scattering technique that provided the first direct measurement of nonlocal heat flux. The heat flux was measured directly from the amplitudes of the Langmuir fluctuations and indirectly through the electron temperature and density profiles (q_SH =-κ∇T_e), and were enabled by setting the Thomson-scattering geometry to probe Langmuir fluctuations with phase velocities near the range of the heat-carrying electrons (v_φ∼3.5_th). The measured heat flux agreed with classical SH values when λ_ei/L_T<10^-2, but in the opposite limit, the differences were as large as a factor of 2. Vlasov–Fokker–Planck simulations self-consistently calculated the electron distribution functions used to reproduce the measured Thomson-scattering spectra and to determine the heat flux. The multigroup nonlocal Schurtz–Nicolaï–Busquet (SNB) model overpredicted for all values of λ_ei/L_T, demonstrating the need to include physics often missing from computationally expedient nonlocal models.