Observation of Nonlocal Heat Flux Using Thomson Scattering

Nonlocal heat flux was measured in laser-produced coronal plasmas using a novel Thomson scattering technique. The measured heat flux was smaller than the classical values inferred from the measured plasma conditions in regions with large temperature gradients and agreed with classical values for weak gradients. 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. Multigroup nonlocal simulations overestimated the measured heat flux.

Figure 1

(a) Calculated Thomson-scattering features (red curve, right axis) from electron plasma waves [Eq. (1)] are shown (${\mathrm{v}}_{\varphi }=\omega /k$) using a Maxwellian (solid blue curve, left axis) electron distribution function and the non-Maxwellian (dashed blue curve) distribution that accounts for classical SH heat flux (${\lambda }_{ei}/L_T=2.2\times {10}^{-3}$, $q/q_{\mathrm{FS}}=3\%$). Inset: For a fixed normalized phase velocity, the ratio ($R$) of the peak scattered power of the up- and downshifted features are shown for calculations that use classical SH (solid curve, top axis) and nonlocal (dashed curve, bottom axis) distribution functions over a range of heat flux. (b) A schematic of the setup is shown.

Figure 2

The measured collective Thomson-scattering spectra (top row) and the corresponding spectral profiles (blue dots) at 1.5 ns (bottom row). The data were fit (red curves) with Eq. (1) using non-Maxwellian electron distribution functions to measure heat flux. Insets: The redshifted features are shown with calculations (black curves) that used the plasma conditions from the fit but a Maxwellian electron distribution function. These spectra recover the location of the scattering features but fail to match their amplitudes. At 1.5 mm, the spectrum was fit (dashed curve) with calculations that use a distribution function consistent with classical SH theory. All spectra are normalized to the peak scattered power.

Figure 3

The heat flux (red points) measured along the target normal is compared with classical heat flux (SH) calculations (blue points) and heat flux values (black points) obtained from the simulations using the SNB model. Both the simulations and calculations were initiated with the measured electron temperatures and densities. For reference, ${\lambda }_{ei}/L_T=1.4\times {10}^{-2}$, $1.4\times {10}^{-2}$, $1.3\times {10}^{-2}$, $1.0\times {10}^{-2}$, $7\times {10}^{-3}$ at 1.1, 1.2, 1.3, 1.4, and 1.5 mm, respectively.

Figure 4

Electron temperature (blue dots, left axis) and density (red squares, right axis) measurements at $t=1.5\mathrm{ns}$. Profiles of electron temperature (dashed blue curve) and density (solid red curve) used in Fokker-Planck simulations. The relative ($1\sigma$ statistical) error bars are shown with the temperature measurements. The absolute error bars are represented in the inset.

Figure 5

The velocity-dependent contribution of heat flux is shown at $1200\mu \mathrm{m}$ for calculations using the Fokker-Planck (dashed red curve), classical (solid blue curve), and SNB (dotted black curve) models. Inset: The corresponding electron distribution functions are shown.