Coupled heat pulse propagation in two-fluid plasmas

Because of the large mass differences between electrons and ions, the heat diffusion in electron-ion plasmas exhibits more complex behavior than simple heat diffusion found in typical gas mixtures. In particular, heat is diffused in two distinct, but coupled, channels. Conventional single fluid models neglect the resulting complexity, and can often inaccurately interpret the results of heat pulse experiments. However, by recognizing the sensitivity of the electron temperature evolution to the ion diffusivity, not only can previous experiments be interpreted correctly, but informative simultaneous measurements can be made of both ion and electron heat channels.

Figure 1

Apparent diffusivity ${\chi }_{\text{app}}$ for ${\chi }_e=1{\mathrm{m}}^2/\mathrm{s},{\chi }_i=2{\mathrm{m}}^2/\mathrm{s}$. (a) ${\chi }_{\text{app}}$ vs frequency for several distances from source. Dotted lines indicate limiting values at ${\chi }_e$ and ${\chi }_e/2(1+\gamma )$. (b) ${\chi }_{\text{app}}$ vs distance from source for low, intermediate, and high driving frequencies. Dotted lines indicate limiting values at ${\chi }_e, ({\chi }_e+{\chi }_i)/2$, and ${\chi }_i$.

Figure 2

Left: Relative diffusivity error ${\chi }_{\text{app}}/{\chi }_e$ as a function of measurement distance and driving frequency. Right: Zoomed-in view of a region of backwards-propagating phase and increasing amplitude. Left negative region corresponds to ${\varphi }^{\prime }<0$; right region corresponds to $A^{\prime }<0$. Overlap produces positive values, so a cut along either frequency or position axis containing this overlap would exhibit four resonances.

Figure 3

Composite quantites (a) ${\varphi }^{\prime }/(A^{\prime }/A)$ and (b) ${\varphi }^{\prime }(A^{\prime }/A)$ evaluated at a distance of 20 cm from the source vs driving frequency, for several ion diffusivities.