Driven thermal waves and determination of the thermal conductivity in a magnetized plasma

Results are presented from a basic heat transport experiment using a magnetized electron temperature filament that behaves as a thermal resonator. A small, crystal cathode injects low-energy electrons along the magnetic field into the afterglow of a large preexisting plasma forming a hot electron filament embedded in a colder plasma. A series of low amplitude, sinusoidal perturbations are added to the cathode discharge bias that create an oscillating heat source capable of driving thermal waves. Langmuir probe measurements demonstrate driven thermal oscillations and allow for the determination of the amplitude and parallel phase velocity of the thermal waves over a range of driver frequencies. The results conclusively show the presence of a thermal resonance and are used to verify the parallel thermal wave dispersion relation based on classical transport theory. A nonlinear transport code is used to verify the analysis procedure. This technique provides an alternative measure of the density normalized thermal conductivity, independent of the electron temperature.

Figure 1

Schematic (not to scale) of the experimental setup on the LAPD. In the afterglow phase of the main discharge the ${\mathrm{CeB}}_6$ cathode injects an electron beam into the plasma, creating a temperature plume that is transported down the length of the device forming a narrow filament of elevated temperature. Langmuir probe measurements are made at axial positions $z_1=160\mathrm{cm}$ and $z_2=256\mathrm{cm}$ away from the filament heat source.

Figure 2

(a) In black (middle) is the electron temperature, $T_e$, and in blue (bottom) the density, $n$, obtained from a Langmuir sweep for the applied voltage in red (top). (b) In black, $\delta I_{\text{sat}}$ traces collected at $z_2$ depicting the spontaneous and stimulated thermal waves and in red the normalized applied voltage for ac shots. (i) Single dc shot, (ii) ten dc shots ensemble average, (iii) normalized applied voltage, (iv) single ac shot, and (v) 100 ac shots ensemble average.

Figure 3

Amplitude analysis of $\delta I_{\text{sat}}$ at $z=z_2$ for different driver frequencies, $f_{\text{ac}}$, and amplitudes, $\delta V/V_{\text{dc}}$. The curves are all normalized to the maximum of $\delta V/V_{\text{dc}}=0.40$ and the fractional error at $\delta V/V_{\text{dc}}=0.40$ is similar for the other cases. Inset: the $\sim 8\mathrm{kHz}$ amplitude resonance shows a linear scaling of $\delta I_{\text{sat}}$ with respect to the amplitude of the oscillations in the driving power.

Figure 4

The black diamonds are the experimentally measured phase velocity at different driver frequencies. A weighted least-square error fit of the data to Eq. (1) with ${\kappa }_{\parallel }/n$ as the fitting parameter is indicated by the red line. The result of a transport code used to model the linear analysis is denoted by hollow blue triangles. The inset figure is a spectral analysis of the signal at $z_1$ in the absence of driven oscillations.