Ion acoustic turbulence in a 100-A ${\mathrm{LaB}}_6$ hollow cathode

The temporal fluctuations in the near plume of a 100-A ${\mathrm{LaB}}_6$ hollow cathode are experimentally investigated. A probe array is employed to measure the amplitude and dispersion of axial modes in the plume, and these properties are examined parametrically as a function of cathode operating conditions. The onset of ion acoustic turbulence is observed at high current and is characterized by a power spectrum that exhibits a cutoff at low frequency and an inverse dependence on frequency at high values. The amplitude of the turbulence is found to decrease with flow rate but to depend nonmonotonically on discharge current. Estimates of the anomalous collision frequency based on experimental measurements indicate that the ion acoustic turbulence collision frequency can exceed the classical rate at high discharge current densities by nearly two orders of magnitude.

Figure 1

Photo of the 100-A hollow cathode experimental setup. A retarding potential analyzer (not used in this investigation) and the ion saturation probe array are also indicated.

Figure 2

(a) Electron temperature (b) and plasma density as functions of discharge current at four different flow rates. A representative error bar is shown for the temperature while the density is accurate to within 50%.

Figure 3

Beall plots with increasing current at the flow condition $\dot{m}=10\mathrm{sccm}$: (a) $I_D=30\mathrm{A}$; (b) $I_D=60\mathrm{A}$; and (c) $I_D=110\mathrm{A}$. Each plot is normalized to its maximum and has a frequency resolution of 10 kHz.

Figure 4

Beall intensity plot where aliasing is corrected for the case of $I_D=90\mathrm{A}$ and $\dot{m}=10\mathrm{sccm}$. The dotted line is a best fit to the linear dispersion of the acoustic mode.

Figure 5

(a) Phase velocity of the acoustic mode as a function of discharge current at different mass flow rates. The IAT could not be resolved at $\dot{m}=20\mathrm{sccm}$, and the absence of points in the $\dot{m}=15\mathrm{sccm}$ reflects our inability to detect the dispersion of the mode for these current values. (b) The calculated sound speed $c_s$ at the same conditions.

Figure 6

Power spectra for $\dot{m}=10\mathrm{sccm}$ as a function of increasing current. The top figure (a) illustrates the initial emergence of the IAT while the bottom plot (b) shows the growth of IAT with increasing current.

Figure 7

(a) Natural log-log plot of the measured power spectrum at $I_D=100\mathrm{A}$ and $\dot{m}=10\mathrm{sccm}$. The red line is a best fit to the decay of the spectrum. (b) The slopes of the best fits to the linear decay of the turbulent spectra as a function of discharge current for three different flow rates. The dotted line with value $-2$.4 corresponds to the electron trapping theory for the saturated turbulent spectrum while the solid line at $-2.6$ represents the ion-resonance broadening theory for saturation.

Figure 8

Semilog plots of power spectra for fixed currents and different flow rates: (a) $I_D=80\mathrm{A}$ and (b) $I_D=110\mathrm{A}$.

Figure 9

(a) Anomalous collision frequency due to the IAT. (b) Ratio of anomalous collision frequency to classical electron-ion collision frequency based on measurements of the electron temperature and density. Maximum error is $\pm 30\%$.