Propagation of ion acoustic wave energy in the plume of a high-current ${\mathbf{LaB}}_6$ hollow cathode

A frequency-averaged quasilinear model is derived and experimentally validated for the evolution of ion acoustic turbulence (IAT) along the centerline of a 100-A class, ${\mathrm{LaB}}_6$ hollow cathode. Probe-based diagnostics and a laser induced fluorescence system are employed to measure the properties of both the turbulence and the background plasma parameters as they vary spatially in the cathode plume. It is shown that for the three discharge currents investigated, 100 A, 130 A, and 160 A, the spatial growth of the total energy density of the IAT in the near field of the cathode plume is exponential and agrees quantitatively with the predicted growth rates from the quasilinear formulation. However, in the downstream region of the cathode plume, the growth of IAT energy saturates at a level that is commensurate with the Sagdeev limit. The experimental validation of the quasilinear model for IAT growth and its limitations are discussed in the context of numerical efforts to describe self-consistently the plasma processes in the hollow cathode plume.

Figure 1

(a) Experimental setup of the 100-A ${\mathrm{LaB}}_6$ hollow cathode and cylindrical anode. The ion saturation probe array for dispersion measurements is also shown. (b) Schematic of the experimental setup illustrating the beam path for the laser induced fluorescence system. All experimental measurements are referenced axially with respect to the surface denoted “keeper exit” and radially with respect to the cathode centerline.

Figure 2

Two-dimensional maps of (a) plasma density and (b) electron temperature in the hollow cathode plume for a discharge current of 160 A and flow rate of 15 sccm. The diameter of the keeper orifice at the exit plane (located at 0 mm) is 10 mm.

Figure 3

(a) Plasma density and (b) electron temperature along centerline for the three investigated discharge currents.

Figure 4

Representative plots of the axial ion velocity distribution function at two positions along the cathode centerline. The operating condition was 130 A with 15 sccm flow.

Figure 5

(a) Ion drift velocity along cathode centerline and (b) ion temperature along cathode centerline.

Figure 6

Estimated values for the electron Mach number along cathode centerline.

Figure 7

Power spectrum of IAT energy density at a position 11 mm downstream of the keeper for the operating condition of 130 A and 15 sccm. The result exhibits two dominant oscillations in the plasma: ionization-related and ion acoustic. The dashed line is a 25-degree best-fit polynomial to the IAT spectrum.

Figure 8

The average angular frequency of the IAT spectrum, ${\omega }_0$, along cathode centerline for the three operating conditions investigated.

Figure 9

Group velocity along axial centerline that was measured from best fits to dispersion plots (solid) and calculated from plasma parameters per Eq. (3) (open). The measured group velocity was estimated by assuming a probe separation of 4 mm.

Figure 10

(a) The magnitude of calculated non-dimensional growth factors for the IAT for the operating condition of 130 A and 15 sccm. ${\zeta }_{e,i}$ stems from electron and ion Landau damping, and ${\nu }_i$ is the ion-neutral collision frequency. (b) Calculated spatial growths for the IAT for the three operating conditions investigated.

Figure 11

Semilog plot of the total IAT energy density along cathode centerline for the three investigated operating conditions.

Figure 12

Measured spatial growth rate, $k_i$, and average calculated spatial growth rate, $\langle k_{i\left(L\right)}\rangle$ for the IAT along cathode centerline.

Figure 13

Plot of the calculated saturation IAT energy density along cathode centerline compared to the measured IAT energy density. The constant used to evaluate the calculated saturation values was $\alpha =3\times {10}^{-2}$.