Nonequilibrium phenomena and determination of plasma parameters in the hot core of the cathode region in free-burning arc discharges

We present spectroscopic measurements of plasma parameters (electron density $n_{\mathrm{e}}$, electron temperature $T_{\mathrm{e}}$, gas temperature $T_{\mathrm{g}}$, underpopulation factor $b$) in the hot-core region in front of the cathode of a low-current, free-burning arc discharge in argon under atmospheric pressure. The discharge is operated in the hot-core mode, creating a hot cathode region with plasma parameters similar to high-current arcs in spite of the fact that we use comparatively low currents (less than $20\mathrm{A}$). We use continuum emission and (optically thin) line emission to determine $n_{\mathrm{e}}$ and $T_{\mathrm{e}}$. We apply relaxation measurements based on a power-interruption technique to investigate deviations from local thermodynamic equilibrium (LTE). These measurements let us determine the gas temperature $T_{\mathrm{g}}$. All measurements are performed side-on with charge-coupled-device cameras as detectors, so that all measured plasma parameters are spatially resolved after an Abel inversion. This yields the first ever spatially resolved observation of the non-LTE phenomena of the hot core in the near-cathode region of free-burning arcs. The results only partly coincide with previously published predictions and measurements in the literature.

Figure 1

(Color online) Pictures of the cathode region in the diffuse mode (left) and the hot-core mode (right). The cathode diameter was $0.6\mathrm{mm}$ and the arc current was $12.5\mathrm{A}$ in both cases.

Figure 2

(Color online) Line emission coefficient (LEC) of the $\mathrm{Ar}\mathrm{I}$ line at $7147.04\mathrm{\AA }$ in a PLTE plasma in dependence of the electron temperature $T_{\mathrm{e}}$, the temperature splitting $\beta$, and the underpopulation factor $b$.

Figure 3

(Color online) Overview of the experimental setup for active and passive emission spectroscopy on the free-burning arc.

Figure 4

(Color online) Mapping of the rotated image of the arc plasma onto the entrance slit of the monochromator.

Figure 5

Spectrum from the center of the discharge (still Abel integrated) for the first axial position $(z=50\mathrm{\mu }\mathrm{m})$ in front of the cathode at $I=12.5\mathrm{A}$. All identified lines belong to transitions of $\mathrm{Ar}\mathrm{II}$. Additional line data can be found in [32, 33].

Figure 6

(Color online) Radially and temporally resolved relaxation process following a fast power interruption. The abscissa shows the temporal evolution ($t=0$ denotes the beginning of the power interruption) and the ordinate shows the radial resolution of the $\mathrm{Ar}I$ LEC (displayed in pseudo colors). The measurement was carried out for the first axial position $(z=50\mathrm{\mu }\mathrm{m})$ in front of the cathode at $I=12.5\mathrm{A}$. The temporal resolution (gate width) for the exposure of the iCCD camera was $200\mathrm{ns}$.

Figure 7

(Color online) LEC for the $\mathrm{Ar}\mathrm{I}$ line at $7147\mathrm{\AA }$ for different axial distances from the cathode after Abel inversion (measured with the slow-scan CCD camera). The arc was operated in the hot-core mode under atmospheric pressure at $I=12.5\mathrm{A}$. Close to the cathode the off-axis Larenz maxima appear, indicating that the center of the discharge has exceeded the norm temperature.

Figure 8

(Color online) LEC’s for the $\mathrm{Ar}\mathrm{I}$ line at $7147\mathrm{\AA }$ for the first five axial positions in front of the cathode after Abel inversion (measured with the iCCD camera). The arc was operated in the hot-core mode under atmospheric pressure at $I=12.5\mathrm{A}$. Curves with solid symbols display emission for a continuously operated discharge, whereas open symbols display the transient emission maximum during power interruption.

Figure 9

(Color online) Olsen-Richter plot consisting of measured LEC’s for $\mathrm{Ar}\mathrm{II}$ and CEC’s after Abel inversion. Here and in the following figures the notation $4400∕01\mathrm{\AA }$ refers to more than one line being evaluated simultaneously (in the case the lines at $4400\mathrm{\AA }$ and $4401\mathrm{\AA }$). See Table for a list of lines under investgation. The radial position $r$ and the axial position $z$ serve as implicit parameters for these measurements. The arc was operated in the hot-core mode under atmospheric pressure at $I=12.5\mathrm{A}$. For each axial distance a curve starts at high values stemming from the center of the discharge and then decreases radially. The distance between two measured points of a curve is $30\mathrm{\mu }\mathrm{m}$ due to the applied $2\times 2$ hardware binning of the slow-scan camera. Results of an LTE calculation parametrized with temperature are displayed for comparison with the measurements.

Figure 10

(Color online) Extended, three-dimensional Olsen-Richter plot showing measured $\mathrm{Ar}\mathrm{II}$ LEC’s, CEC’s, and the relaxation quotient together with a calculated LTE curve. The measurements contain radial distributions (roughly from left to right, with the center of the discharge being in the upper left corner) for the first five axial positions in front of the cathode and three different currents (colors and line types).

Figure 11

(Color online) Electron densities and electron temperatures determined from the measurements presented in Fig. 9.

Figure 12

(Color online) Radially resolved electron temperature profiles determined from the measurements presented in Fig. 9.

Figure 13

(Color online) Pseudocolor plot of the radially and axially resolved electron density distribution determined from the measurements presented in Fig. 9.

Figure 14

(Color online) Radially resolved profiles for the temperature splitting $\beta$ determined from the relaxation experiment with Eq. (4) using values for $T_{\mathrm{e}}$ from Fig. 12.

Figure 15

(Color online) Pseudocolor plot of the radially and axially resolved gas temperature distribution determined from Fig. 14.

Figure 16

(Color online) Radially resolved profiles for the underpopulation factor $b$ determined from the data presented in Fig. 11 and Fig. 14.

Figure 17

(Color online) Pseudocolor plot of the radially and axially resolved distribution of the underpopulation factor according to Fig. 16.

Figure 18

(Color online) Pseudocolor plot of the radially and axially resolved distribution of the electric field strength according to Eq. (5).