Modulated Electron Cyclotron Drift Instability in a High-Power Pulsed Magnetron Discharge

The electron cyclotron drift instability, implicated in electron heating and anomalous transport, is detected in the plasma of a planar magnetron. Electron density fluctuations associated with the mode are identified via an adapted coherent Thomson scattering diagnostic, under direct current and high-power pulsed magnetron operation. Time-resolved analysis of the mode amplitude reveals that the instability, found at MHz frequencies and millimeter scales, also exhibits a kHz-scale modulation consistent with the observation of larger-scale plasma density nonuniformities, such as the rotating spoke. Sharply collimated axial fluctuations observed at the magnetron axis are consistent with the presence of escaping electrons in a region where the magnetic and electric fields are antiparallel. These results distinguish aspects of magnetron physics from other plasma sources of similar geometry, such as the Hall thruster, and broaden the scope of instabilities which may be considered to dictate magnetron plasma features.

Figure 1

Dispersion relation results from linear kinetic theory, showing ECDI resonances (dashed line) and smoothed resonances (solid line). In this example, $n_e={10}^{18}{\mathrm{m}}^{-3}$, $V_{te}/V_d=0.64$, and ${\omega }_{ce}/{\omega }_{pe}=\mathrm{0.027.}{n}_e$, $V_{te}$ and ${\omega }_{pe}$ are the electron density, electron thermal velocity, and electron plasma frequency, respectively.

Figure 2

(a) Definition of observation wave vector $\overrightarrow{k}$ from the incident $\overrightarrow{k_i}$ and scattered wave vectors $\overrightarrow{k_s}$. The gray region is the observation volume formed by the local oscillator and primary beam intersection. (b) A view of the observation wave vector orientation angle $\alpha$ and positioning at a distance $d$ from the cathode surface. Magnets behind the cathode and typical magnetic field lines (in blue) are shown.

Figure 3

FFT of signal time series for a pulsed-operation experiment. Broad frequency peaks around $\pm 1\mathrm{MHz}$ are visible on the blue line. The black line is a plot of the photonic noise signal. HIPIMS: peak $U_d=504\mathrm{V}$, peak $I_d=8.6\mathrm{A}$, $P=15\mathrm{mTorr}$; $\alpha =100°$, $k=5600\mathrm{rad}/\mathrm{m}$.

Figure 4

Examples of the azimuthal mode dispersion relations, determined in dc (triangles) and HIPIMS (circles) regimes. dc: $U_d=388\mathrm{V}$, $I_d=0.5\mathrm{A}$, $P=22.5\mathrm{mTorr}$; $\alpha =85°$ HIPIMS: peak $U_d=575\mathrm{V}$, peak $I_d=22\mathrm{A}$, $P=15\mathrm{mTorr}$; $\alpha =100°$.

Figure 5

Variation in (a) mode amplitude and (b) frequency with orientation angle $\alpha$ in the ($\overrightarrow{E}$, $\overrightarrow{E}\times \overrightarrow{B}$) plane [see Fig. 2]. $O$ represents the center of the cathode. dc: $U_d=370\mathrm{V}$, $I_d=0.4\mathrm{A}$; $k=5600\mathrm{rad}/\mathrm{m}$.

Figure 6

Pulse characteristics and mode features. (a) Current (blue) and discharge voltage (green) profiles within the chosen pulse, (b) spectrogram of the scattered signal within the pulse envelope [amplitudes equal to $10{\log }_{10}|P_s|$, where $P_s$ is the power spectral density (PSD)], and (c) time variation of power spectral density at 1 MHz, showing low-frequency periodicity. HIPIMS: peak $U_d=494\mathrm{V}$, peak $I_d=7\mathrm{A}$, $P=15\mathrm{mTorr}$; $\alpha =100°$, $k=5600\mathrm{rad}/\mathrm{m}$.