Characteristics of the plasma impedance probe with constant bias

Abstract

The impedance of a small spherical probe immersed in a uniform plasma is measured by recording the reflection coefficient of an applied signal using a network analyzer. This impedance has a resonance at the plasma frequency where the imaginary part goes to zero, a feature that has made this measurement a good way of determining electron density. When the plasma potential is positive with respect to the sphere—for example, if the sphere is electrically floating or grounded, a second resonance occurs at ω<ωpe due to the capacitance created by the depleted electron density in the sheath. A greatly increased power deposition occurs at this lower resonance, whose frequency can be controlled by applying a dc bias which changes the sheath width. As the bias is increased the value of this frequency becomes smaller until the resonance disappears completely at Vprobe=Vplasma. As the bias is further increased past the plasma potential, an electron sheath forms with its own resonance, which is at a lower frequency than the resonance associated with the ion sheath. The impedance of the electron sheath can be approximated using sheath transit time perturbation theory for a space charge limited diode. As with the ion sheath resonance, the largest energy deposition occurs at the lower of the two resonant frequencies.