Measurement of electric field and gradient in the plasma sheath using clusters of floating microspheres

A method for measuring the time-averaged vertical electric field and its gradient in the plasma sheath using clusters with $n=2$ or 3 floating microspheres of known mass is described. The particle charge $q$ is found by determining the ratio of the breathing frequency to the center-of-mass frequency for horizontal (in-plane) oscillations. The electric field at the position of the particles is then calculated using the measured charge-to-mass ratio, and the electric-field gradient is determined from the vertical resonance frequency. The Debye length is also found. Experimental results are in agreement with a simple sheath model.