Ion acceleration in a helicon source due to the self-bias effect

Time-averaged plasma potential differences up to 165 V over several hundred Debye lengths are observed in low pressure (pn \u3c 1 mTorr) expanding argon plasmas in the Madison Helicon eXperiment (MadHeX). The potential gradient leads to ion acceleration greater than that predicted by ambipolar expansion, exceeding Ei≈7 kTe in some cases. RF power up to 500 W at 13.56 MHz is supplied to a half-turn, double-helix antenna in the presence of a nozzle magnetic field, adjustable up to 1 kG. A retarding potential analyzer (RPA) measures the ion energy distribution function (IEDF) and a swept emissive probe measures the plasma potential. Single and double probes measure the electron density and temperature. Two distinct mode hops, the capacitive-inductive (E-H) and inductive-helicon (H-W) transitions, are identified by jumps in density as RF power is increased. In the capacitive (E) mode, large fluctuations of the plasma potential (Vp-p≥140V, Vp-p/Vp ≈ 150%) exist at the RF frequency and its harmonics. The more mobile electrons can easily respond to RF-timescale gradients in the plasma potential whereas the inertially constrained ions cannot, leading to an initial flux imbalance and formation of a self-bias voltage between the source and expansion chambers. In the capacitive mode, the ion acceleration is not well described by an ambipolar relation, while in the inductive and helicon modes the ion acceleration more closely follows an ambipolar relation. The scaling of the potential gradient with the argon flow rate and RF power are investigated, with the largest potential gradients observed for the lowest flow rates in the capacitive mode. The magnitude of the self-bias voltage agrees with that predicted for RF self-bias at a wall. Rapid fluctuations in the plasma potential result in a time-dependent axial electron flux that acts to neutralize the accelerated ion population, resulting in a zero net time-averaged current through the acceleration region when an insulating upstream boundary condition is enforced. Grounding the upstream endplate increases the self-bias voltage compared to a floating endplate