Symmetry Considerations for Grid-Launched Ion-Acoustic Waves

Immersion of a fine-mesh grid (or set of parallel grids) into a plasma is widely used to stimulate ion-acoustic waves. The grid structure is usually biased so as to reflect electrons and transmit ions. The effect upon the ions due to applied rf fields in the grid region is to provide some combination of velocity and density modulation. The associated applied electric field perturbations will possess a combination of odd and even spatially symmetric parts, about the plane of symmetry of the grid system. The steady-state solution of the governing differential equation in the ion-acoustic limit is shown to depend critically upon this source symmetry, and to reduce to the usual solution only for the case of odd symmetry. Experiments designed to test these symmetry predictions have been carried out using an apparatus described previously, except that a four-grid transmitter has been substituted for the three-grid one. The outer two grids are grounded and the inner two grids can be driven either in phase (odd E-field symmetry), or 180° out of phase (even E-field symmetry). For odd symmetry, the observed spatial disturbance is similar to that reported previously with clear evidence of Fresnel interference. For even symmetry, wavelike signals are not observed near the grids, indicating a strong decrease in coupling between the free-streaming source ions and an ion-acoustic wave.