Symmetric plasmas composed of positive and negative ions of equal mass lend themselves to applications in fusion energy research, plasma processing, and ion propulsion. Reported here are new aspects of the trapping, acceleration, and transport of such plasmas. For trapping and acceleration, electric quadrupoles driven at radio frequencies (RFQs) are employed. The trapped particle density scales inversely with quadrupole aperture size; the plasma density is increased by shrinking the quadrupole, and total beam currents are increased by paralleling small quadrupoles in place of a large one. The acceleration process breaks the beam into alternating bunches of positive and negative ions; an additional RFQ can debunch and neutralize the beam. The trapping scaling theory as well as experimental and computational results are presented. Also, a theoretical basis for the ability of a sufficiently dense symmetric plasma beam to transport across a magnetic field and pertinent simulation results are presented. This work is supported by DOE through contract DE-FG03-00ER54575 and the Fusion Energy Sciences Fellowship.