The ALPHA (Antihydrogen Laser Physics Apparatus) collaboration creates and performs precise measurements on antihydrogen to test Charge-Parity-Time (CPT) symmetry. Prior to creating antihydrogen we must prepare the antiproton and positron plasmas to have optimal and repeatable parameters. This thesis presents the development of a new method to simultaneously control the number of particles and plasma density of lepton plasmas, developments that increased our antihydrogen trapping rate, precision physics measurements performed on antihydrogen, and other plasma studies still under development. The method to stabilize the number of particles was based on a zero-temperature plasma model, which states that the plasma's on-axis self potential and density uniquely define a plasma. [...]