[en] The tandem high-density hydrogen negative-ion-source system is optimized to identify the largest possible ion concentrations and extracted ion currents. The optimization includes varying the length of the second chamber, varying neutral gas and electron densities, and varying the ratio of atomic to molecular density. Vibrational excitation occurs via high-energy electron excitation (E-V process) and H₂⁺ surface neutralization (s-V process). These processes are considered separately and acting in parallel. The solutions are presented in terms of a dimensional scale factor, R. For a system scale length R = 1 cm, optimum extracted current densities are in the range 50 to 100 mA cm^-2. A single-chamber s-V system with the high-energy electron component suppressed can provide larger ion concentrations than a tandem E-V, s-V system. 14 references, 4 figures