Emission of positively charged ions from a plasma emitter irradiated by a counterpropagating electron beam is studied theoretically. A bipolar diode with a plasma emitter in which the ion temperature is lower than the electron temperature and the counter electron flow is extracted from the ion collector is calculated in the one-dimensional model. An analog of Bohm’s criterion for ion emission in the presence of a counterpropagating electron beam is derived. The limiting density of the counterpropagating beam in a bipolar diode operating in the space-charge-limited-emission regime is calculated. The full set of boundary conditions on the plasma emitter surface that are required for operation of the high-current optics module in numerical codes used to simulate charged particle sources is formulated.