This paper introduces a new method for stacking beams in the longitudinal phase space. It uses RF barriers to confine and compress beams in an accelerator, provided that the machine momentum acceptance is a few times larger than the momentum spread of the injected beam. This is the case for the Fermilab Main Injector. A barrier RF system employing Finemet cores and high-voltage solid-state switches is under construction. The goal is to double the number of protons per cycle on the production target for Run2 and NuMI experiments.
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