An alternative cooling approach to prevent rf breakdown in magnetic fields is described that simultaneously reduces all six phase-space dimensions of a muon beam. In this process, cooling is accomplished by reducing the beam momentum through ionization energy loss in discrete absorbers and replenishing the momentum loss only in the longitudinal direction through gas-filled rf cavities. The advantage of gas filled cavities is that they can run at high gradients in magnetic fields without breakdown. With this approach, we show that our channel can achieve a decrease of the 6-dimensional phase-space volume by several orders of magnitude. With the aid of numerical simulations, we demonstrate that the transmission of our proposed channel is comparable to that of an equivalent channel with vacuum rf cavities. Finally, we discuss the sensitivity of the channel performance to the choice of gas and operating pressure.
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