INTRODUCTION
The concept of a Helical Cooling Channel (HCC) [1] with a continuous homogeneous absorber has already shown considerable promise to cool the 6D emittance of a muon beam [2]. A recent extension of the HCC concept is to use or momentum-dependent field strengths for new beam cooling applications [3]. Thus, the number of uses of a HCC has increased. Examples of these new applications of a HCC that we have examined so far include: 1) a precooling device to cool a muon beam as it decelerates by energy loss in a continuous, homogeneous absorber, where the cooling can be all transverse, all longitudinal, or any combination; 2) a device similar to the precooler above, but used as MANX [3], a muon cooling demonstration experiment; 3) a transition section between two HCC sections with different dimensions as when the RF frequency can be increased once the beam has been cooled sufficiently to allow smaller and more effective cavities and magnetic coils, and 4) as an alternative to the original HCC filled with pressurized RF cavities. In this case, muons would lose a few hundred MeV/c by ionizing liquid hydrogen in a HCC section with momentum dependent fields and then pass through several RF cavities to replenish the lost energy. This sequence could be repeated several times.