A six-dimensional muon ionization cooling in a helical magnet channel has been studied. The cooling performance which is analytically evaluated by solving the exact Hamiltonian is reproduced in numerical simulation. One of the key beam elements for the helical channel is a dense-hydrogen gas-filled RF cavity which realizes a compact cooling channel. Besides, a beam-induced gas plasma in the cavity can generate a plasma-focusing effect. This will generate extremely small betatron function, which realizes extremely low emittance beam.
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