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Establish the scaling of the safe gradient with B, frequency and wall material up to $B \\sim 1e5\\,\\mathrm{G}$ and above, as required for 6D muon ionization cooling channels.","problem_ref":null,"references":"","settled_by":"Gradient-limit measurements versus B up to the cooling-channel field for at least two wall materials and frequencies, compared with an electron-focusing heating model.","status_note":"Beryllium-walled and high-pressure gas-filled cavities reached approximately $0.5\\,\\mathrm{MeV}/\\mathrm{cm}$ in fields near $3e4\\,\\mathrm{G}$ at the Fermilab MuCool Test Area (reported around 2020); higher fields remain untested.","title":"Breakdown limit of RF cavities inside strong solenoid 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