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Abstract

A new Penning-trap experiment aiming at a measurement of the ground-state hyperfine structure
of ³He⁺ and the nuclear magnetic moment of ³He²⁺ is being set up at the Max Planck
Institute for Nuclear Physics. The hyperfine structure measurement will provide values for the
bound state 6-factors of the electron and nucleus with relative uncertainties of 10^-10 and 10^-9,
respectively. Additionally, the zero-field hyperfine splitting will be determined to 10^-10 precision
or better. As there has been no previous measurement on a system of interacting nuclear
and electron spin in a Penning trap, calculations are made to connect the established theoretical
results used in Penning trap 6-factor experiments to the hyperfine structure measurement. In
order to drive the hyperfine transitions, waveguides need to couple microwaves from a room
temperature source to the cryogenic Penning traps over a distance of about 2 m. A numerical
mode matching technique building on the mode propagation in waveguides is developed.
Together with finite element calculations, it is used to optimise the waveguide for maximum
transmission under the experimental constraints. It is argued that stainless steel oversized
waveguide components are more practical than standard components and that the difficulties
arising with them can be dealt with. Transmission measurements with the assembled system
complement the numerical studies and show that the transmission line provides enough microwave
power to drive the transitions of the hyperfine structure.