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要旨

In this thesis, theoretical calculations of a Penning trap are performed, which
verify the practical realisation of sympathetic laser cooling and serve as a
basis for the implementation in the helium-3 experiment at the Max Planck
Institute for Nuclear Physics.
The aim of this experiment is an accurate determination of the g-factor
of helium-3. For this, a strongly cooled helium-3 nucleus must be present,
which is to be realised with sympathetic laser cooling. Sympathetic laser
cooling is based on the Coulomb interaction between two charged particles,
which exchange energy via the interaction, comparable to a coupled oscillator.
The aim is to transfer energy from the ion to be analyzed to the optically
active ion, which can be laser cooled. This allows energy to be dissipated
from the system of the two ions, which is equivalent to cooling. To achieve
the strongest possible interaction of the ions, a small distance between the
ions is necessary. For this purpose, a model of a coupled Penning trap with a
common endcap, which is significantly shortened, is created. The calculations
of the optimal parameters of this coupled Penning trap, which ensure stable
storage with additional alignment of the axial frequencies of the ions, are
presented in this thesis. The optimal parameters remain within the range of
what can be realised experimentally.
Furthermore, a precision voltage source of the UM-series from Stahl-
Electronics is checked for its suitability for the helium-3 experiment. This
voltage source is necessary to precisely adjust the voltages at the electrodes
of the coupled Penning trap. Specifically, the temperature dependence and
the noise behavior of the output voltage are analyzed.