The goal of the THe-Trap experiment is to measure the tritium/helium-3 mass ratio in order to deduce the Q value of the tritium β-decay. A relative uncertainty of 10 parts per trillion in the mass ratio would allow determining the Q value with a precision of 30 meV. This value is of relevance for the Karlsruhe Tritium Neutrino (KATRIN) collaboration, which is building a spectrometer to measure the mass of the electron antineutrino. In this contribution, we present the progress made in the past 2 years. We can, e.g., store, manipulate and detect single ions. To demonstrate the current accuracy, we measured the carbon-12 to oxygen-16 mass ratio with a relative uncertainty of 120 parts per trillion in early 2013. The improvements, current status and future perspectives will be presented

An ion in a Penning trap induces image charges on the surfaces of the trap electrodes. These induced image charges are used to detect the ion's motional frequencies, but they also create an additional electric field, which shifts the free-space cyclotron frequency typically at a relative level of several 10 −11. In various high-precision Penning-trap experiments, systematics and their uncertainties are dominated by this so-called image charge shift (ICS). The ICS is investigated in this work by a finite-element simulation and by a dedicated measurement technique. Theoretical and experimental results are in excellent agreement. The measurement is using singly stored ions alternately measured in the same Penning trap. For the determination of the ion's magnetron frequency with relative precision of better than 10 parts per billion, a Ramsey-like technique has been developed. In addition, numerical calculations are carried out for other Penning traps and agree with older ICS measurements.

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The ideal Penning trap consists of a uniform magnetic field and an electrostatic quadrupole potential. In the classical low-energy limit, the three characteristic eigenfrequencies of a charged particle trapped in this configuration do not depend on the amplitudes of the three eigenmotions. No matter how accurate the experimental realization of the ideal Penning trap, its harmonicity is ultimately compromised by special relativity. Using a classical formalism of first-order perturbation theory, we calculate the relativistic frequency-shifts associated with the motional degrees of freedom for a spinless particle stored in an ideal Penning trap, and we compare the results with the simple but surprisingly accurate model of relativistic mass-increase

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