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Singly ionised Lutetium has recently been suggested as a potential clock candidate. Here we report a joint experimental and theoretical investigation of Lu + . Measurements relevant to practical clock operation are made and compared to atomic structure calculations. Calculations of scalar and tensor polarizabilities for clock states over a range of wavelengths are also given. These results will be useful for future work with this clock candidate.

We investigate the feasibility of precision frequency metrology with large ion crystals. For clock candidates with a negative differential static polarisability, we show that micromotion effects should not impede the performance of the clock. Using Lu + as a specific example, we show that quadrupole shifts due to the electric fields from neighbouring ions do not significantly affect clock performance. We also show that effects from the tensor polarisability can be effectively managed with a compensation laser at least for a small number of ions ( 10 3 ). These results provide new possibilities for ion-based atomic clocks, allowing them to achieve stability levels comparable to neutral atoms in optical lattices and a viable path to greater levels of accuracy.

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In this paper, we estimate the uncertainty in complex permittivity measurements performed in a shielded dielectric resonator, by using the Monte Carlo Method. We selected this approach since the theoretical expressions required to interpret the experimental results are highly non-linear. Furthermore the resonant frequency of the system and its quality factor are highly correlated. Thus we propose a model for the measurement process which considers the major sources of uncertainty previously reported in published experimental results. The proposed model combined with the Monte Carlo method was used to propagate the probability distributions of each uncertainty contribution, obtaining a) the approximate probability density function for the measured complex permittivity, and b) the estimated expanded uncertainty for the mode TE 011 . The results show that this procedure leads to small uncertainty intervals for the real part of the dielectric permittivity, while it is not very reliable in the loss tangent measurement. Additionally, for each input quantity, we calculated the standard deviation in the experimental results produced independently by each uncertainty contribution.

Abstract-Throughout the performance of a RF immunity test according IEC 61000-4-3 there are several factors that should be taken into account to ensure the quality and to estimate the uncertainty associated to the results. One phenomenon that should be considered to calculate uncertainty is the disturbing effect produced by the EUT over the electric field generated within the calibrated uniform field area; nevertheless the mentioned effect is not easily quantifiable because the measuring process using additional antennas or field probes inside the semianechoic chamber could also alter the electric field distribution. An experimental method for quantifying the mentioned uncertainty contribution is presented. The method is based upon the fact that antenna-EUT coupling and reflection effects could be measured through changes in the input impedance of the field generation antenna. A validation procedure for the proposed method is also described. Hence, a relationship between the reflection coefficient at the antenna input port and the electric field strength is derived. The uncertainty contribution is calculated through the maximum relative change in the E-field intensity magnitude for the frequency range of 80-1000 MHz, considering the worst case for several EUT positions.

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