Schematic of a single particle axial frequency detection system in a cylindrical Penning trap. The trap is represented by three cylindrical electrodes. The oscillation of the charged particle in the axial direction is indicated by the double arrow. The resonator is a parallel tank circuit consisting of an inductance , an effective resistance , and a parasitic capacitance . The signal is coupled to a cryogenic amplifier.
(a) On-axis magnetic field of the superconducting magnet. (b) Schematic of the experimental setup. The thermal conduction rods are connected to the cold stage of a pulse tube cooler. The cooled resonator can be moved horizontally into the superconducting magnet. Therefore, the field can be varied between 5 mT and 1.2 T.
(a) Schematic of the -value measurement with a HP3385A network analyzer. The excitation signal is weakly coupled to the tuned circuit. The rf field in the resonator is probed with a low inductance coil. (b) -value as a function of the rf amplitude setting at the network analyzer. For small amplitudes the -value is constant. At higher amplitudes a decrease in the -value is observed. All further measurements were performed in the regime of constant , with an amplitude setting at the network analyzer of −65 dBm.
Sketch of the superconducting resonator. The coil is wound on a PTFE core, the core is fixed to the bottom of the cylindrical housing with brass screws. The lid is fixed to the cylinder with 12 screws (not shown), since good contact between both parts is essential.
-value (filled circles) and residual series resistance (filled triangles) of the resonator for different optimization steps. The details of the respective optimization steps are described in the text.
Quality factor of the tuned circuit as a function of the external magnetic field . Series 1: resonator cooled in vanishing magnetic field . Series 2: resonator cooled in high magnetic field. Series 3: resonator cooled in ambient magnetic field of actual position. All data sets show a -value decrease with increasing magnetic dc-field. For further details see text.
Residual resistance as a function of the average dc field. The squares represent the measured data; the solid line is the result of a fit based on the combination of our model with the CCT. For further details see text.
Comparison of the surface resistance of copper with a RRR of 140 (solid line) and field penetrated NbTi as a function of the resonance frequency of the tuned circuit.
Quality factor (dots) and residual resistance (triangles) as a function of temperature.
Sketch of a real trap experiment using a compensated cylindrical Penning trap. The signal is picked up at one of the correction electrodes. The amplifiers input is modeled as a parallel -circuit with a resistance and a parasitic capacitance . The cryogenic feedthrough is also modeled as a parallel with resistance and capacitance . The dc-bias circuitry of the pick-up-electrode is blocked by means of a high impedance resistor . The capacitances represent the parasitic coupling between the resonator and the dc-biasing network of the neighbored electrodes and other low impedance lines guided near the signal pick-up line.
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