Resistive and sympathetic cooling of highly-charged-ion clouds in a Penning trap

We present measurements of resistive and sympathetic cooling of ion clouds confined in a Penning trap. For resistive cooling of a cloud consisting of one ion species, we observe a significant deviation from exponential cooling behavior which is explained by an energy-transfer model. The observed sympathetic cooling of simultaneously confined ion species shows a quadratic dependence on the ion charge state and is hence in agreement with expectations from the physics of dilute non-neutral plasmas.

Figure 1

Schematic of the Penning trap. Left: Homogeneous axial magnetic field inside the trap for radial ion confinement. Center: Stack of hollow cylinder electrodes forming the physical trap. Right: Simplified electric potential created inside the trap for axial ion confinement.

Figure 2

Schematic of the spectral distributions of an ion oscillation and the impedance $Z\left(\omega \right)$ of a resonant circuit. In our experiment we choose ${\omega }_z={\omega }_R$.

Figure 3

Schematic of the present energy reservoirs and energy transfers. Arrows indicate the direction of energy flow in the present situation, with time constants indicated.

Figure 4

Calculated ion signal as a function of time. Solid curve, cooling after initial excitation to 10 eV; dotted curve, the same for 1 eV. Upper inset: Value of indicated ${\tau }_A$ as a function of time. Lower inset: The same for ${\tau }_R$.

Figure 5

Measured signal of 30 ${\mathrm{C}}^{5+}$ ions as a function of time for different excitation amplitudes $V_e$.

Figure 6

Ion cooling curve from Fig. 5 for the highest excitation voltage, $V_e=12$ V. Inset: A fit to the data within the initial 5 s.

Figure 7

Cooling time constants resulting from a fit to the initial 2.5 s of the signals as shown in Fig. 5.

Figure 8

Spectrum of the trap content upon ion creation. The square of the detection voltage $V$ is plotted as a function of the set trap voltage $U_0$.

Figure 9

Integrated ion signal for the ${\mathrm{C}}^{4+}$ peak from Fig. 8 as a function of the time. A simple exponential decay has been fitted to the data.

Figure 10

Resulting cooling time constants for all ion species in the spectrum as a function of $q^2/m$. A linear fit has been applied to the data.