Using OpAmps to amplify a low voltage/High noise DC signal
The preferred technique for measuring the current of an ion beam is using a transimpedance amplifier (TIA) configuration. I'm think here of gas mass spectrometers but generally it is a good idea because it keeps the target potential at near zero volts. Imagine what happens to your ion beam as the "cup" starts charging up - will it deflect the beam and make measurement errors? Possibly so. Anyway this is the sort of circuit I believe makes most sense: -



The output voltage is R x input current and you might find that R needs to be in the order of giga ohms. There are specialist op-amps that suit this application too because leakage currents from the op-amp inputs can produce a significant error given the size that R needs to be. Check out TI and ADI's portfolios of specialist op-amps for what is available that has low bias currents.

The input impedance seen by the ion beam is nominally zero and the op-amp achieves that with negative feedback thus maintaining the inverting input at the same potential as the non-inverting input i.e. 0V.