Sensitive AC detector circuit
So, as far as I understand the field mill (not familiar with it, looks neat), you have a sinusoidal voltage at some frequency (couldn't read the time division on the scope), and you want to convert it to a value that an Arduino can read.

First off, it'd be helpful to know the absolute peak voltage this thing is going to generate in a thunderstorm or something. In the video, it looks like it goes above 5V.

Here's how I'd go about it:

First, clamp the input to a sane range. Let's say -0.7V to 15V. This will require some diodes (ideally two). This eliminates troublesome voltages that will ruin the rest of the circuit.

Next, run the signal through a precision peak detector (a regular peak detector outputs one diode drop below the input, and won't work for your low input voltages). This will eliminate the sine wave, and give you a slowly-varying (almost DC) voltage. Here is a helpful document for designing precision peak detectors. Googling will give you many more resource for designing precision peak detectors.

Feed this signal through a voltage divider (and maybe another low-pass filter to clean it up), and then into your datalogger's ADC. This assumes that the field mill output voltage range is actually more than the 0-5V ADC range (because that's what I saw in the video). If this is not true, you should add a small gain stage to scale the voltage appropriately.

Edit: WhatRoughBeast raises a good point: motor noise can disturb the peak detector circuit. So, an alternative: 

Clamp the input, as before. Run the signal through a precision half-wave rectifier. Low-pass filter this signal, and run it into the ADC, amplifying or attenuating as needed.