Here I used HF CT to measure current on ground strap and large Capacitance transformer ( not shown) to measure 50~100kV voltage impulse with C ratio that scales voltage down to safe levels for 50 Ohm termination inside scope. High quality coax is critical. Here V impulse is 10V input 50 Ohms or 2 watts which when concentrated in a dust particle in oil filled transformer is enough to create a finite amount of Hydrogen.
Result below is a partial discharge PD inside insulation of 5MVA transformer, known to operate normally except for rising H2 levels dissolved in oil.
Here the waveform was probably 10ps wide or less but limited to <1ns risetime from scope @ 300MHz.
In physics they use integration method with scintillation detectors. In Spectral Analyzers they use quasi-peak detectors which are not fast enough.
There are many other methods to measure peaks and duration by integration methods. Transient voltage using tapped bushings for capacitance ratio is common. We call these Cap transformers as opposed to magnetic transformers.
To detect voltage transients , easy method is to use scope ground shorted to tip and create a loop antenna for near field measurements. Resonant frequency of loop can be determined from size.
Coax loop gives better results/
If you have Hipot or HV DC generator you can measure breakdown in air, oil or any fluid and effects of contamination by PD measurements before breakdwon occurs using any scope nearby with shiorted loop nearby or around ground wire.
Be care what you dig for. High Vdc E-fields accumulate voltage and reach very far away.