As i understand, you want to acquire very small current pulses having very small amplitudes and a bandwidth of 1.5 GHz. From my point of view, there are some solutions.
The first and elegant solution is to use the low noise amplifies designed for the advanced wireless communication system such as the WIFI and the WiMAX. There are two types, as per data sheets the base band type and the band pass type. The base band types are more suitable for your application. They have sufficient gain and bandwidth for your signal when cascaded . The remaining question is how to couple your signal with the amplifier i would propose to push your output signal from the fast Faraday cup in a 50 ohm metallic resistor.. The voltage developed on this resistance is to be applied on the low noise amplifier. The output of the amplifier is suitable to acquire it with the available high frequency oscilloscopes.
You can find a suitable amplifier in site www.rfmd.com/cs/documents/br_wifi-wimax-lna.pdf
I have an other solution which needs more effort from you. I postpone its introduction till i get your response on the first solution