Suitable Half Bridge Driver to control capacitve load
Capacitor: 40uF, DC
Power Source: 100V, DC
Switching time: ~us (originally nanoseconds)

Current in a capacitor can be calculated from the derivative vs time of voltage across it:
\$ i = C dv/dt \$
With dt=1µs, dv=100V, C=40µF we got i=4000 A. This is quite impractical.
If the charger does not use inductive energy storage, instead simply connecting a capacitor to the output of a (presumed) stiff low impedance power supply, then the same amount of energy that will be stored in the cap at the end of charge will also be dissipated in the switch and various resistances in the circuit.
\$ E = \frac{1}{2} CV^2 \$
Here E=0.2 Joules which is low enough to not make large things explode. MOSFET semiconductor die are not that large though.

Source Output impedance: order of milliohms ~20mOhm (originally 50 ohm)

Under high di/dt pulsed current, the inductance of power supply wires will be a larger problem than the output impedance.
But... to charge the cap, the current has to ramp up first, and preferably the ramp-up has to be shorter than the duration of the pulse. Current should also ramp down at the end. For current in an inductor to go from 0A to 4000A in 100ns with 100V across it, the inductor has to be:
\$ e = L \frac{di}{dt} \rightarrow L = e \frac{dt}{di} = 2.5 nH\$
This is ironically doable, barely, if the target capacitor has low enough inductance. But it will need a power supply of very low output inductance, which means lots of capacitors charged to a rather high voltage on the board... and capacitors don't discriminate, they'll discharge into anything that makes contact, including you.
Note current in wires creates magnetic fields, and a wire with current flowing through it in a magnetic field will be pushed by a force. With this kind of current you can expect things to jump around, and I wouldn't be surprised if the charged capacitor flies across the room. Whoever catches it will have a bad day.
Honestly this project is going to be expensive, complicated, and pretty lethal. If you say &quot;I am very new to electrical engineering&quot; I would recommend less dangerous stuff... or maybe the thing you actually want to do can be achieved by less &quot;mad-scientist&quot;-ey means.
Happy ending:
If the goal is to store energy, then a 1nF cap charged under 20kV also stores 0.2 Joules, and it can easily be charged in a microsecond with a current of only 20 Amps. Obviously, it is even more lethal.