Charging a capacitor in a tesla coil

[p75213]

Can somebody explain how it is possible to charge a capacitor using ac voltage? The way I see it is the capacitor wouldn't have time to charge as the voltage is constantly switching. In the case of 60Hz - 120 times a second.
I have attached a schematic of a tesla coil which is how I come to think about it.

 

[Simon Bridge]

and if the cap charges quickly but discharges slowly...

 

[p75213]

I have made some enquiries and it appears that it is not AC voltage but rather pulsed DC.

 

[Simon Bridge]

You have the same issue - when the pulse is low the cap can discharge.

 

[p75213]

You have the same issue - when the pulse is low the cap can discharge.

Your right. It must be a capacitor which operates at high frequencies. I don't have any practical experience so I never new such capacitors were available until I had a look around the net.