By my (probably wrong) calculations one of these capacitors when charged up to its max of 4kV can deliver 16 Joules per second at discharge.
It does not work quite like that..
For a rough analogy, think of the capacitor something like a balloon; it can be filled to store energy and that energy released.
The maximum pressure the balloon can stand is equivalent to its maximum voltage limit, before it bursts (the insulation fails).
How much current it can stand is a bit like how big the pipe is that connects the balloon.
For plastic film or pulse-rated capacitors, the charge/discharge limit is generally given as the maximum permissible rate of change of charge level, in volts per microsecond.
The current that rate corresponds to depends on the value of that specific capacitor.
You can work it back from the basic Coulomb equation: A current of one amp causes a voltage change of one volt per second, with a one farad capacitor.
(So eg. in proportion, one amp with a one microfarad cap will cause a voltage change of one volt per microsecond; a millionth the capacitance so a million times faster change).
Example - this capacitor, just because it looks a bit like the ones in your photo...
Look in the data sheet for it:
The entry for that is part way down page 4; It's a 250V rated, 13mm diameter x 31.5mm long body type.
Go back to the reference data table on page 2, and for a 250V rated and 31.5mm body one, the maximum dV/dT is 6V per uS.
For electrolytic capacitors, it's very different.
The maximum "ripple current" rating is given directly, for specific frequencies - but also the life expectancies for electrolytics are stated as very short times, like typically 1000 to 5000 hours; around 40 to 200 days....
Those figures are based on them being run at maximum at all ratings, like voltage, temperature, current etc..
The makers then give calculations for life factor based on how much you under-run the cap - so eg. at half voltage, half ripple current and moderate temperature, the lifetime may be thousands of times longer than the base figure.