That's 6.5J, so a lossy charge must dissipate 6.5J for a total of 13J consumed.
You'll need a pretty big transistor to do that all at once in a hurry; or a slower (current limited) charge, giving time for the heat to spread out; or a saturating transistor with a ballast resistor that's similarly rated for the energy and power.
The SQJA20EP is only rated 16mJ avalanche, so good luck doing it pulsed. That's fine; you're already looking at the resistor method. Then, how much does the transistor dissipate?
If the Rds(on) is typ. 50mohm, then it will absorb about 1/100th the energy of a 5.1 ohm resistor, or 65mJ. Still above par.
The time constant is 1.3mF * 5.1R = 6.6ms, so the most energy will be dropped in the first few ms, and essentially all of it after about 20ms.
1ms SOA is almost 600W, or 600mJ total (single pulse, from 25C).
But our pulse is longer, so the total allowed energy can only be higher still (10ms is like 180W, or 1.8J), and it's fine, even if it were a square pulse.
This would seem to be fine.

T_J initial is 25C in the SOA, and T_J final is 175C, the maximum rating. With the pulse delivering somewhere around 1/10 to 1/30 the allowable energy at these SOA curves, presumably the temperature rise is 1/10 to 1/30 of 150C, or 5-15C. So T_J max for your case should be less than 160C.
I would recommend a comparator and latch, to watch for:
- Overcurrent, in case the resistor fails shorted or something else nasty happens to the circuit
- Charge (current * time), or capacitor voltage, in case the capacitor isn't charging (load short?)
- Maybe temperature? It seems you have quite some margin here, so a simple limit at 150 or even 125C should be quite safe.
It seems you could also perhaps use a smaller (cheaper?) transistor.
Obviously, you need to run the same check for the resistor; it's dissipating 2kW peak and 6.4J total, so a modest power resistor will be needed. Wirewound resistors tend to be good at this, with vitreous enameled types preferred over molded types (including metal-case types which are sealed with plastic).
Tim