It's just a 220v power source, which is arrived at by using what is basically a car battery that's connected to an inverter, which increases the voltage to 220v and changes the current from DC to AC. The only thing that's "special" about these things (except for the price) is that it needs to be clean power, because flash heads (and other electronic items) need clean power.
Your flash head uses conventional technology, basically if you set the flash power to half then it charges up the capacitors half way,and when you fire the flash all of the power stored in the capacitor is discharged through the flash tube.
For HSS to work, there needs to be a large number of low powered flashes so close to each other that they are touching, making what is in effect a continuous light that stays on long enough for your camera shutter to complete its cycle. To do that, the flash head needs to use an entirely different technology, IGBT. With IGBT, when to set the flash power to say half, the capacitors fill up completely and the flash fires at full power, but only for half as long, leaving the other half in the capacitors for the next shot. This allows a large number of low powered flashes to be fired in very quick succession so, no IG BT = no HSS.
See
this link on the Lencarta website for an explanation of these terms.
No, I did mean the power doubler. This is basically a Y connector, it fits into each terminal on the power pack and terminates in a single terminal that goes to the flashgun, halving the recharge rate. Without it, HSS isn't possible on the 360 model.
Here it is on the Lencarta website