I am going to try again, to respond to you, regarding this circuit.
The use of a HUGE capacitor to generate a power pulse is highly un-practical.
Reason ONE : The frequency is low and the rise time due to the ESR ( effective Series Resistance of the capacitor plus the Equivalent resistance of the Darlington going ON to discharge the capacitor is high.
Most to the energy is dissipated by the huge capacitor and the Darlington transistor, this transistor may be getting quite warm since it takes around 80 to 85 % of the energy that YOU pretend to transfer to the battery.
The energy transfer is the ratio of the battery internal resistance and the sum of the Mosfet plus the ESR of the Capacitor, which is going to be close to to 12 times higher than the battery ESR.
The discharge time may be close to 140,000 micro-farads * around 1 OHM = 0.14 seconds, the peak current pulse may run around 30 amps.
BEST SOLUTIONS to this problem is the arrangement of pulsing the battery with a fast current pulse.
Drop the Capacitor, it is totally un-necessary and it is just a load to you.
You will accomplish the same if, You drop the lower semiconductor, the capacitor and leave the upper Darlington or You replace it with a MosFet, with one ( 1) Ohm series resistance.
The one ohm, is to protect the MosFet.
If you are interested in a practical circuit along these lines, let me know.
Nando