You can try this:
Sorry about the quality - it was scribbled and photographed on my phone!
It is completely untested, just drawn while I was working on something else and the values are not optimized but should work. I tried to keep as much as possible to the parts you already have but made these changes:
1. The 555 was producing a 66% on 33% off waveform, I changed the resistor values to make it about 90% / 10% because you only need short pulses of current.
2. (if I got it right) the output of the 555 is high most of the time so I added the bipolar transistor to invert the signal. It's collector should go high for about 10% of each cycle.
3. I changed to a MOSFET output transistor, these have much lower input current requirements than bipolar types so I increased the gate feed resistor to 470 Ohms, this also reduces the collector current in the bipolar transistor making it easier to find a suitable one.
You can use almost any small NPN transistor, and I would suggest easy to find MOSFETS are IRF530, IRF540 or IRF640 but any rated at >100V and >10A should work.
As I pointed out - it isn't tested!!! In a commercial design it would have several additional safety components but I kept it a simple as possible.
Brian.