Well.... there are 2 problems...
The first is about safety.... You are not isolated from the Main 120Volts
house current... you risk electrocuting yourself...
You should have at least a 120VAV to 120VAC isolation transformer...
The second problem is that you do not have 9Vdc... what you have is
Half Wave ripple DC...
The single diode is chopping every cycle of the 60 cycles in half...
You are only getting... +VDC then 0VDC then +VDC then
0VDC and so on.... 60 times a second... Your DC is pulsing...
What you need is a Bridge Rectifier (made up of 4 diodes) that will give
you
Full Wave ripple DC....
Then you need to filter the DC with a capacitor of around 1000uF to 4000UF
at the proper Voltage of your maximum PS voltage (times 2 is a good safety
margin)...
I would suggest getting a 120Vac to 12Vac Transformer as the input power
source instead... it is much safer and the Capacitor will be much cheaper...
a good voltage rating for the Electrolytic Capacitor would be 25Vdc.
You would use your Variac before the 120Vac to 12Vac step-down transformer...
For an Electronic LD Driver to work properly... you need clean filtered
DC...
Jerry