High Voltage & Current Circuit From Small Power Source
You want a 10kV source that can supply 1A. We know P=VI, so that's a 10kW supply.

Now look at your little 12V lead-acid. Ignoring efficiency losses, that battery must supply all 10kW of power. Since the battery's voltage is (nearly) constant at 12V, then it must supply 833A of current.

Do you think it's realistic your lead-acid battery can supply 833A?