continuous static arc

What's a "continuous static arc?" Things that are static oriented, even a van de graff generator store charge in capacitance and discharge it as impulses not a continuous spark or ark. For a continuous arc get a neon sign transformer or a high voltage dc or ac supply. What are you trying to do? A

Yes, for example you can use a 555 timer and a high voltage mosfet or igbt to drive an automobile ignition coil. To get an idea what some high voltage circuits look like, go to

It could be possible with discharge lamps. Here is info to get you started:

Avoid low pressure lamps such as fluorescent and low-pressure sodium, as their arcs are considerably longer than 1 cm. High-pressure sodium, mercury, and metal halide can operate on dc under special conditions (see the above link).

Mark

p.s. a key phrase for a search would be "dc discharge" and not "continuous static".

to start a spark across a gap that wide you need about 10000V there's numerous different designs for high-voltage generators out there.