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
15KV neon transformer will easily do what you have asked for.
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).
p.s. a key phrase for a search would be "dc discharge" and not