I know how a carbon arc lamp works, but knowing that an arc lamp of inert gas, ignited by a discharge of high voltage that ionizes the gas inside, I wonder if it would be possible to cause the ignition of an arc lamp with carbon electrodes by high voltage discharge instead of the separation of the electrodes ...
Already been done. See PDF for diagram [PDF]
The problem: Striking a carbon arc requires ionization of the gap by mechanically reducing gap size, auxiliary starting electrodes, ultraviolet radiation, or "seeding" the gap to lower the required ionization potential. The mechanical method risks electrode contact and resultant contamination plus erosion. The other methods require complicated equipment. The solution: Inserting a high-voltage, low-current pulse in series with the arc power supply. This auxil- -iary supply efficiently ignites the arc and is easily and economically produced. How it's done: An inductor is placed in the negative line between the arc power supply and the negative electrode (tungsten rod). An auxiliary high-voltage, low-current igniting power supply charges the capacitor to provide the igniting pulse to the inductor. The arc power supply is turned on-about three seconds prior to the arc strike signal to ensure arc power at the electrodes when the igniting pulse arrives. The arc strike signal closes the relay, discharging the capacitor across the inductor. This applies the high-voltage pulse in series with the arc power supply ionizing the gap and igniting the arc. Notes: 1. This circuit should be of use wherever arc burners, arc searchlights, or plasma jets are used.
enter link description here I was almost certain that you could try to light the electric arc with carbon electrodes using a high voltage, but I was very surprised that NASA has already implemented it.
As for how to avoid, that the high voltage pulse does not damage the DC power source, the answer for Bryan Boettcher is as follows:
There are two ways to realize an igniter for arc lamps (now including a carbon arc lamp !!), the first is a series ignitor and the second is a parallel ignitor, the series ignitor superimposes the high voltage pulse by discharge Of a capacitor in the primary of a pulse transformer, to be induced in its secondary (that is connected in series with the arc lamp), a pulse of amplitude maximum of 20Kv to 30Kv, this pulse does not damage because the output of The DC (multi-ampere) source is connected in series by the secondary winding end with the lowest instantaneous potential, since the other end of said secondary winding will always be at a potential of 20 to 30 Kv with respect thereto. I attach a development of ignitor of xenon arc lamp where these concepts are explained very well.