Power supply current is not the major issue in your case. Increased numbers for coil turns would gave you the needed voltage jumped to break spark gap with same current breaking, with increased inductance of coil the current breaking voltage would increased across coil as V= (do/di)(di/dt) = L(di/dt) = do/dt the small vareation of flux with time, to produce needed breaking voltage across gap....

An excellent question, but unfortunately it is not my specialty

I am so sorry to bother but I know the V is Voltage and L is Inductance in your formulation, but I have not come across the letter "d" as a representation of anything as of yet, which I assume di (the i is current) and dt (the t is total) but what is the "d" and what is the "o" I am so sorry, I am only in my 1st YEAR of Electric Utility and with COVID have had ZERO hands on experience, if you would be so kind as to explain a little further. Sorry if I seem "stupid" I am just NOT yet experiences, and VERY very new to all of this... plus the only power supply I HAVE myself is one that I bought to connect too my mini Tesla (only a 15V, 2A output). I DO know if I merely increase the # of turns in the secondary and the primary that it will indeed step up the amount of voltage, but I do not know what can be used to then power it, or how? An externally made battery Bank, As I would like to make one more powerful than one that operates of A SINGLE battery (as some of the videos I have seen- of course MAKING MY OWN tiny one would be MORE IMPRESSIVE than displaying an unimpressionable one that all I did was order it Preassembled... I figured I could use it as a 3D mii Visual for what I am trying to achieve, although it may not look as neatly set on a circuit board, so much as hot glued to a base of some sort. Plus I don't know how to solder connections so I am in possession of a 12 terminal/barrier strip to make any connections with only stripping the wire and putting it it into my barrier strip to make the connection (with tightening the screw obviously). I am really trying here, even with my lack of knowledge- I just wish I understood once I build this, how the heck I am supposed to power it if I build it (as I said the one I ordered had a little connection terminal for an external power supply which, as I said I bought with it- but if I build it, it's not going to have that piece and even IF IT DID, I don't think I can just go get external power supplies in any voltage needed LOL... and here's a question I SHOULS+D KNOW THE ANSWER TO but now that I think of it I am unsure.... DOES THE VOLTAGE AND THE CURRENT both increased with the N of Turns of wire in the Primary/Secondary? I know like a Taser for instance is ALL VOLTAGE which is why it doesn't KILL a person, the CURRENT IS WHAT KILLS.... clearly I need to increase both the voltage and the current- but NOT BY TOO MUCH- IT MUST BE SAFE TO OPERATE BOTH AT HOME WHILE BUILDING AND IN MY CLASSROOM FOR THE ACTUAL DEMO!!! I know I am asking a lot, but if someone, even the same lovely person who already replied could break it down a little more into LAYMANS terms (think of it, as if I have NO BACKGROUND in this field when explaining things to me) since BASICALLY that is PRECISELY how I feel when reading some responses, like "whaaaaat?? Did I even ask that?!? LOL!

Sorry, y'all, as I said I am VERY NEW TO THIS, and with COVID MORE is expected of me than is realistic with what/how we learned this past year

do/di, variation(delta)of flux with current,(called, Derieveti of flux with respect to current) is inductance (L).

di/dt, variation of current with time.

do/dt, variation of flux with time, needed for inducing voltage in coil....