Need a little help with a Chinese tesla coil

Question

I bought a little tesla coil kit that can play music. I soldered it all up, and a friend of mine distracted me at the last second when I was hooking it up...
I blew the original "BD243" transistor up on accident, at this point, by mixing up positive and negative leads while using a laptop power supply (rated at 19v by 3.8Amps).
I replaced it with a tip31ag transistor. It has 30% less gain, and I assumed that it would just throw slightly weaker sparks; it however barely mak3s a spark more than a few millimeters when fully amplified by my sound equipment.
I am just looking for some advice to amplify it more. The schematic says that the primary is 1 wrap, and the secondary is 350. I would like to make it better. Any help would be great. I can take extra pictures if needed.
I have so many extra components. I can make do; if I have to desolder some old stuff lying around, then so be it. Any help is appreciated.

Answer 1

The BD243 transistor is chosen carefully for this application of boosting voltage by driving the collector hard with gain. The product of the gain and max current or \$\dfrac{Ic^2_{max}}{I_b}=h_{FE_{Min}}*I_c=15*6=90A\$ for BD243
(This is just a Figure of Merit FOM, not actual current )
THe other critical metrics or FOMs are; \$R_{ce} , f_t, V_{ceo}, Pd\$

The Rce=Vce(sat)/Isat of the transistor and supply voltage is what limits the Pd=Vce(sat)²/Rce @ Ic when the base is driven hard (Ic/hFE(min) to saturate. Consult graphs in datasheets for these.

Any replacement ought to meet or exceed these FOM's

Stock and cheap at Digikey

Match these characterisitics from this list for above product and Vceo or buy the same or better part. The Ft toggle speed is also critical as the rate of change of current is a gain factor for producing voltage. V=LdI/dt If the part doesn't get warm, you can always raise the supply voltage carefully.