Falstad's animated simulator has a tesla coil in its Circuits menu. The run starts with voltage close to the level where spark occurs (10kV in positive portion of cycle. -10kV in negative portion).
View attachment 154921
The simulator portrays current direction and intensity.
The circuit is in the link below. (I created additional scope traces so that waveforms can be viewed more easily.)
Click to:
1) Open falstad.com/circuit
2) Load schematic in simulator
3) Run it on your computer
https://tinyurl.com/y3vkq234
It's easy to add more scope traces, or change component values. Right-click and choose Edit, View in scope, etc.