Initial noise prior to square pulse
This 20 MHz resonance is due to your layout.  

For example with wire being 10nH/cm and twisted pair being 40~50 pF/m

Hypothetically I can imagine your 20Mhz resonance caused by emissions, crosstalk pF and mutual inductance.  You can get this even with ground inductance from a 10MOhm 10:1 probe with a ground lead being 10cm long on a 1m coax.

suggestions


Use twisted pair for all signals.
use ferrite clamp around the arc paired wires or use coax.
locate pairs or cables at right angles to minimize crosstalk.
Use STP or shielded twisted pair. 
Lower the load impedance. 
add a LPF + xxMHz notch filter as a last resort.
Keep supplies decoupled 
keep grounds clean with heavy braid.
minimize arc loop area.