Most Stun guns use a ferrite Rod simular to what he has.
Yes a Closed core is More Efficient, but when your looking at a Real Stun Gun, It is nearly Impossible to insulate the 50,000 or more volts from arcing to a Closed Core.
Here is one of my articles on Stun Guns and it shows a typical HV Output transformer. (Pulsed trigger Coil)
**broken link removed**
The 5KV Circuits with Multipliers can put out the High Voltage with a Tiny amount of continuous current. Almost Useless and No where near as effective as a Pulsed Trigger Coil, simular to what I have made.
The Pulses on a commerical Stun Gun are much Higher current and the Pulsing Frequency gives a Much more Penitrating effect.
Not that I really suggest Anyone Build or Use a Stun Gun.
I only did it to see if I could and How high of an output Icould get.
Those articles I presented are the Lower powered ones that I made.