A science question for you, why no smoke ring with an electric smoker?
The smoke ring, as we refer to it as, is not actually a product of the smoke itself. It is caused from the burning of organic material to fire/heat a grill or smoker, such as propane gas, natural gas (methane), charcoal briquettes, lump charcoal, or hardwood (stick burners).
Nitric Oxide reacts with the hemoglobin in meats causing the pink color in the surface/sub-surface of the meats creating a stabilized pigment. When using an electric appliance, there is an absence of fuel burning, other than in the case of smoldering wood chips/pellets/sawdust if using an electric smoker. I've read that nitric oxide forms at temperatures of 600*F and above, so very little would be formed by smoldering smoke woods, if that is true.
I've noticed a slightly reduced depth, and at times lighter color smoke ring when I use a propane fired smoker instead of charcoal, which indicates that a solid fuel fired smoker generates a higher nitric oxide content in the smoke chamber gases, possibly due to a less complete burn of the fuel.
If smoke ring is a major factor with your product, either for personal gratification, or during bbq competitions/cook-offs where some judges may not have been well educated or may be inexperienced on the subject and don't understand that the smoke ring doesn't effect flavor or indicate the doneness of the meat, then a solid fuel fired smoker is what you want to use (charcoal, lump or hardwood).
There is a ton of science out there about the smoke ring.
Actually, if you are getting smoke, and if you like the taste of the grub, I wouldn't sweat the smoke ring thing that much. Others will jump me for that, and I know about the competition thing and all. But if you are getting smoke, and if you and your family likes the food? Who is hurt?
Good luck and good smoking!