Mr. fingers,
The e-collar is for training the dog. By using a slight electric shock, it will make the dog get off the wrong track such as a deer, cat, coon or possum. It can also stop them before they get hit by a car near the road or save the dog's butt if he winds up cornering a possum or coon. Zap him and he will usually get out of there and stop following those scent trails. Beagles aren't usually mean enough or big enough to handle an aggressive coon. They don't often get mixed up with them, but it does happen. The e-collar sounds mean, but it is also a very useful safety device for the dog. Plus, if he follows deer, he really could wind up in the next county. The e-collar is a good tool.
Learn your dogs bark when it is on a trail and you may well be able to figure out if he is on rabbits or something else. I know the beagles we use sound slightly different if they get on a cat or something. It has only happened 2 times though, they just didn't have the same level of excitement in their voices.
Finally, run your dog with other already trained beagles if you can. It will help him learn faster. If you do shoot a rabbit, leave it lay until the dog gets to it. Let him chew on it for a second or two and then give him a treat. Reinforcement!