From the behaviors you've described, I would just let things be and see how they go. The Alpha chasing the Beta away is totally normal behavior. It sounds like that is your main concern, but it's what any dominant male would do in that situation. Watch any of the nature shows and the beta males spend their days on the outskirts of the group of females, waiting for the Alpha to be distracted so they can stealth mate a female. It's pretty much how they spend their time. The beta doesn't spend all day mopping and whining about how he has no friends and the other male is mean to him and he just wants to hang out....he spends his day thinking "how can I get past him to nail that pretty little pullet and not get my butt kicked too hard?" It bothers you way more than it bothers him, I guarantee it.
That said, there may come a day when the beta decides he's man enough to take on the Alpha, and there will be a fight. How much of a fight is impossible to predict. I've had coups that were completely bloodless, I hardly knew the older rooster had been de-throned until I saw he wan't mating the hens. Since you have lots of space, the chance of one rooster killing another is pretty small, since the loser has lots of room to run away from the winner. You may run into a pretty beat up rooster one day, at that point you'll have to make a decision about how to manage your population.