Do you mean a field or a whole stadium? If it's like 350 by 150, you can get netting and fishing line for an okay price, and at least cover some of it. My old run was 35 by 100 and we covered it using bird net attached to 8 ft bamboo sticks ($1 from local garden store) held up inside potted plants.
DH says it is about this size, approx. 100 by 35-ish. I am not good at estimating dimensions, apparently.
Typically the way hawks attack, you don't have to cover every inch, just enough that they can't easily dive in from overhead.
Also, you can tempt the native bird population over to your area using cheap bird seed.
Just a week ago a rth swooped at my flock maybe 20 feet away from me. She hung out until two tiny scissortails chased her away. Crows are especially good flock friends, I've heard.
We have lots of wild birds around! Cardinals and blue jays, juncos and woodpeckers, wrens and hummingbirds and crows (yay!) and all sorts I can't remember or identify, depending on the season.
If you aren't going to put up fishing line or netting, you really need shrubbery (shrubbery!) and an attentive roo. My roo sounds the alarm and the birds run for cover fairly regularly. At least once I've seen an attack averted that way.
Two roos, and noisy hens and an alert little Sheltie....
If you do nothing, you might not have any sightings for a few weeks or even years, then suddenly your birds are getting picked off one by one again. Guaranteed any predator that scores once will be back.
True that!
Finally, I've made the sad error of mistaking a predator id before. In your case it sounds like the hawk was the culprit, but I swear it feels like all the predators talk to each other. I recommend taking this time to do a security check for foxes, possums, stray dogs and feral cats, etc.
We lost a hen or two this spring to ground predators, but we took care of them. This was definitely a hawk. But thanks, note taken!
If your birds are too scared to roam, it's very likely that more than one thing is out there watching them.