Re: Killing and preventing grass/weeds for an arena?
Couple of options. If you want to kill the ground, something like Mojave 70EG will do the trick for quite some time. It's not cheap, but it works really well, stuff you spray with this will stay dead a long time. I often mix it with Roundup for a fast/forever kill. Use it on my driveway, sidewalks, etc where I want "dead forever" because that's what this stuff does.
For a slightly less devastating kill, I use Roundup mixed with Surflan AS. Good stuff, also not cheap, but it stops seeds from germinating. That's more a multi-use product for me, mixed with Roundup, it's a bareground chemical, used on it's own, you can spray it over things you want to keep but it'll keep new stuff from sprouting.