Tam..all I can think of is these two tuber crops might be competing for similar nutrients and moisture.
I have (after years of trying to remove)about 12 sq ft of J/A's and all they let grow nearby is shallow rooted weeds.
Could also be that the J/A's might rob the potatoes of enough sun so you might want the potatoes to grow on the perimeter. My J/A's grow at least 12' tall but they are reaching for what sun they can get. Maybe in a better,sunnier spot they will be shorter but they still have lots of leaves and cast a lot of shade.

What do you do with the chokes beside peel and eat raw in salads? How are they cooked?

Ask Melvin -Ralph's brother- how to use them. He grows tons of them up in the mountains (and sells them). He made some amazing pickles with some that he shared at the last swap. Not sure his screen name, but Ralph would know. I know you can boil them like potatoes and mash them- said to be low glycemic (or maybe it's carb) and very good tasting and good for you.

Since this is the first i've grown them i'm not sure how tall these will get for me. They came from the fair and there they probably got to 6' or so. I did plant the sw pots on the outside of the artichokes, so hopefully they'll do ok, room & sun wise. It's pretty wide open back there for now and i'll keep the weeds down hopefully, so they can wander at will. It's very difficult to water back there, but the ground seems to hold moisture pretty well. Once i get them mulched i'm sure it will be better, too. I doubt i'd do it more than just this yr together, but since the manure pile was on it- i imagine there are enough nutrients for both crops this yr.

Ha..pickled J/A..I'd have never thought of that..
Trust me though..once you plant J/A's no matter how many you think you harvested you'll always leave some behind.
They are a forever plant unless you use a backhoe and a soil sifter or brush killer.

Well, ironically, i did try ja's in the back once before, more than 15 yrs ago when it was fairly shady, and they died out on me within a yr. But now with the sun, i expect & hope it'll be a forever crop. We love chokes, so getting something else with the same flavor that's easier to grow is great. The pickled ja's are really something else- you still get the artichoke flavor, but the pickling is delicious! Hoping Ralph can get the recipe from Melvin (hint, hint) :)

Tam, I just harvested this years J/A's. Already had them in soup and no big deal flavor wise. They do tend to hold together no matter how well cooked so they don't go to mush in soup/stew unless you purposely mash them.

Reading up on J/As..they are a significant source of fructose as are the stalks and are being considered as an ethanol source instead of corn. The stalks produce more ethanol than the tubers (if harvested at the right time) and that means the tubers can be left in-situ while the stalks are harvested.
Yuck..back to washing the J/As to slice,parboil and freeze.
I'm sorely tempted to pour concrete on top of them to stop them from growing but I'll just have to resolve to use Round-up for the next three autumns

You'll have to get ralph's brother, melvin to post his recipe for artichoke pickles. He brought them to the swaps and they are divine. He doesn't post much but maybe ralph will see this and ask him (hint hint!) :)