I've looked at the magnetic bottle (hydrogen plasma/fusion) idea as a potential basis for extrapolating what technology might be capable of doing with plasma fields 1000 years into the future...which is when my novel is set...but I'm worried about the heat it might give off, as well as the large electromagnetic field needed, which could cause the people inside or within a certain radius of the dome to be killed. Additionally, a magnetic bottle would be disrupted by the interference of the soil/ground, if it were just one magnetic bottle per dome. Maybe a series of magnetic bottle-like plasma fields - vertically or horizontally arranged - in a dome-like shape could work?
TL;DR You would have a fancy city sized crock pot
You would need to replace your atmosphere inside the dome with liquid nitrogen in order to keep the steel in the buildings from igniting. While there are states of plasma that don't burn hot as the sun, they would be about as useful to protect a city as wet toilet paper seeing as they are not dense enough to stop solid objects. If you had the plasma hot enough to protect your city it would need to be able to heat metal up enough to melt or at least deform it, which is insanely high for most metals. I didn't do the math, (If someone wants to comment it feel free.) but lets just say it would take several thousand k to melt even a small car enough to stop its function. It gets worse too, as if your city is attacked by ballistic ammo it will be going somewhere between fast, (792 meters per second in the case of a 3 inch m5 cannon from WW2,) to Ludicrous speed (2,520 meters per second the case of the navy's new rail-gun). At these speeds you would either need a much thicker plasma wall or much hotter plasma in order to melt the round. Although this would just spread melted steel and lead like a shotgun, so you would want to make it hot enough to evaporate. Lead evaporates when it reaches 1750c(3182f), and iron roughly 3134c(5673.2f). If your city has walls this hot, you will not have a city, you'll have a gaseous crater. I also think containment would be a problem, as the magnets might rip the hemoglobin out of your body due to how strong they would have to be and any electronic within the city would instantly fry.