Outside grid for fusor

I, for a while now, wanted to build a little Farnsworth desk fusor. Nothing too powerful, simply a small "desk lamp" if you will. As the fusor needs 2 grids, I was wondering, if it might be possible to position the outer grid outside of the vacuum chamber, as to make the inner grid a bit bigger. Just an idea, nothing solid yet. Just want to know if it’s possible/feasable.