Can I have a J1 visa if I'm already married to a Permanent resident?

Hello,

Can I have a J1 visa if I'm already married to a Permanent resident?

Thanks
You can with minimal chance to be granted because by marriage to PR you showed intention to immigrate unless you have a very stong application by joining to solid research program or so. Not just by joining to any thing (those training programs for few months ....etc) to be in the states despite the fact the place will sponsor J visa.
 
What do you mean by by joining to solid research program?

I mean that you are qullified enough for J visa in an important program for example you have a very high scores in your field and you are going to join for example Harvard University to do PhD or conduct research in an important field. Not to join community college to study for 3 months with J visa or to do teacher exchange program with J visa or to be trained as recioptionist in Hotel with J visa and so on. You need to convince department of state that your J visa application is very competitive to get around the intention of your immigration by marriage to PR
 
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