How can I contact potential PhD advisors without jeopardizing my position in my current PhD program?
I don’t have an answer to the first part, but the only possible answer to the second part is to say something along the lines of:


  Due to unreconcilable personal issues, I’m unable to complete my PhD at the University of Stack Exchange. I have the highest regard for the faculty there and Professor Advisor was an excellent supervisor, but I could not continue to pursue my studies there. These issues would not interfere with my ability to pursue a PhD at the University of Overflow.


You shouldn’t lie and pretend there was some kind of problem with the university. I think that making it clear that you have no issue with the university and your professor is probably the best thing you can do to avoid accidentally starting any rumors or make it seem like you’re besmirching the old university. I think it’s important to simultaneously stress the the issues are personal and that they won’t follow you to your new location.

I do think that being forthright and honest, but vague, is your best approach. I would seriously recommend putting this in your statement of purpose as well. At the end of the day it’s never not going to occur to the people reading your application to ask, and you’re usually better off heading off and explaining obvious worries than letting them sit there in their mind.

I know someone who was sexually assaulted by a community member at his university and found himself in a similar position. This is along the lines of what he did.