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I am not satisfied with my PhD and the research group and I was thinking of looking somewhere else. I would like to stay in Academia for now and I want to apply to other programs (in an other country and university).
Should I tell my supervisor that I am looking for an other position? Or is it better to tell him once I have found something?
The problem is that I have to contact some professors and there is a minimal possibility that they know each other...
Morally yes. There are also a number of practical benefits. How is your supervisor in general as they could be understanding and help you get a new position. They can also be helpful for advice as they will know what other supervisors/research groups are like, especially if they know the reason you are quitting their group.
If you are applying in a similar field there is a good chance they have met at conferences. Telling eliminates this risk.
Of course if you do tell it will be seen as you quitting your PhD and your funding will likely be cut (depending on how it is structured). If you don't find a new position, I have no idea how confident you are of securing a new position, it could mean you get left with no position at all. Of course your supervisor could also be understanding and let you use that group as a fall back. It would save them the trouble of hiring someone new.
Finally, and this possibly be first, have you exhausted all options to fix your current PhD such as working with your supervisor to limit/remove the issues you have. You could potentially switch topics but stick with the same supervisor for instance and work less with the research group itself, my own PhD did not involve anyone else in the same university working on the same topic as me (aside from my supervisor who also worked on different topics as well).
The above is very dependent on the personality of your supervisor and the reasons you are unhapppy though so don't apply it blindly but I would lean towards telling them.
