I have had fantastic luck applying for jobs, and my (currently modest) PhD salary will be multiplied by about 5 after I graduate. I have been living a fantastic (but relatively frugal) life during my PhD: I have managed about a 30% savings rate during this time while doing a lot of travel (camping and surf trips), going out to bars pretty regularly with friends, but keeping an eye on my spending and avoiding big ticket items (I have a very old car, and always go for the cheapest accommodation etc).
I see no reason to inflate my lifestyle much in the next few years, so the plan is to live off about one fifth of my new pre-tax salary, and save/invest all of the rest in the most tax-optimal way possible. It is pretty clear this will involve maxing my 401k, but beyond this I really don't know what to do with the extra money. Can I put it in tax advantaged account like a Roth IRA? Are there limits to how much I can put into retirement accounts?
The issue is somewhat complicated by the fact that I may return to Europe (probably the UK) in <5 years. I would hope that at the very least the money could be transferred in a tax efficient way to a retirement account outside of the US. It would be even better if it was possible to access the funds tax efficiently a few decades before turning 65. Incase it is relevant: I do not expect to have US citizenship at any time in the future.