Dissertation Committee Invitation Letter
Ideally you want the advisor to commit to you ahead of time, to advocate for your application when it arrives, and to use her clout to get you the most generous funding packages offered by the program. Some programs do not attach admittees to advisors ahead of time (although I would hazard to say that the best programs do).
Or it is possible that the advisor with whom you came to work has left for another university, and you must find a replacement. In any case, sometimes students find themselves needing to approach a professor to serve as their dissertation advisor after they are already underway.
I have to write a letter after 3 years of not talking to my dissertation committee members (except for my advisor).
You must show that your past record proves you are highly self-directed and finish what you start without prodding and drama.
If you have any questions, please feel free to email me, and I am readily available for a chat if you would rather meet in person. Grad-Student-With-Fairly-Common-Last-Name: I have NO IDEA who this person is, what his/her project is, or WHY he/she thought my expertise might be a valuable addition to the thesis committee, nor did (s)he give me any clues.
The only details I removed from that email were my name and his/hers.
I would be honored if you would consider being a member of my supervisory committee.
Once I have a list of potential faculty members, I will, at a later date, arrange for a committee meeting early next year.