How to ask my advisor from another department for research assistantship?
Just ask.  Generalities from the Internet are not going to be so helpful here.


  Would you be willing to consider me for a research assistantship at some point? 
  
  What would you expect me to accomplish to get to that point? 
  
  If I had an assistantship, what would you expect me to work on?  Would it be part of my dissertation research?  If not, how should I plan to balance the two?
  
  Given that I'm enrolled in another department, are there any bureaucratic obstacles to this, and is there anything I can do to help with them?