I think my research interests and experience are perfectly aligned with a professor. And I plan on applying to the department when the admissions open.
But when is the right time to email the professor as a prospective PhD student? I don't want to shoot off an email and get ignored by being either too early or too late.
In this university (in the US) the admissions are granted by committees and not individual professors. Also I speak as an international student.
The worst time to contact faculty is when they are deliberating the current round of applications and while they are recruiting the accepted students. In the USA, this would be December through April.
Conversely, best time would be May through October.
From my own experience, I would suggest getting in touch as early as possible, after the previous year's recruitment is out of the way. I had made my prospective advisor aware, and we were able to find time to discuss ideas and possible projects, and to even find several possible funding sources.
Perhaps this differs in departments with a more formal application process, but I found that the actual approach to the advisor was the important part - after that point, they were glad to encourage me to apply, since our research were well-aligned.
It does depend on the advisor though - some might not be able to even begin to think about next year... Others (perhaps more senior, and less daunted by thinking about funding someone that far ahead), may be hoping people get in touch. I suggest you find out how the intakes work - we have year-round applications and admissions, but generally people are concentrated around February or October. There's nothing to stop and application to start at another time, however, so obviously doing a bit of homework may help here (if it's not just annual admission in one group).
For your current Ph.D. application and any further activity during your Ph.D. always ask for suggestion/help/support from your Ph.D. supervisor.
You might be align with the activities of a supervisor; however thats one way thinking! It might be the case that he/she has many students and can't take any more regardless how much your previous work matches his/hers. So always ask, there are many nice supervisors that get excited to help their new/potential Ph.D. students.
