My son has been offered admission for PhD studies in the Department of Aerospace Engineering, Nonequilibrium Gas & Plasma Dynamics Laboratory. He is absolutely thrilled!
I want to thank @Juliet and @boneh3ad . They have been a tremendous help for us to understand what needs to be done in order to be a successful applicant. My son started out with a vague idea that he wanted a PhD in aerospace engineering, but generally planned to get a Master’s degree first and then apply to a PhD program. We learned that this was the wrong approach and that he should instead apply directly to a funded PhD program. Why pay for a Master’s degree if the goal was to earn a PhD?
We then learned a year ago or so that my son needed significant research experience to go along with good grades and GRE scores. He had time to apply for and complete a summer research program in Germany last summer and to start solid senior-year research projects this fall. This allowed him to get strong recommendation letters from professors that knew him well and could evaluate his research abilities and enthusiasm.
It was also interesting to watch my son narrow his research focus. A year ago, he knew he was interested in space propulsion. We visited both Michigan, a leader in plasma/electric propulsion, and Purdue, a leader in chemical propulsion. After those visits, he decided to focus on plasma propulsion. He was able to take a course last spring in plasma propulsion from a recent Michigan PhD and a course this fall in computational fluid dynamics. He realized that there were two options for him, more hands-on experimental research into vacuum thrusters, or alternatively, research concerning more theoretical modeling of plasma propulsion and other plasma applications (fusion, high-speed aerodynamics, materials processing, atmospheric re-entry, etc.). My son decided he was more excited about theoretical modeling. There are only a handful of aerospace engineering departments in the country that conduct this research, so this allowed him to tailor his application directly toward a professor that he hoped would advise him, rather than a general application to a good, general, aerospace engineering department. As an example, Georgia Tech is very strong in experimental plasma propulsion but was not strong in plasma modeling. This eliminated Georgia Tech from his application list, just as he had eliminated Purdue a year ago. Ultimately my son only applied to three universities, with Michigan his first choice.
This is consistent with what @Juliet, @boneh3ad, and others have said. A prospective PhD student needs to not just have a vague desire to get a PhD or to identify colleges that he or she think would look cool on a resume. He or she should have a passion for research, identify universities that are strong in the general field, e.g. aerospace engineering, and then if possible narrow the search to universities that are strong in one or two research areas of interest. Ultimately one should end up if possible effectively applying not just to the university and department, but also to a particular lab and professor.
Basically, you should have a strong reason to want to conduct this type of research and the professor should have a good reason to want to “hire” you to do the research. A PhD application is really a job application. As an example, one of my son’s professors got his PhD from Princeton (lower ranked overall in aerospace engineering than Michigan, but a top Ivy League university). My son applied to Princeton at his urging, but it really wasn’t a good fit. Princeton’s plasma researchers generally are affiliated with the Department of Astrophysical Sciences. My son could not really tell a good story about why he was even applying to Princeton’s Department of Mechanical and Aerospace Engineering. He was rejected earlier this week.
At Michigan, my son knew what he wanted to do and who he wanted to work with. He could successfully demonstrate to his hoped-for advisor his passion for and likely success conducting plasma modeling research, through grades, relevant coursework, GRE scores, research, personal statement, and recommendations. He was also able to directly communicate via email with his hoped-for advisor before and after applying to demonstrate interest and to get questions answered.
