I had this problem with my aerogarden a while back. This is a fungus caused by poor airflow and/or too much moisture near the base of your plant.
To prevent this problem make sure the water/nute solution is only applied to the roots, not at the top near the main stem. Also make sure you have proper
air circulation around your plant. To fix the issue remove the stones at the top and soak them in bleached water for about 30 mins then scrub/rinse them
in clean water a set aside to dry off on clean paper towel or tissue paper. While those are drying take moist paper towels or tissue and begin carefully removing
as much as the fungus as possible and be careful not to spread it. Once you feel you have gotten as much of it off the steam area ect. mix baking soda (2 tablespoons per gallon of water)
and clean the affected areas with the mixture. Be sure to use clean tissue or paper towels again. Repeat the backing soda clean a few times switching out for new tissue/paper towel.
Once your finished with the clean replace the dried washed stones back into your pot.
That is just a quick fix until you have the time and money to pick some of this up:
http://www.amazon.com/Nutrilife-NLSM901L-SM-90-Quart/dp/B0002I5Y10
SM90 is what I have have used in my last grow and it works great to keep the fungus away as well as a host of other benefits.
I wish your lil lady luck
