The multiphoton ionization of hydrogen in strong parallel microwave and sta
tic fields is a fundamental problem of great complexity which has been the
subject of recent experimental and theoretical studies. We show that the su
perposition of an additional held, namely a static, relatively weak magneti
c field, results in rapid oscillations of the ionization survival probabili
ty. These rapid oscillations can be used as a very sensitive method for mea
suring weak magnetic fields.