Wave instabilities in open, driven systems cause bursty emission. Loca
l burst properties are combined with global power balance to predict t
he source dynamics, energy conversion efficiency, and distribution of
power levels. Sporadic growth near marginal stability is characterized
by noninteger scaling exponents and an exponential distribution of po
wer levels, unlike self-organized criticality or stochastic growth. Pr
edictions are confirmed by particle-in-cell simulations of driven cycl
otron instabilities. Solar microwave bursts are found to have the pred
icted distribution of power levels.