  We introduce modes of instantaneous optimal growth of free energy for the
fully electromagnetic gyrokinetic equations. We demonstrate how these "optimal
modes" arise naturally from the free energy balance equation, allowing its
convenient decomposition, and yielding a simple picture of energy flows.
Optimal modes have a number of other favorable features, such as their
low-dimensionality, efficiency of computation, and the fact that their growth
rates provide a rigorous and "tight" upper bound on both the nonlinear growth
rate of energy, and the linear growth rate of traditional gyrokinetic (normal
mode) instabilities. We provide simple closed form solutions for the optimal
growth rates in a number of asymptotic limits, and compare these with our
previous bounds.
