  The free energy balance equation for gyrokinetic fluctuations is derived and
applied to instabilities. An additional term due to electromagnetic sources is
included. This can provide a simpler way to compute the free energy balance in
practical applications, and is also conceptually clarifying. The free energy
balance, by itself, is not sufficient to determine an eigenfrequency. The
preceding results are derived in general geometry. The charge flux constraint
in gyrokinetics can provide a necessary additional relation, and the
combination of these two can be equivalent to a dispersion relation. The charge
flux constraint can prevent the appearance of an unstable eigenmode even though
the free energy balance would allow strongly growing fluctuations. The
application of these concepts to simplified kinetic models in simplified
geometry is also indicated.
