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The free energy balance equation for gyrokinetic fluctuations is derived andapplied to instabilities. An additional term due to electromagnetic sources isincluded. This can provide a simpler way to compute the free energy balance inpractical applications, and is also conceptually clarifying. The free energybalance, by itself, is not sufficient to determine an eigenfrequency. Thepreceding results are derived in general geometry. The charge flux constraintin gyrokinetics can provide a necessary additional relation, and thecombination of these two can be equivalent to a dispersion relation. The chargeflux constraint can prevent the appearance of an unstable eigenmode even thoughthe free energy balance would allow strongly growing fluctuations. Theapplication of these concepts to simplified kinetic models in simplifiedgeometry is also indicated.

The free energy balance equation applied to gyrokinetic instabilities,  the effect of the charge flux constraint, and application to simplified  kinetic models