SONNE, the SOlar NeutroN Experiment proposed for Solar Probe Plus, is designed to measure solar neutrons from 1-20 MeV and solar gammas from 0.5-10 MeV. SONNE is a double scatter instrument that employs imaging to maximize its signal-to-noise ratio by rejecting neutral particles from non-solar directions. Under the assumption of quiescent or episodic small-flare activity, one can constrain the energy content and power dissipation by fast ions in the low corona. Although the spectrum of protons and ions produced by nanoflaring activity is unknown, we estimate the signal in neutrons and γ−rays that would be present within thirty solar radii, constrained by earlier measurements at 1 AU. Laboratory results and simulations will be presented illustrating the instrument sensitivity and resolving power.