Relative dispersion of trapped ion granulations in sheared flows

The life time of trapped ion granulations (trapped ions correlated by resonance) in sheared flows is calculated. The dynamics of trapped ion granulations, in the presence of sheared flows, is formulated in terms of two point correlation function of phase space density fluctuations. The evolution equation is closed by a simplified closure calculation of the triplet term. Based on the closed equation, the life time of the relative dispersion of trapped ion granulations is calculated. The result shows that i.) a relevant time scale enters via a hybrid of decorrelation and shearing, (Δω_cν′²_y)^1/3 and ii.) small scale singularities in the absence of collisional dissipation enters through logarithmic divergence.