Mode-space energy distribution in instability-driven plasma turbulence

Energy transfer to damped modes in gyrokinetic ion temperature gradient driven turbulence is studied to understand the transfer dynamics and find scaling representations for the heavily populated mode space. Proper orthogonal and linear eigenmode decompositions are introduced and examined to assess whether modes are well-resolved and what scales they encompass. It is observed that damped modes across a range of inhomogeneous scales receive energy simultaneously and directly from the unstable mode, constituting a form of parallel transfer, distinct from the serial mode-to-mode transfer of the wavenumber cascade of hydrodynamic turbulence. Controlling for modes that are well resolved and labeling the modes of the linear decomposition in order of damping rate, energy transfer in the mode space satisfies an equipartition of the energy dissipation rate, leading to a simple rule for the distribution of energy in the space of damped modes. Energy dissipation rate equipartition is the form that the canonical nonlinear invariance of energy transfer assumes in a dissipation range with parallel rather than serial transfer.