Generalized universal instability: Transient linear amplification and subcritical turbulence

Abstract

In this work we numerically demonstrate both significant transient (i.e. non-modal) linear amplification and sustained nonlinear turbulence in a kinetic plasma system with no unstable eigenmodes. The particular system considered is an electrostatic plasma slab with magnetic shear, kinetic electrons and ions, weak collisions, and a density gradient, but with no temperature gradient. In contrast to hydrodynamic examples of non-modal growth and subcritical turbulence, here there is no sheared flow in the equilibrium. Significant transient linear amplification is found when the magnetic shear and collisionality are weak. It is also demonstrated that nonlinear turbulence can be sustained if initialized at sufficient amplitude. We prove these two phenomena are related: when sustained turbulence occurs without unstable eigenmodes, states that are typical of the turbulence must yield transient linear amplification of the gyrokinetic free energy.

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• Energetic bounds on gyrokinetic instabilities. Part II. Modes of optimal growth
• Calculating the linear critical gradient for the ion-temperature-gradient mode in magnetically confined plasmas
• Energetic bounds on gyrokinetic instabilities. Part III. Generalized free energy
• The non-modal onset of the tearing instability
• On the nonlinear stability of a quasi-two-dimensional drift kinetic model for ion temperature gradient turbulence