Göttingen 2025 – wissenschaftliches Programm

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P: Fachverband Plasmaphysik

P 17: Poster Session II

P 17.44: Poster

Mittwoch, 2. April 2025, 16:15–18:15, ZHG Foyer 1. OG

Tightest possible energetic bounds on local gyrokinetic instabilities — •Paul Costello and Gabriel Plunk — Max Planck Institute for Plasma Physics, Greifswald, Germany

The turbulence in fusion plasmas, which hampers their performance in many respects, is best understood with gyrokinetic theory. Recent work has shown that energetic upper bounds on the growth of turbulence causing gyrokinetic instabilities can be derived by seeking optimal modes, states of the gyrokinetic equation which maximise the growth of an energy norm [2]. Typically, an energy norm is chosen which is a nonlinear invariant of the gyrokinetic equation, such that the bounds are valid linearly and nonlinearly.

The growth of unstable linear eigenmodes, which are the focus of much theoretical and numerical work, is also bounded by the optimal mode growth rate. A natural question, which we seek to answer in this work, is, ``How tightly can the linear eigenmode growth be bounded?'' We find that using a special energy norm which is not a nonlinear invariant in most systems gives an upper bound equal to the growth of the most unstable linear eigenmode. This energy norm is a sum of projection coefficients in the linear eigenmode basis and is positive definite by the completeness of these modes [2]. Systems for which this energy norm is a nonlinear invariant are free from subcritical turbulence and may form a simple paradigm for turbulence saturation [3].

[1] G. G. Plunk & P. Helander. JPP 2022.

[2] K. M. Case. Annals of Physics 1959.

[3] G. G. Plunk. Phys. Plasmas 2015.

Keywords: Instabilities; Turbulence; Gyrokinetics