Tightening energetic bounds on linear gyrokinetic instabilities

Fuente: arXiv
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Main Authors: Costello, P. J., Plunk, G. G.
Format: Preprint
Published: 2025
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author Costello, P. J.
Plunk, G. G.
author_facet Costello, P. J.
Plunk, G. G.
contents Bounding energetic growth of gyrokinetic instabilities is a complementary approach to linear instability analyses involving normal eigenmodes. Previous work has focused on upper bounds which are valid linearly and nonlinearly. However, if an upper bound on linear instability growth is desired, these nonlinearly valid bounds may be a poor predictor of the growth of the most unstable eigenmode. This is most evident for the simplest of instabilities: the ion-temperature-gradient (ITG) mode in slab geometry. In this work, we derive energetic upper bounds specifically for linear instability growth, focusing on the slab ITG. We show that there is no fundamental limitation on how tightly linear growth can be bounded by an energetic norm, with the tightest possible bound being given by a special energy comprised of projection coefficients of the linear eigenmode basis. Additionally, we consider `constrained optimal modes' that maximise energy growth subject to constraints that are also obeyed by the linear eigenmodes. This yields computationally efficient upper bounds that closely resemble the linear growth rate, capturing effects connected to the real frequency of instabilities, which have been absent in the energetic bounds considered thus far.
format Preprint
id arxiv_https___arxiv_org_abs_2505_17757
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Tightening energetic bounds on linear gyrokinetic instabilities
Costello, P. J.
Plunk, G. G.
Plasma Physics
Bounding energetic growth of gyrokinetic instabilities is a complementary approach to linear instability analyses involving normal eigenmodes. Previous work has focused on upper bounds which are valid linearly and nonlinearly. However, if an upper bound on linear instability growth is desired, these nonlinearly valid bounds may be a poor predictor of the growth of the most unstable eigenmode. This is most evident for the simplest of instabilities: the ion-temperature-gradient (ITG) mode in slab geometry. In this work, we derive energetic upper bounds specifically for linear instability growth, focusing on the slab ITG. We show that there is no fundamental limitation on how tightly linear growth can be bounded by an energetic norm, with the tightest possible bound being given by a special energy comprised of projection coefficients of the linear eigenmode basis. Additionally, we consider `constrained optimal modes' that maximise energy growth subject to constraints that are also obeyed by the linear eigenmodes. This yields computationally efficient upper bounds that closely resemble the linear growth rate, capturing effects connected to the real frequency of instabilities, which have been absent in the energetic bounds considered thus far.
title Tightening energetic bounds on linear gyrokinetic instabilities
topic Plasma Physics
url https://arxiv.org/abs/2505.17757