Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Energetic bounds on gyrokinetic instabilities. Part II. Modes of optimal
  growth   We introduce modes of instantaneous optimal growth of free energy for the
fully electromagnetic gyrokinetic equations. We demonstrate how these "optimal
modes" arise naturally from the free energy balance equation, allowing its
convenient decomposition, and yielding a simple picture of energy flows.
Optimal modes have a number of other favorable features, such as their
low-dimensionality, efficiency of computation, and the fact that their growth
rates provide a rigorous and "tight" upper bound on both the nonlinear growth
rate of energy, and the linear growth rate of traditional gyrokinetic (normal
mode) instabilities. We provide simple closed form solutions for the optimal
growth rates in a number of asymptotic limits, and compare these with our
previous bounds.

31
The categories of this paper are: ao-sci
0
The categories of this paper are: hep-ph
29
The categories of this paper are: funct-an
27
The categories of this paper are: comp-gas
34
The categories of this paper are: chem-ph
13
The categories of this paper are: quant-ph
8
The categories of this paper are: hep-ex
14
The categories of this paper are: math-ph
30
The categories of this paper are: q-alg
1
The categories of this paper are: cs
4
The categories of this paper are: cond-mat
33
The categories of this paper are: plasm-ph
7
The categories of this paper are: hep-th
9
The categories of this paper are: nlin
36
The categories of this paper are: cmp-lg
15
The categories of this paper are: nucl-ex