Linear Collisionless Landau Damping in Hilbert Space
Alessandro Zocco
TL;DR
This paper proves the equivalence between the Laplace and Hermite transform methods for solving the linear collisionless Landau damping problem, providing a unified mathematical framework.
Contribution
It establishes a rigorous proof of the equivalence between two mathematical approaches to Landau damping analysis.
Findings
Laplace and Hermite transform solutions are mathematically equivalent.
The proof unifies different analytical methods for collisionless plasma damping.
Provides a foundation for further analytical and numerical studies in plasma physics.
Abstract
The equivalence between the Laplace transform [Landau L., J. Phys. USSR, 10 (1946), 25] and Hermite transform [Zocco and Schekochihin, Phys. Plasmas, 18, 102309 (2011)] solutions of the linear collisionless Landau damping problem is proven.
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