Abstract Details
Abstracts
Author: Samuel W. Freiberger
Requested Type: Poster
Submitted: 2026-03-20 16:38:26
Co-authors: Sophia Guizzo, Christopher J. Hansen, Carlos Paz-Soldan
Contact Info:
Columbia University
500 W. 120th Street #200
New York, New York 10027
USA
Abstract Text:
Physical systems like plasmas can exhibit large transient growth over short time scales not captured by asymptotic analysis techniques such as eigenvalue decomposition. This poster presents preliminary results and progress in a new nonmodal analysis of the tearing instability for the Harris sheet problem, following the work of MacTaggart [1]. First, a finite element-based simulation of the resistive magnetohydrodynamics (MHD) equations in two dimensions allows for the construction of a linearized resistive MHD operator. Since the resistive MHD equations are known to be nonmodal, a perturbative analysis of the linearized operator can reveal initial conditions that lead to transient algebraic growth, even when asymptotically stable. Using an operator-valued function that describes sensitivity to perturbations called the resolvent, we also compute the initial conditions that generate maximal transient growth. The pseudospectrum, a set of level curves of the resolvent operator for different perturbation magnitudes, shows the maximal transient growth that can be expected for a given perturbation magnitude. In particular, we examine the discretized resistive MHD operator for Harris sheet reconnection at varying magnetic Lundquist numbers to determine the maximum transient growth rate of perturbations to the prescribed equilibrium state near marginal stability.
[1] D. MacTaggart. J. Plasma Phys. 2018.
Characterization: 6.0
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