Investigating the role of stable eigenmodes in the nonlinear dynamics of resistive tearing instabilities

The tearing instability and its subsequent nonlinear dynamics are ubiquitous to plasmas, seen across a wide range of parameter space from the sawtooth crashes in fusion plasmas to coronal mass ejections in solar plasmas. This work explores the role that stable eigenmodes play in the nonlinear dynamics that result from the resistive tearing instability. Prior work has demonstrated the significance of linearly stable fluctuations to turbulence driven by a number of different plasma instabilities. Importantly, these stable modes act as an energy sink existing at the same spatial scales as the linear instability, preventing energy from cascading to smaller scales. An analysis of a Harris sheet equilibrium reveals the presence of a large number of stable modes present concurrently with a single unstable tearing mode. The contributions of each of these modes to the nonlinear state of the tearing mode dynamics is evaluated over a range of different magnetic Prandtl numbers. Simulations show that a small number of stable modes contribute significantly to the dynamics alongside the unstable mode. The effectiveness of a truncated eigenmode expansion as a means of describing the fully nonlinear system is quantified and discussed.