arXiv subjects

N. Arcis

Publications and source records attributed to N. Arcis.

3 recordsLinked to original sources

arXiv2008

Influence of higher-order harmonics on the saturation of the tearing mode

The nonlinear saturation of the tearing mode is revisited in slab geometry by taking into account higher-order harmonics in the outer solution. The general formalism for tackling this problem in the case of a vanishing current gradient at the resonant surface is derived. It is shown that, although the higher-order harmonics lead to corrections in the final saturation equation, they are of higher order in the perturbation parameter, which provides a formal proof that the standard one-harmonic approach is asymptotically correct.

physics.plasm-ph↗

arXiv2006

Rigorous approach to the nonlinear saturation of the tearing mode in cylindrical and slab geometry

The saturation of the tearing mode instability is described within the standard framework of reduced magnetohydrodynamics (RMHD) in the case of an $r$-dependent or of a uniform resistivity profile. Using the technique of matched asymptotic expansions, where the perturbation parameter is the island width $w$, the problem can be solved in two ways: with the so-called flux coordinate method, which is based on the fact that the current profile is a flux function, and with a new perturbative method that does not use this property. The latter is applicable to more general situations where an external forcing or a sheared velocity profile are involved. The calculation provides a new relationship between the saturated island width and the $Δ'$ stability parameter that involves a $\ln{w/w_{0}}$ term, where $w_{0}$ is a nonlinear scaling length that was missing in previous work. It also yields the modification of the equilibrium magnetic flux function.

physics.plasm-ph↗

arXiv2005

Perturbative approach to the nonlinear saturation of the tearing mode for any current gradient

Within the traditional frame of reduced MHD, a new rigorous perturbation expansion provides the equation ruling the nonlinear growth and saturation of the tearing mode for any current gradient. The small parameter is the magnetic island width w. For the first time, the final equation displays at once terms of order w ln(1/w) and w which have the same magnitude for practical purposes; two new O(w) terms involve the current gradient. The technique is applicable to the case of an external forcing. The solution for a static forcing is computed explicitly and it exhibits three physical regimes.

physics.plasm-ph↗