Global current profile effects on the evolution and saturation of magnetic islands

Abstract

The nonlinear evolution of magnetic islands is investigated by means of numerical simulations. The growth and saturation of the island are shown to depend not only on asymptotic tearing mode stability parameter D 0 but also on the initial global current profile. Presence of the external current sheets leads to the formation of different island state for the same value of D 0 . It is found that the flow vorticity generated by the interacting current sheets is an important feature of nonlocal interactions and nonlocal effects in magnetic islands dynamics. V C 2013 American Institute of Physics. [http://dx.Magnetic islands are ubiquitous in space and magnetic fusion plasmas. Magnetic islands associated with magnetic reconnection precede the destruction of flux ropes in solar corona and energy release in the Earth magnetotail. 1,2 In tokamaks, magnetic islands are a major cause of the degradation of plasma confinement and disruptions. 3 Within the boundary layer approach, the stability and growth of the tearing mode are determined by the stability parameter D 0 which characterizes the jump of the magnetic field function at the resonant surface. 4,5 This is a common paradigm of the analytical theory when all non-local effects such as the global current profile and boundary conditions are cast into the parameter D 0 and the predictions of the asymptotic island size require only the knowledge of D 0 and the current profile (current gradients) at the resonant surface. 6,7 This approach has also been adopted in numerical studies 8 including those for practical applications such as control and suppression of magnetic islands with external current drive and heating. 9 The asymptotic approach of the boundary layer is applicable in the regimes of small D 0 , typically D 0 L ? < 1, where L ? is the characteristic length scale of the outer linear region. In fact, in many applications to realistic current profiles, the value of D 0 is not small, rather D 0 L ? can easily be of the order of 10, 10 and even higher in case of the externally driven island. In this letter, the non-local effects of the current profile are investigated in high D 0 regimes. It is shown that the equilibrium current profile far from the resonance can strongly impact the nonlinear dynamics and saturation of magnetic islands and that this impact is not captured by the D 0 stability parameter. We perform a series of numerical experiments with different current profiles (but identical values of D 0 Þ to investigate the quantitative behavior and mechanisms of global effects beyond the D 0 parameterization.In the following, we use a 2D slab reduced MHD model in the low plasma pressure limit. 5,11 The coupled equations for electrostatic potential fluctuations / and the magnetic flux fluctuations w are

Higher order and asymmetry effects on saturation of magnetic islands

“…The m ¼ 0 harmonic of H nl ðx; nÞ, described by the function dw 0 gðxÞ in Eq. (13), modifies the equilibrium current. It can be determined from the general solution for H nl 0 ðx; nÞ as follows:…”

Impact of electric potential and magnetic drift on microtearing modes stability

“…Where L s is magnetic shear length L s = qR/ŝ, L T e is the electron temperature gradient length scale and ρ e is the electron Larmor radius. Inside the layer where a current develops, A is assumed to vary slowly consistently with a "constant A " approximation (A is constant in the current layer) 36 . The matching of the internal and external solutions in physical space is presented in 33,36 .…”

“…Inside the layer where a current develops, A is assumed to vary slowly consistently with a "constant A " approximation (A is constant in the current layer) 36 . The matching of the internal and external solutions in physical space is presented in 33,36 . Here the same procedure is translated in the ballooning space.…”

Stability of a slab collisional microtearing mode

“…Inside the current sheet, δA ∥ is supposed to be constant. The matching between the two solutions is simply represented by the so‐called Δ ′ parameter, which for a slab current sheet of width δ J is defined as …”