title: The linear stability of line-tied coronal magnetic fields

authors: Foote, B.J.

abstract: The problem of the linear stability of cylindrically symmetric force-free magnetic equilibria is addressed. The aim is to quantify the severity of ideal MHD disturbances on a variety of line-tied coronal equilibria. Accordingly methods are developed which determine, at high spatial resolution, the dominant eigenmodes of the problem. We first introduce a family of equilibrium force-free fields parameterized by the local dimensionless twist T = rν which includes the well-known Gold-Hoyle field in the case ν = 0. The stability problem is then formulated, and the numerical techniques required for its solution are derived. As a preliminary test of our methods we present convergence results for the critical length of the Gold-Hoyle field, obtaining the result lc = 2.46π (dimensionless units). Next, the severity of the instability is quantified. The kink instability (m = 1) is found to be weak even for long lengths (l ≳ 4lc), generating dimensionless force eigenvalues less than O(10-2). The Gold-Hoyle field is shown to be the most unstable member of the family for large l, yet is the most susceptible to line-tying and so possesses the longest critical length. Preliminary investigations for higher m have not yielded instabilities for the moderate tube lengths of interest. The significance of these results to flare theories cannot be known definitively without results from finite-amplitude studies. Our results show, however, that the power release over the linear phase is at least three orders of magnitude below dimensional expectation. This implies that unstable coronal flux tubes cannot be expected to collapse violently on the MHD time scale.

text: The linear stability of line-tied coronal magnetic fields The problem of the linear stability of cylindrically symmetric force-free magnetic equilibria is addressed. The aim is to quantify the severity of ideal MHD disturbances on a variety of line-tied coronal equilibria. Accordingly methods are developed which determine, at high spatial resolution, the dominant eigenmodes of the problem. We first introduce a family of equilibrium force-free fields parameterized by the local dimensionless twist T = rν which includes the well-known Gold-Hoyle field in the case ν = 0. The stability problem is then formulated, and the numerical techniques required for its solution are derived. As a preliminary test of our methods we present convergence results for the critical length of the Gold-Hoyle field, obtaining the result lc = 2.46π (dimensionless units). Next, the severity of the instability is quantified. The kink instability (m = 1) is found to be weak even for long lengths (l ≳ 4lc), generating dimensionless force eigenvalues less than O(10-2). The Gold-Hoyle field is shown to be the most unstable member of the family for large l, yet is the most susceptible to line-tying and so possesses the longest critical length. Preliminary investigations for higher m have not yielded instabilities for the moderate tube lengths of interest. The significance of these results to flare theories cannot be known definitively without results from finite-amplitude studies. Our results show, however, that the power release over the linear phase is at least three orders of magnitude below dimensional expectation. This implies that unstable coronal flux tubes cannot be expected to collapse violently on the MHD time scale.

year: 1990

title: Linear transport of solar wind fluctuations

authors: Oughton, Sean

subjects: linear transport

abstract: Numerical solutions for the linear transport of solar wind fluctuations are presented. The model used takes into account the effects of advection, expansion, and wave propagation, as well as the recently illuminated effects of (non-WKB) “mixing” terms. The radial evolution of the fluctuating kinetic and magnetic energies and of the cross helicity is computed, and it is demonstrated that in appropriate limits the solutions converge to the WKB forms. In more general cases, however, where the fluctuations consist of a superposition of various types of turbulence, mixing leads to solutions which differ substantially from those predicted by WKB theory. The degree of mixing shows considerable dependence on the nature of the turbulence, giving rise to varying levels, at 1 ∼ AU, of the ratio of “inward” and “outward” fluctuation energies and the ratio of kinetic and magnetic fluctuation energies. The transport properties described here may provide a partial explanation for the observed decrease of cross helicity with increasing heliocentric distance in the solar wind.

text: Linear transport of solar wind fluctuations Numerical solutions for the linear transport of solar wind fluctuations are presented. The model used takes into account the effects of advection, expansion, and wave propagation, as well as the recently illuminated effects of (non-WKB) “mixing” terms. The radial evolution of the fluctuating kinetic and magnetic energies and of the cross helicity is computed, and it is demonstrated that in appropriate limits the solutions converge to the WKB forms. In more general cases, however, where the fluctuations consist of a superposition of various types of turbulence, mixing leads to solutions which differ substantially from those predicted by WKB theory. The degree of mixing shows considerable dependence on the nature of the turbulence, giving rise to varying levels, at 1 ∼ AU, of the ratio of “inward” and “outward” fluctuation energies and the ratio of kinetic and magnetic fluctuation energies. The transport properties described here may provide a partial explanation for the observed decrease of cross helicity with increasing heliocentric distance in the solar wind.

year: 1995

title: Claiming spaces: Prioritising Maaori worldview

authors: Penehira, Mera

subjects: Maori

abstract: Ohomairangi Trust was established as a provider of early intervention services in February 2002. It is funded and accredited by the Ministry of Education, and is the first Kaupapa Maaori based early intervention service to be accredited by the Ministry of Education. Essentially Ohomairangi was developed because of a need in the community for a service that could focus on developing and providing early intervention in a uniquely Maaori way, without the constraints of a crown agency. The Ohomairangi early intervention team has a commitment to supporting both the positive developments for Maaori within the Ministry of Education, and the continued independent research and development of Kaupapa Maaori services. The primary purpose of Ohomairangi is to develop and provide a Kaupapa Maaori based early intervention service across Taamaki Makaurau, which meets recommended practice guidelines. This evolves from a starting point of Kaupapa Maaori theory.

text: Claiming spaces: Prioritising Maaori worldview Ohomairangi Trust was established as a provider of early intervention services in February 2002. It is funded and accredited by the Ministry of Education, and is the first Kaupapa Maaori based early intervention service to be accredited by the Ministry of Education. Essentially Ohomairangi was developed because of a need in the community for a service that could focus on developing and providing early intervention in a uniquely Maaori way, without the constraints of a crown agency. The Ohomairangi early intervention team has a commitment to supporting both the positive developments for Maaori within the Ministry of Education, and the continued independent research and development of Kaupapa Maaori services. The primary purpose of Ohomairangi is to develop and provide a Kaupapa Maaori based early intervention service across Taamaki Makaurau, which meets recommended practice guidelines. This evolves from a starting point of Kaupapa Maaori theory.

year: 2008