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: Extracting the MESA SR4000 Calibrations

authors: Charleston, Sean A.

subjects: Science & Technology

abstract: Time-of-flight range imaging cameras are capable of acquiring depth images of a scene. Some algorithms require these cameras to be run in `raw mode', where any calibrations from the off-the-shelf manufacturers are lost. The calibration of the MESA SR4000 is herein investigated, with an attempt to reconstruct the full calibration. Possession of the factory calibration enables calibrated data to be acquired and manipulated even in “raw mode.” This work is motivated by the problem of motion correction, in which the calibration must be separated into component parts to be applied at different stages in the algorithm. There are also other applications, in which multiple frequencies are required, such as multipath interference correction. The other frequencies can be calibrated in a similar way, using the factory calibration as a base. A novel technique for capturing the calibration data is described; a retro-reflector is used on a moving platform, which acts as a point source at a distance, resulting in planar waves on the sensor. A number of calibrations are retrieved from the camera, and are then modelled and compared to the factory calibration. When comparing the factory calibration to both the “raw mode” data, and the calibration described herein, a root mean squared error improvement of 51:3mm was seen, with a standard deviation improvement of 34:9mm. © (2015) COPYRIGHT Society of Photo-Optical Instrumentation Engineers (SPIE). Downloading of the abstract is permitted for personal use only.

text: Extracting the MESA SR4000 Calibrations Time-of-flight range imaging cameras are capable of acquiring depth images of a scene. Some algorithms require these cameras to be run in `raw mode', where any calibrations from the off-the-shelf manufacturers are lost. The calibration of the MESA SR4000 is herein investigated, with an attempt to reconstruct the full calibration. Possession of the factory calibration enables calibrated data to be acquired and manipulated even in “raw mode.” This work is motivated by the problem of motion correction, in which the calibration must be separated into component parts to be applied at different stages in the algorithm. There are also other applications, in which multiple frequencies are required, such as multipath interference correction. The other frequencies can be calibrated in a similar way, using the factory calibration as a base. A novel technique for capturing the calibration data is described; a retro-reflector is used on a moving platform, which acts as a point source at a distance, resulting in planar waves on the sensor. A number of calibrations are retrieved from the camera, and are then modelled and compared to the factory calibration. When comparing the factory calibration to both the “raw mode” data, and the calibration described herein, a root mean squared error improvement of 51:3mm was seen, with a standard deviation improvement of 34:9mm. © (2015) COPYRIGHT Society of Photo-Optical Instrumentation Engineers (SPIE). Downloading of the abstract is permitted for personal use only.

year: 2015

title: Bilingual/Immersion education: Indicators of good practice

authors: May, Stephen

subjects: Maori

abstract: Based on a review of national and international research on bilingualism and bilingual/immersion education, this report explores effective approaches for bilingual education. While the focus was on Māori-medium education, the indicators of good practice can also be applied to other bilingual contexts in Aotearoa/New Zealand, such as Pasifika bilingual education.

text: Bilingual/Immersion education: Indicators of good practice Based on a review of national and international research on bilingualism and bilingual/immersion education, this report explores effective approaches for bilingual education. While the focus was on Māori-medium education, the indicators of good practice can also be applied to other bilingual contexts in Aotearoa/New Zealand, such as Pasifika bilingual education.

year: 2004