Sausage Instabilities on Top of Kinking Lengthening Current-Carrying Magnetic Flux Tubes - Data underlying figures 3 & 4

Background

This is the code used in the analysis and to generate all plots of the paper "Sausage Instabilities on Top of Kinking Lengthening Current-Carrying Magnetic Flux Tubes".

Flux tube experiments can be classified by the flux tube’s evolution in a configuration space described by a normalized inverse aspect-ratio k̄ and current-to-magnetic flux ratio λ̄. A lengthening current-carrying magnetic flux tube traverses this k̄ - λ̄ space and crosses stability boundaries. We derive a single general criterion for the onset of the sausage and kink instabilities in idealized magnetic flux tubes with core and skin currents. The criterion indicates a dependence of the stability boundaries on current
profiles and shows overlapping kink and sausage unstable regions in the k̄ - λ̄ space with two free parameters. Numerical investigation of the stability criterion reduces the number of free parameters to a single one that describes the current profile, and confirms the overlapping sausage and kink unstable regions in k̄ - λ̄ space. A lengthening, ideal current-carrying magnetic flux tube can therefore become sausage unstable after it becomes kink unstable.

Accesing Data

This data set contains:

1. SQL database: output.db
2. Human readable database in JSON format: output.txt
3. Data arrays: 3 dated .npz files
4. Human readable data arrays: 8 .dat files.

The database files list all parameters of a run of the analysis code. The date identifies the run. The SQL database can be inspected with e.g. Firefox's SQLite Manager extension. The contents of the human redable output.txt file are identical.

The data arrays include the k̄ meshes and  λ̄ meshes which define the coordiante system and arrays of normalized \(\delta W\) for kink and susage modes.

Each .npz file contains arrays defining the k̄ - λ̄ space and the stability calculation results.

Each .npz file is an array file generated with python numpy.savez(). It can be opened with:

import numpy as np

data = np.load('meshes.npz')

The data is an python dictionary. The dictionary keys can be displayed with:

print data.keys()

The numpy arrays can be accessed by keyname:

print data['keyname']

The keys are:

k_a_mesh: 2D array of k̄ values.

lambda_a_mesh: 2D array of λ̄ values.

d_w_raw_m_0: 2D array of perturbed potential energy for m=0 sausage pertubations.

d_w_raw_m_neg_1: 2D array of perturbed potential energy for m=-1 kink pertubations.

d_w_m_0: 2D array of normalized perturbed potential energy for m=0 sausage pertubations.

d_w_m_neg_1: 2D array of normalized perturbed potential energy for m=-1 kink pertubations.

delta_m_0: 2D array of delta for m=0 sausage pertubations plugged into minimized perturbed potential energy equations  to calculate dw values.

delta_m_neg_1: 2D array of delta for m=-1 kink pertubations plugged into minimized perturbed potential energy equations  to calculate dw values.

external_m_neg_1: 2D bool array of stability against external m=-1 kink pertubations. X

suydam_m_neg_1: 2D bool array of stability against suydam instabilities. 

external_m_0: 2D bool array of stability against external m=0 sausage pertubations. 

suydam_m_0: 2D bool array of stability against suydam instabilities. Since m=0 has no singularties in the Euler-Lagrange equation this should be true everywhere.