Extended Martin-Taylor map

Overview

   Project name: Extended Martin-Taylor map
        Author : Michele Mugnaine  
           Date: 17/July/2023

Contact: mmugnaine@gmail.com

Description:

Code and data repository accompanying the publication "A nontwist field line mapping in a tokamak with ergodic magnetic limiter" .

Both data and codes are available in the file "codes.zip".

Requirements

Fortran compiler (gfortran, ifort, ...).
Octave (software or OctaveOnline )
Files available in "codes.zip".

Figure 1

To obtain all the data used in Figure 1, run: $ gfortran Parameters.f90 Fig1.f90; ./a.out .

Figure 1 (a) - OMT_profile.dat
Figure 1 (b) - EMT_profile.dat
Figure 1 (c) - ShearParameter.dat

Figure 2

To obtain the data used in Figure 2 (a), run: $ gfortran Parameters2.f90 Fig2a.f90; ./a.out .

Figure 2 (a) - PhaseSpaceOMT.dat

To obtain the data used in Figure 2 (b), run: $ gfortran Parameters2.f90 Fig2b.f90; ./a.out .

Figure 2 (b) - PhaseSpaceEMT.dat

Figure 3

To obtain the data used in Figure 3 (a), run: $ gfortran Parameters3.f90 Fig3a.f90; ./a.out .

Figure 3 (a) - 'WindingNumberOMT.dat

To obtain the data used in Figure 3 (b), run: $ gfortran Parameters3.f90 Fig3b.f90; ./a.out .

Figure 3 (b) - WindingNumberEMT.dat

Figure 4

To obtain all the data used in Figure 4, run: $ gfortran Fig4.f90; ./a.out .

Figure 4 (a) - PhaseSpace1.dat
Figure 4 (b) - PhaseSpace2.dat
Figure 4 (c) - PhaseSpace3.dat
Figure 4 (d) - PhaseSpace4.dat
Figure 4 (e) - PhaseSpace5.dat
Figure 4 (f) - PhaseSpace6.dat

Figure 5

Data were generated by constructing the phase spaces for the Original Martin-Taylor map (Figure 2 a) and calculating the half-width of the largest island. The results are in the files:

Figure 5 (a) - Imax_ILP_m_1.dat
Figure 5 (b) - Imax_ILP_m_2.dat
Figure 5 (c) - Imax_ILP_m_3.dat
Figure 5 (d) - Imax_ILP_m_4.dat

The pendulum approximation data for each value of m are in the files:

Figure 5 (a) - ImaxPend_ILP_m_1.dat
Figure 5 (b) - ImaxPend_ILP_m_2.dat
Figure 5 (c) - ImaxPend_ILP_m_3.dat
Figure 5 (d) - ImaxPend_ILP_m_4.dat

Figure 6

Data were generated by constructing the phase spaces for the Extended Martin-Taylor map (Figure 2 b) and calculating the half-width of the largest upper and lower island, for m =3. The results are in the files:

Figure 6 (a) - Imax_LowerChain.dat and Imax_UpperChain.dat

The pendulum approximation data are in the files

Figure 6 (a) - ImaxPend_LowerChain.dat and ImaxPend_UpperChain.dat

To obtain all the data used in Figure 6 (b) and 6 (c), run: $ gfortran Fig6.f90; ./a.out .

Figure 6 (b) - PhaseSpace_b.dat
Figure 6 (c) - PhaseSpace_c.dat

Figure 7

Figure 7 (a) - PendularIsland.dat data were generated by the Sympletic LSODE solver of Octave. To obtain the data, run the code " Pendulum.m " at Octave.
Figure 7 (b) - LowerIsland.dat data were generated by the code " Fig2b.f90 " .
Figure 7 (c) - UpperIsland.dat data were generated by the code " Fig2b.f90 " .

Figure 8

To obtain the data used in Figure 8 (a), run: $ gfortran Fig8a.f90; ./a.out .

Figure 8 (a) - Data_Fig8_a.dat

To obtain the data used in Figure 8 (b) and 8 (c), run: $ gfortran Fig8b_c.f90; ./a.out .

Figure 8 (b) - Fig8b-c_ShearlessCurve1.dat and Fig8b-c_ShearlessCurve2.dat
Figure 8 (c) - Fig8b-c_ShearlessCurve3.dat and Fig8b-c_ShearlessCurve4.dat

To obtain the data used in Figure 8 (d), run: $ gfortran Fig8d.f90; ./a.out .

Figure 8 (d) - Data_Fig8_d.dat

To obtain the data used in Figure 8 (e) and 8 (f), run: $ gfortran Fig8e_f.f90; ./a.out .

Figure 8 (e) - Fig8e-f_ShearlessCurve1.dat and Fig8e-f_ShearlessCurve2.dat
Figure 8 (f) - Fig8e-f_ShearlessCurve3.dat and Fig8e-f_ShearlessCurve4.dat