sol_ops Module Reference

Operations on the solution vectors such as decompososing the energy, etc... More...

Functions/Subroutines
subroutine, public	plot_sol_vals (sol, last_unstable_id)
	Plots Eigenvalues. More...
integer function, public	plot_sol_vec (mds_X, mds_sol, grid_eq, grid_X, grid_sol, eq_1, eq_2, X, sol, XYZ, X_id, plot_var)
	Plots Eigenvectors. More...
integer function, public	plot_harmonics (mds, grid_sol, sol, X_id, res_surf)
	Plots the harmonics and their maximum in 2-D. More...
integer function, public	decompose_energy (mds_X, mds_sol, grid_eq, grid_X, grid_sol, eq_1, eq_2, X, sol, vac, X_id, B_aligned, XYZ, E_pot_int, E_kin_int)
	Decomposes the plasma potential and kinetic energy in its individual terms for an individual Eigenvalue. More...
integer function	calc_e (mds_X, mds_sol, grid_eq, grid_X, grid_sol, eq_1, eq_2, X, sol, vac, B_aligned, X_id, E_pot, E_kin, E_pot_int, E_kin_int)
	Calculate the energy terms in the energy decomposition. More...
integer function, public	print_output_sol (grid, sol, data_name, rich_lvl, remove_previous_arrs)
	Print solution quantities to an output file: More...

Variables
logical, public	debug_plot_sol_vec = .false.
	plot debug information for plot_sol_vec() More...
logical, public	debug_calc_e = .false.
	plot debug information for calc_E() More...
logical, public	debug_x_norm = .false.
	plot debug information X_norm More...
logical, public	debug_du = .false.
	plot debug information for calculation of DU More...

Detailed Description

Operations on the solution vectors such as decompososing the energy, etc...

Function/Subroutine Documentation

calc_e()

integer function sol_ops::calc_e	(	type(modes_type), intent(in)	mds_X,
		type(modes_type), intent(in)	mds_sol,
		type(grid_type), intent(in)	grid_eq,
		type(grid_type), intent(in)	grid_X,
		type(grid_type), intent(in)	grid_sol,
		type(eq_1_type), intent(in)	eq_1,
		type(eq_2_type), intent(in)	eq_2,
		type(x_1_type), intent(in)	X,
		type(sol_type), intent(in)	sol,
		type(vac_type), intent(in)	vac,
		logical, intent(in)	B_aligned,
		integer, intent(in)	X_id,
		complex(dp), dimension(:,:,:,:), intent(inout), allocatable	E_pot,
		complex(dp), dimension(:,:,:,:), intent(inout), allocatable	E_kin,
		complex(dp), dimension(7), intent(inout)	E_pot_int,
		complex(dp), dimension(2), intent(inout)	E_kin_int
	)

Calculate the energy terms in the energy decomposition.

Note

see explanation of routine in decompose_energy().

Returns

ierr

Parameters

[in]	mds_x	general modes variables in perturbation grid
[in]	mds_sol	general modes variables in solution grid
[in]	grid_eq	equilibrium grid
[in]	grid_x	perturbation grid
[in]	grid_sol	and solution grid
[in]	eq_1	flux equilibrium
[in]	eq_2	metric equilibrium
[in]	x	perturbation variables
[in]	sol	solution variables
[in]	vac	vacuum variables
[in]	b_aligned	whether grid is field-aligned
[in]	x_id	nr. of Eigenvalue
[in,out]	e_pot	potential energy
[in,out]	e_kin	kinetic energy
[in,out]	e_pot_int	integrated potential energy
[in,out]	e_kin_int	integrated kinetic energy

Definition at line 1205 of file sol_ops.f90.

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decompose_energy()

integer function, public sol_ops::decompose_energy	(	type(modes_type), intent(in)	mds_X,
		type(modes_type), intent(in)	mds_sol,
		type(grid_type), intent(in)	grid_eq,
		type(grid_type), intent(in)	grid_X,
		type(grid_type), intent(in)	grid_sol,
		type(eq_1_type), intent(in)	eq_1,
		type(eq_2_type), intent(in)	eq_2,
		type(x_1_type), intent(in)	X,
		type(sol_type), intent(in)	sol,
		type(vac_type), intent(in)	vac,
		integer, intent(in)	X_id,
		logical, intent(in)	B_aligned,
		real(dp), dimension(:,:,:,:), intent(in), optional	XYZ,
		complex(dp), dimension(7), intent(inout), optional	E_pot_int,
		complex(dp), dimension(2), intent(inout), optional	E_kin_int
	)

Decomposes the plasma potential and kinetic energy in its individual terms for an individual Eigenvalue.

Use is made of variables representing the potential and kinetic energy [17].

• \(E_\text{pot}\):
  • normal line bending term: \(\frac{1}{\mu_0} \frac{Q_n^2}{h^{22}}\),
  • geodesic line bending term: \(\frac{1}{\mu_0} \mathcal{J}^2 \frac{h^{22}}{g_{33}} Q_g^2\),
  • normal ballooning term: \(-2 p' X^2 \kappa_n\),
  • geodesic ballooning term: \(-2 p' X U^* \kappa_g\),
  • normal kink term: \(-\sigma X^*Q_g\),
  • geodesic kink term: \(\sigma U^*Q_n\),
• \(E_\text{kin}\):
  • normal kinetic term: \(\rho \frac{X^2}{h^{22}}\),
  • geodesic kinetic term: \(\rho \mathcal{J}^2 \frac{h^{22}}{g_{33}} U^2\).

The energy terms are calculated normally on the sol grid, interpolating the quantities defined on the eq grid, and angularly in the eq grid.

Optionally, the results can be plotted by providing X, Y and Z. By default, they are instead written to an output file.

Also, the fraction between potential and kinetic energy can be returned, compared with the eigenvalue.

Returns

ierr

Parameters

[in]	mds_x	general modes variables in pertubation grid
[in]	mds_sol	general modes variables in solution grid
[in]	grid_eq	equilibrium grid
[in]	grid_x	perturbation grid
[in]	grid_sol	solution grid
[in]	eq_1	flux equilibrium
[in]	eq_2	metric equilibrium
[in]	x	perturbation variables
[in]	sol	solution variables
[in]	vac	vacuum variables
[in]	x_id	nr. of Eigenvalue
[in]	b_aligned	whether grid is field-aligned
[in]	xyz	X, Y and Z for plotting
[in,out]	e_pot_int	integrated potential energy
[in,out]	e_kin_int	integrated kinetic energy

Definition at line 991 of file sol_ops.f90.

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plot_harmonics()

integer function, public sol_ops::plot_harmonics	(	type(modes_type), intent(in)	mds,
		type(grid_type), intent(in)	grid_sol,
		type(sol_type), intent(in)	sol,
		integer, intent(in)	X_id,
		real(dp), dimension(:,:), intent(in)	res_surf
	)

Plots the harmonics and their maximum in 2-D.

Returns

ierr

Parameters

[in]	mds	general modes variables in solution grid
[in]	grid_sol	solution grid
[in]	sol	solution variables
[in]	x_id	nr. of Eigenvalue (for output name)
[in]	res_surf	resonant surfaces

Definition at line 646 of file sol_ops.f90.

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plot_sol_vals()

subroutine, public sol_ops::plot_sol_vals	(	type(sol_type), intent(in)	sol,
		integer, intent(in)	last_unstable_id
	)

Plots Eigenvalues.

Parameters

[in]	sol	solution variables
[in]	last_unstable_id	index of last unstable EV

Definition at line 37 of file sol_ops.f90.

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plot_sol_vec()

integer function, public sol_ops::plot_sol_vec	(	type(modes_type), intent(in)	mds_X,
		type(modes_type), intent(in)	mds_sol,
		type(grid_type), intent(in)	grid_eq,
		type(grid_type), intent(in)	grid_X,
		type(grid_type), intent(in)	grid_sol,
		type(eq_1_type), intent(in)	eq_1,
		type(eq_2_type), intent(in)	eq_2,
		type(x_1_type), intent(in)	X,
		type(sol_type), intent(in)	sol,
		real(dp), dimension(:,:,:,:), intent(in)	XYZ,
		integer, intent(in)	X_id,
		logical, dimension(2), intent(in)	plot_var
	)

Plots Eigenvectors.

This is done using the angular part of the the provided equilibrium grid and the normal part of the provided solution grid.

The perturbation grid is assumed to have the same angular coordinates as the equilibrium grid, and the normal coordinates correspond to either the equilibrium grid (X_grid_style 1), the solution grid (X_grid_style 2) or the enriched equilibrium grid (X_grid_style 3).

The output grid, furthermore, has the angular part corresponding to the equilibrium grid, and the normal part to the solution grid.

Note

The normalization factors are taken into account and the output is transformed back to unnormalized values:

\[\begin{aligned} \vec{\xi} &\sim \frac{X_0}{R_0 B_0} \ , \\ \vec{Q} &\sim \frac{X_0}{R_0^2} \ , \\ \end{aligned}\]

which translates to

\[\begin{aligned} X &\sim X_0 \ , \\ U &\sim \frac{X_0}{R_0^2 B_0} \ , \\ Qn &\sim \frac{X_0 B_0}{R_0} \ , \\ Qg &\sim \frac{X_0}{R_0^3} \ , \end{aligned}\]

where \(X_0\) is not determined but is common to all factors.

Returns

ierr

Parameters

[in]	mds_x	general modes variables in perturbation grid
[in]	mds_sol	general modes variables in solution grid
[in]	grid_eq	equilibrium grid
[in]	grid_x	perturbation grid
[in]	grid_sol	solution grid
[in]	eq_1	flux equilibrium
[in]	eq_2	metric equilibrium
[in]	x	perturbation variables
[in]	sol	solution variables
[in]	xyz	X, Y and Z of extended eq_grid
[in]	x_id	nr. of Eigenvalue (for output name)
[in]	plot_var	whether variables are plotted (1: plasma perturbation, 2: magnetic perturbation)

Definition at line 116 of file sol_ops.f90.

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print_output_sol()

integer function, public sol_ops::print_output_sol	(	type(grid_type), intent(in)	grid,
		type(sol_type), intent(in)	sol,
		character(len=*), intent(in)	data_name,
		integer, intent(in), optional	rich_lvl,
		logical, intent(in), optional	remove_previous_arrs
	)

Print solution quantities to an output file:

• sol:
  • val
  • vec

If rich_lvl is provided, "_[R_rich_lvl]" is appended to the data name if it is >0.

Returns

ierr

Parameters

[in]	grid	solution grid variables
[in]	sol	solution variables
[in]	data_name	name under which to store
[in]	rich_lvl	Richardson level to print
[in]	remove_previous_arrs	remove previous variables if present

Definition at line 1566 of file sol_ops.f90.

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Variable Documentation

debug_calc_e

logical, public sol_ops::debug_calc_e = .false.

plot debug information for calc_E()

Note

Debug version only

Definition at line 29 of file sol_ops.f90.

debug_du

logical, public sol_ops::debug_du = .false.

plot debug information for calculation of DU

Note

Debug version only

Definition at line 31 of file sol_ops.f90.

debug_plot_sol_vec

logical, public sol_ops::debug_plot_sol_vec = .false.

plot debug information for plot_sol_vec()

Note

Debug version only

Definition at line 27 of file sol_ops.f90.

debug_x_norm

logical, public sol_ops::debug_x_norm = .false.

plot debug information X_norm

Note

Debug version only

Definition at line 30 of file sol_ops.f90.