eq_vars::eq_2_type Type Reference

metric equilibrium type More...

Public Member Functions
procedure	init (eq, grid, setup_e, setup_f)
	initialize
procedure	copy (eq_i, grid_i, eq_o)
	copy
procedure	dealloc (eq)
	deallocate

Public Attributes
real(dp), dimension(:,:,:,:,:,:), allocatable	r_e
	R in E(quilibrium) coord.
real(dp), dimension(:,:,:,:,:,:), allocatable	z_e
	Z in E(quilibrium) coords.
real(dp), dimension(:,:,:,:,:,:), allocatable	l_e
	L(ambda) in E(quilibrium) coords.
real(dp), dimension(:,:,:,:,:,:,:), allocatable	g_c
	in the C(ylindrical) coord. system
real(dp), dimension(:,:,:,:,:,:,:), allocatable	g_e
	in the E(quilibrium) coord. system
real(dp), dimension(:,:,:,:,:,:,:), allocatable	h_e
	in the E(quilibrium) coord. system
real(dp), dimension(:,:,:,:,:,:,:), allocatable	g_f
	in the F(lux) coord. system with derivs. in V(MEC) system
real(dp), dimension(:,:,:,:,:,:,:), allocatable	h_f
	in the F(lux) coord. system with derivs. in V(MEC) system
real(dp), dimension(:,:,:,:,:,:,:), allocatable	g_fd
	in the F(lux) coord. system with derivs in F(lux) system
real(dp), dimension(:,:,:,:,:,:,:), allocatable	h_fd
	in the F(lux) coord. system with derivs in F(lux) system
real(dp), dimension(:,:,:,:,:,:,:), allocatable	t_vc
	C(ylindrical) to V(MEC).
real(dp), dimension(:,:,:,:,:,:,:), allocatable	t_ef
	E(quilibrium) to F(lux).
real(dp), dimension(:,:,:,:,:,:,:), allocatable	t_fe
	F(lux) to E(quilibrium).
real(dp), dimension(:,:,:,:,:,:), allocatable	det_t_ef
	determinant of T_EF
real(dp), dimension(:,:,:,:,:,:), allocatable	det_t_fe
	determinant of T_FE
real(dp), dimension(:,:,:,:,:,:), allocatable	jac_e
	jacobian of E(quilibrium) coord. system
real(dp), dimension(:,:,:,:,:,:), allocatable	jac_f
	jacobian of F(lux) coord. system with derivs. in V(MEC) system
real(dp), dimension(:,:,:,:,:,:), allocatable	jac_fd
	jacobian of F(lux) coord. system with derivs. in F(lux) system
real(dp), dimension(:,:,:), allocatable	s
	magnetic shear
real(dp), dimension(:,:,:), allocatable	kappa_n
	normal curvature
real(dp), dimension(:,:,:), allocatable	kappa_g
	geodesic curvature
real(dp), dimension(:,:,:), allocatable	sigma
	parallel current
real(dp), dimension(2)	estim_mem_usage
	expected memory usage

Detailed Description

metric equilibrium type

The arrays here are of the form

• (angle_1,angle_2,r) for scalars without derivs.
• (angle_1,angle_2,r,D123) for scalars with derivs.
• (angle_1,angle_2,r,6/9,D1,D2,D3) for tensors with derivs.
  where it is refered to the discussion of the grid type for an explanation of the angles angle_1 and angle_2.

The last index refers to the derivatives in coordinate 1, 2 and 3, which refer to the coordinates described in [17].

• For E(quilibrium) coordinates, they are \(\left(r,\theta,\zeta\right)_\text{E}\).
• For F(lux) coordinates, they are \(\left(\alpha,\psi,\gamma\right)_\text{F}\), where
  • \(\alpha = \zeta - q \theta\) and \(\gamma = \theta\) for pol. flux,
  • \(\alpha = -\theta + \iota \zeta\) and \(\gamma = \zeta\) Nfor tor. flux.

The fourth index for tensorial variables correspond to the 9 or 6 (symmetric) different values:

\[ \left( \begin{array}{ccc}1&4&7\\2&5&8\\3&6&9\end{array} \right) \ \text{or} \quad \left( \begin{array}{ccc}1& & \\2&4& \\3&5&6\end{array} \right) \]

Note

Fortran only allows for 7 dimensions in arrays.

Definition at line 114 of file eq_vars.f90.

Member Function/Subroutine Documentation

copy()

procedure eq_vars::eq_2_type::copy	(	class(eq_2_type), intent(in)	eq_i,
		type(grid_type), intent(in)	grid_i,
		type(eq_2_type), intent(inout)	eq_o )

copy

Returns

ierr

Parameters

[in]	eq_i	eq_2 to be copied
[in]	grid_i	grid of eq_i
[in,out]	eq_o	copied eq_1

Definition at line 150 of file eq_vars.f90.

dealloc()

procedure eq_vars::eq_2_type::dealloc

(

class(eq_2_type), intent(inout)

eq

)

deallocate

Parameters

[in,out]

eq

equilibrium to be deallocated

Definition at line 152 of file eq_vars.f90.

init()

procedure eq_vars::eq_2_type::init	(	class(eq_2_type), intent(inout)	eq,
		type(grid_type), intent(in)	grid,
		logical, intent(in), optional	setup_e,
		logical, intent(in), optional	setup_f )

initialize

See also

For explanation see init_eq_1().

Note

The maximum derivative degree for R, Z and lambda is one higher than max_deriv, because their first derivative already appears in g_C and h_C.

Parameters

[in,out]	eq	equilibrium to be initialized
[in]	grid	equilibrium grid
[in]	setup_e	whether to set up E
[in]	setup_f	whether to set up F

Definition at line 148 of file eq_vars.f90.

Member Data Documentation

det_t_ef

real(dp), dimension(:,:,:,:,:,:), allocatable eq_vars::eq_2_type::det_t_ef

determinant of T_EF

Definition at line 132 of file eq_vars.f90.

det_t_fe

real(dp), dimension(:,:,:,:,:,:), allocatable eq_vars::eq_2_type::det_t_fe

determinant of T_FE

Definition at line 133 of file eq_vars.f90.

estim_mem_usage

real(dp), dimension(2) eq_vars::eq_2_type::estim_mem_usage

expected memory usage

Note

Debug version only

Definition at line 144 of file eq_vars.f90.

g_c

real(dp), dimension(:,:,:,:,:,:,:), allocatable eq_vars::eq_2_type::g_c

in the C(ylindrical) coord. system

Definition at line 120 of file eq_vars.f90.

g_e

real(dp), dimension(:,:,:,:,:,:,:), allocatable eq_vars::eq_2_type::g_e

in the E(quilibrium) coord. system

Definition at line 121 of file eq_vars.f90.

g_f

real(dp), dimension(:,:,:,:,:,:,:), allocatable eq_vars::eq_2_type::g_f

in the F(lux) coord. system with derivs. in V(MEC) system

Definition at line 123 of file eq_vars.f90.

g_fd

real(dp), dimension(:,:,:,:,:,:,:), allocatable eq_vars::eq_2_type::g_fd

in the F(lux) coord. system with derivs in F(lux) system

Definition at line 125 of file eq_vars.f90.

h_e

real(dp), dimension(:,:,:,:,:,:,:), allocatable eq_vars::eq_2_type::h_e

in the E(quilibrium) coord. system

Definition at line 122 of file eq_vars.f90.

h_f

real(dp), dimension(:,:,:,:,:,:,:), allocatable eq_vars::eq_2_type::h_f

in the F(lux) coord. system with derivs. in V(MEC) system

Definition at line 124 of file eq_vars.f90.

h_fd

real(dp), dimension(:,:,:,:,:,:,:), allocatable eq_vars::eq_2_type::h_fd

in the F(lux) coord. system with derivs in F(lux) system

Definition at line 126 of file eq_vars.f90.

jac_e

real(dp), dimension(:,:,:,:,:,:), allocatable eq_vars::eq_2_type::jac_e

jacobian of E(quilibrium) coord. system

Definition at line 135 of file eq_vars.f90.

jac_f

real(dp), dimension(:,:,:,:,:,:), allocatable eq_vars::eq_2_type::jac_f

jacobian of F(lux) coord. system with derivs. in V(MEC) system

Definition at line 136 of file eq_vars.f90.

jac_fd

real(dp), dimension(:,:,:,:,:,:), allocatable eq_vars::eq_2_type::jac_fd

jacobian of F(lux) coord. system with derivs. in F(lux) system

Definition at line 137 of file eq_vars.f90.

kappa_g

real(dp), dimension(:,:,:), allocatable eq_vars::eq_2_type::kappa_g

geodesic curvature

Definition at line 141 of file eq_vars.f90.

kappa_n

real(dp), dimension(:,:,:), allocatable eq_vars::eq_2_type::kappa_n

normal curvature

Definition at line 140 of file eq_vars.f90.

l_e

real(dp), dimension(:,:,:,:,:,:), allocatable eq_vars::eq_2_type::l_e

L(ambda) in E(quilibrium) coords.

Definition at line 118 of file eq_vars.f90.

r_e

real(dp), dimension(:,:,:,:,:,:), allocatable eq_vars::eq_2_type::r_e

R in E(quilibrium) coord.

Definition at line 116 of file eq_vars.f90.

s

real(dp), dimension(:,:,:), allocatable eq_vars::eq_2_type::s

magnetic shear

Definition at line 139 of file eq_vars.f90.

sigma

real(dp), dimension(:,:,:), allocatable eq_vars::eq_2_type::sigma

parallel current

Definition at line 142 of file eq_vars.f90.

t_ef

real(dp), dimension(:,:,:,:,:,:,:), allocatable eq_vars::eq_2_type::t_ef

E(quilibrium) to F(lux).

Definition at line 129 of file eq_vars.f90.

t_fe

real(dp), dimension(:,:,:,:,:,:,:), allocatable eq_vars::eq_2_type::t_fe

F(lux) to E(quilibrium).

Definition at line 130 of file eq_vars.f90.

t_vc

real(dp), dimension(:,:,:,:,:,:,:), allocatable eq_vars::eq_2_type::t_vc

C(ylindrical) to V(MEC).

Definition at line 128 of file eq_vars.f90.

z_e

real(dp), dimension(:,:,:,:,:,:), allocatable eq_vars::eq_2_type::z_e

Z in E(quilibrium) coords.

Definition at line 117 of file eq_vars.f90.

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The documentation for this type was generated from the following file:

• /Users/toonweyens/Code/PB3D/Modules/eq_vars.f90