The field modules and programs

Module mag_dipole_line

Module : mag_field_line

Purpose : single field line

class field_line_t

A field line object

type

Parameters

• vr(:,:) – xyz position along the field line; index 1: x, y, or z dimension, so values are 1:3, index 2: s dimension, so values are 1:n – real(WP), allocatable

• s(:) – the length along the field line – real(WP), allocatable

• vB(:,:) – magnetic field along the field line; index 1: x, y, or z dimension, so values are 1:3, index 2: s dimension, so values are 1:n – real(WP), allocatable

• n – number of grids along field line – integer

• i_0 – zero-point index where forwards and backwards tracing along a field meet – integer

• foot_N – boolean for the north magnetic foot point being on the star – integer

• foot_S – boolean for the south magnetic foot point being on the star – integer

init_fl(n) result (fl)

Construct a field line

space for type variables vr, s, vB is allocated; type variable n is set

type variables foot_N and foot_S are initialized to .FALSE.

function

Parameters

n – number of points on the field line – integer, intent(in)

Rtype fl

returned field line with vr, s, vB, and n initialized – field_line_t

init_fl_trace_point(pf, st, r_0, R_outer, ds, tol, max_steps) result (fl)

Construct a field line by tracing from an arbitrary specified point

calls trace_point

function

Parameters

• pf – potential field – pot_field_t, target, intent(in)

• st – star – star_t, target, intent(in)

• r_0(:) – the specified point – real(WP), intent(in)

• R_outer – outer radius for field-line calculation – real(WP), intent(in)

• ds – step size along the field line – real(WP), intent(in)

• tol – tolerance – real(WP), intent(in)

• max_steps – maximum steps along the field line – integer, intent(in), optional

Rtype fl

computed and returned field line – field_line_t

init_fl_trace_star(pf, st, theta_0, phi_0, R_outer, ds, tol, max_steps) result (fl)

Construct a field line by tracing from a specified point on the star

function

Parameters

• pf – potential field – pot_field_t, target, intent(in)

• st – star – star_t, target, intent(in)

• theta_0 – polar coordinate for field line tracing to start – real(WP), intent(in)

• phi_0 – azimuthal coordinate for field line tracing to start – real(WP), intent(in)

• R_outer – outer radius for field-line calculation – real(WP), intent(in)

• ds – step size along the field line – real(WP), intent(in)

• tol – tolerance – real(WP), intent(in)

• max_steps – maximum steps along the field line – integer, intent(in), optional

Rtype fl

computed and returned field line – field_line_t

discrim_star(vr) result (D)

Calculate the discriminant for r being outside the star

D = st_m%D_surf(vr)

function

Parameters

vr(:) – position of discriminant calcualtion – real(WP), intent(in)

Rtype D

calculated and returned discrimant – real(WP)

discrim_source(vr) result (D)

Calculate the discriminant for r being outside the source surface

D = NORM2(vr) - R_source_m

function

Parameters

vr(:) – position of discriminant calculation – real(WP), intent(in)

Rtype D

calculated and returned discrimant – real(WP)

discrim_outer(vr) result (D)

Calculate the discriminant for r being outside the outer boundary

D = NORM2(vr) - R_outer_m

function

Parameters

vr(:) – position of discriminant calculation – real(WP), intent(in)

Rtype D

calculated and returned discriminant – real(WP)

read_fl(hg, fl)

Read various attributes of a field line

reads n, i_0, foot_N, foot_S, vr, s, vB

only if hdf5

subroutine

Parameters

• hg – hdf5 data set – hgroup_t, intent(inout)

• fl – field line – field_line_t

write_fl(hg, fl)

Write various assets of a field line

writes n, i_0, foot_N, foot_S, vr, s, vB

only if hdf5

subroutine

Parameters

• hg – hdf5 data set – hgroup_t, intent(inout)

• fl – field line – field_line_t, intent(in)

bcast_fl(fl, root_rank)

Broadcast a field line

vr, s, vB, n, i_0, foot_N, foot_S are broadcasted

only if MPI

subroutine

Parameters

• fl – field line to broadcast – field_line_t, intent(inout)

• root_rank – rank of root processor – integer, intent(in)

trace_point(pf, st, r_0, R_outer, ds, tol, max_steps, fl)

Construct a field line by tracing from a specified point

does the calculation here; traces forwards and backwards, then puts the results together

computes vr, s, vB, n, i_0, foot_N, foot_S for field line class

subroutine

Parameters

• pf – potential field – pot_field_t, target, intent(in)

• st – star – star_t, target, intent(in)

• r_0(:) – the specified point – real(WP), intent(in)

• R_outer – outer radius for field-line calculation – real(WP), intent(in)

• ds – step size along the field line – real(WP), intent(in)

• tol – tolerance – real(WP), intent(in)

• max_steps – maximum steps along the field line – integer, intent(in), optional

Rtype fl

computed and returned field line – field_line_t, intent(out)

trace_star(pf, st, theta_0, phi_0, R_outer, ds, tol, max_steps, fl)

Construct a field line by tracing from a specified point on the star

does the calculation here; traces forwards only since starting from the star

computes vr, s, vB, n, i_0, foot_N, foot_S for field line class

subroutine

Parameters

• pf – potential field – pot_field_t, target, intent(in)

• st – star – star_t, target, intent(in)

• theta_0 – polar coordinate for field line tracing to start – real(WP), intent(in)

• phi_0 – aziumthal coordinate for field line tracing to start – real(WP), intent(in)

• R_outer – outer radius for field-line calculation – real(WP), intent(in)

• ds – step size along the field line – real(WP), intent(in)

• tol – tolerance – real(WP), intent(in)

• max_steps – maximum steps along the field line – integer, intent(in), optional

Rtype fl

computed and returned field line – field_line_t, intent(out)

trace_1(s, vr, bound, vr_0, del_s, tol, max_steps)

Trace from the specified point in one direction

called by both trace_point and trace_star

subroutine

Rtype s(:)

position along ray in ray coordinate system – real(WP), allocatable, intent(out)

Rtype vr(:,:)

3D position of loop; index 1 is dimension, index 2 is loop point – real(WP), allocatable, intent(out)

Rtype bound

notes whether inside the star, outside the calculation domain, or in a region to continue computing the loop – integer, intent(out)

Parameters

• vr_0(:) – initial point – real(WP), intent(in)

• del_s(:) – change in physical distance along the loop – real(WP), intent(in)

• tol – tolerance – real(WP), intent(in)

• max_steps – maximum steps along loop – integer, intent(in), optional

trace_1_inside()

Trace inside the source surface using ODEPACK

part of trace_1 subroutine

subroutine

trace_1_outside()

Trace outside the source surface using radial extrapolation

part of trace_1 subroutine

subroutine

trace_1_dipole()

Trace a dipole field

part of trace_1 subroutine

subroutine

odepack_rhs(neq, s, vr, vdr_ds)

Calculate the rhs vector for ODEPACK

subroutine

Parameters

• neq – number of first-order ODEs; hardwired to 3 – integer, intent(in)

• s – initial value of the independent variable – real(WP), intent(in)

• vr(neq) – array of initial values – real(WP), intent(in)

Rtype vdr_ds(neq)

v*dr/ds; computed from vB of potential field – real(WP), intent(out)

odepack_dummy()

Dummy subroutine

subroutine

odepack_discrim(neq, s, vr, ng, g_out)

Calculate the root discriminant for ODEPACK

subroutine

Parameters

• neq – number of first-order ODEs; hardwired to 3 – integer, intent(in)

• s – initial value of the independent variable – real(WP), intent(in)

• vr(neq) – array of initial values – real(WP), intent(in)

• ng – number of constraint functions; hardwired to 2 – integer, intent(in)

Rtype g_out(ng)

output of root information – real(WP), intent(out)

nudge(vr, discrim, outside)

Nudge r in the radial direction, so it lies inside or outside the surface represented by the discriminant function discrim

subroutine

Parameters

• vr(:) – point from where the nudge occurs – real(WP), intent(inout)

• discrim – evaluate the discriminant – function discrim (vr) result (D)

• vr(:) – point for evaluating the discriminant; within funciton discrim – real(WP), intent(in)

• D – discriminant; within function discrim – real(WP)

• outside – outside the surface (true) or not (false) – logical, intent(in)

expand_1(a, n)

Expand 1D array until it has a size of at least n

subroutine

Parameters

• a(:) – the array to expand – real(WP), allocatable, intent(inout)

• n – the minimum size of the expanded array – integer, intent(in)

expand_2(a, n)

Expand 2D array in its last dimension until it has a size of at least n

subroutine

Parameters

• a(:,:) – the array to expand – real(WP), allocatable, intent(inout)

• n – the minimum size of the second dimension of the expanded array – integer, intent(in)

Module mag_field_line

Module : mag_field_line

Purpose : single field line

class field_line_t

A field line object

type

Parameters

• vr(:,:) – xyz position along the field line; index 1: x, y, or z dimension, so values are 1:3, index 2: s dimension, so values are 1:n – real(WP), allocatable

• s(:) – the length along the field line – real(WP), allocatable

• vB(:,:) – magnetic field along the field line; index 1: x, y, or z dimension, so values are 1:3, index 2: s dimension, so values are 1:n – real(WP), allocatable

• n – number of grids along field line – integer

• i_0 – zero-point index where forwards and backwards tracing along a field meet – integer

• foot_N – boolean for the north magnetic foot point being on the star – integer

• foot_S – boolean for the south magnetic foot point being on the star – integer

field_line_t_(n) result (fl)

Construct a field line

space for type variables vr, s, vB is allocated; type variable n is set

type variables foot_N and foot_S are initialized to .FALSE.

function

Parameters

n – number of points on the field line – integer, intent(in)

Rtype fl

returned field line with vr, s, vB, and n initialized – field_line_t

field_line_t_trace_point_(pf, st, vr_0, R_outer, ds, tol, max_steps, move_s0_foot) result (fl)

Construct a field line by tracing from an arbitrary specified point

calls trace_point

function

Parameters

• pf – potential field – pot_field_t, target, intent(in)

• st – star – star_t, target, intent(in)

• vr_0(:) – the specified point – real(WP), intent(in)

• R_outer – outer radius for field-line calculation – real(WP), intent(in)

• ds – step size along the field line – real(WP), intent(in)

• tol – tolerance – real(WP), intent(in)

• max_steps – maximum steps along the field line – integer, optional, intent(in)

• move_s0_foot – enforce s=0 at northern end – logical, optional, intent(in)

Rtype fl

computed and returned field line – field_line_t

field_line_t_trace_star_(pf, st, theta_0, phi_0, R_outer, ds, tol, max_steps) result (fl)

Construct a field line by tracing from a specified point on the star

function

Parameters

• pf – potential field – pot_field_t, target, intent(in)

• st – star – star_t, target, intent(in)

• theta_0 – polar coordinate for field line tracing to start – real(WP), intent(in)

• phi_0 – azimuthal coordinate for field line tracing to start – real(WP), intent(in)

• R_outer – outer radius for field-line calculation – real(WP), intent(in)

• ds – step size along the field line – real(WP), intent(in)

• tol – tolerance – real(WP), intent(in)

• max_steps – maximum steps along the field line – integer, intent(in), optional

Rtype fl

computed and returned field line – field_line_t

discrim_star_(vr) result (D)

Calculate the discriminant for r being outside the star

D = st_m%D_surf(vr)

function

Parameters

vr(:) – position of discriminant calcualtion – real(WP), intent(in)

Rtype D

calculated and returned discrimant – real(WP)

discrim_source_(vr) result (D)

Calculate the discriminant for r being outside the source surface

D = NORM2(vr) - R_source_m

function

Parameters

vr(:) – position of discriminant calculation – real(WP), intent(in)

Rtype D

calculated and returned discrimant – real(WP)

discrim_outer_(vr) result (D)

Calculate the discriminant for r being outside the outer boundary

D = NORM2(vr) - R_outer_m

function

Parameters

vr(:) – position of discriminant calculation – real(WP), intent(in)

Rtype D

calculated and returned discriminant – real(WP)

read_(hg, fl)

Read various attributes of a field line

reads n, i_0, foot_N, foot_S, vr, s, vB

only if hdf5

subroutine

Parameters

• hg – hdf5 data set – hgroup_t, intent(inout)

• fl – field line – field_line_t

write_(hg, fl)

Write various assets of a field line

writes n, i_0, foot_N, foot_S, vr, s, vB

only if hdf5

subroutine

Parameters

• hg – hdf5 data set – hgroup_t, intent(inout)

• fl – field line – field_line_t, intent(in)

bcast_(fl, root_rank)

Broadcast a field line

vr, s, vB, n, i_0, foot_N, foot_S are broadcasted

only if MPI

subroutine

Parameters

• fl – field line to broadcast – field_line_t, intent(inout)

• root_rank – rank of root processor – integer, intent(in)

trace_point_(pf, st, vr_0, R_outer, ds, tol, fl, max_steps, move_s0_foot)

Construct a field line by tracing from a specified point

does the calculation here; traces forwards and backwards, then puts the results together

computes vr, s, vB, n, i_0, foot_N, foot_S for field line class

subroutine

Parameters

• pf – potential field – pot_field_t, target, intent(in)

• st – star – star_t, target, intent(in)

• vr_0(:) – the specified point – real(WP), intent(in)

• R_outer – outer radius for field-line calculation – real(WP), intent(in)

• ds – step size along the field line – real(WP), intent(in)

• tol – tolerance – real(WP), intent(in)

• max_steps – maximum steps along the field line – integer, optional, intent(in)

• move_s0_foot – enforce s=0 at northern end – logical, optional, intent(in)

Rtype fl

computed and returned field line – field_line_t, intent(out)

trace_star_(pf, st, theta_0, phi_0, R_outer, ds, tol, max_steps, fl)

Construct a field line by tracing from a specified point on the star

does the calculation here; traces forwards only since starting from the star

computes vr, s, vB, n, i_0, foot_N, foot_S for field line class

subroutine

Parameters

• pf – potential field – pot_field_t, target, intent(in)

• st – star – star_t, target, intent(in)

• theta_0 – polar coordinate for field line tracing to start – real(WP), intent(in)

• phi_0 – azimuthal coordinate for field line tracing to start – real(WP), intent(in)

• R_outer – outer radius for field-line calculation – real(WP), intent(in)

• ds – step size along the field line – real(WP), intent(in)

• tol – tolerance – real(WP), intent(in)

• max_steps – maximum steps along the field line – integer, optional, intent(in)

Rtype fl

computed and returned field line – field_line_t, intent(out)

trace_1_(s, vr, bound, vr_0, del_s, tol, max_steps)

Trace from the specified point in one direction

called by both trace_point and trace_star

subroutine

Rtype s(:)

position along ray in ray coordinate system – real(WP), allocatable, intent(out)

Rtype vr(:,:)

3D position of loop; index 1 is dimension, index 2 is loop point – real(WP), allocatable, intent(out)

Rtype bound

notes whether inside the star, outside the calculation domain, or in a region to continue computing the loop – integer, intent(out)

Parameters

• vr_0(:) – initial point – real(WP), intent(in)

• del_s(:) – change in physical distance along the loop – real(WP), intent(in)

• tol – tolerance – real(WP), intent(in)

• max_steps – maximum steps along loop – integer, optional, intent(in)

trace_1_inside_()

Trace inside the source surface using ODEPACK

part of trace_1 subroutine

subroutine

trace_1_outside_()

Trace outside the source surface using radial extrapolation

part of trace_1 subroutine

subroutine

trace_1_dipole_()

Trace a dipole field

part of trace_1 subroutine

subroutine

odepack_rhs_(neq, s, vr, vdr_ds)

Calculate the rhs vector for ODEPACK

subroutine

Parameters

• neq – number of first-order ODEs; hardwired to 3 – integer, intent(in)

• s – initial value of the independent variable – real(WP), intent(in)

• vr(neq) – array of initial values – real(WP), intent(in)

Rtype vdr_ds(neq)

v*dr/ds; computed from vB of potential field – real(WP), intent(out)

odepack_dummy_()

Dummy subroutine

subroutine

odepack_discrim_(neq, s, vr, ng, g_out)

Calculate the root discriminant for ODEPACK

subroutine

Parameters

• neq – number of first-order ODEs; hardwired to 3 – integer, intent(in)

• s – initial value of the independent variable – real(WP), intent(in)

• vr(neq) – array of initial values – real(WP), intent(in)

• ng – number of constraint functions; hardwired to 2 – integer, intent(in)

Rtype g_out(ng)

output of root information – real(WP), intent(out)

nudge_(vr, discrim, outside)

Nudge r in the radial direction, so it lies inside or outside the surface represented by the discriminant function discrim

subroutine

Parameters

• vr(:) – point from where the nudge occurs – real(WP), intent(inout)

• discrim – evaluate the discriminant – function discrim (vr) result (D)

• vr(:) – point for evaluating the discriminant; within funciton discrim – real(WP), intent(in)

• D – discriminant; within function discrim – real(WP)

• outside – outside the surface (true) or not (false) – logical, intent(in)

expand_1_(a, n)

Expand 1D array until it has a size of at least n

subroutine

Parameters

• a(:) – the array to expand – real(WP), allocatable, intent(inout)

• n – the minimum size of the expanded array – integer, intent(in)

expand_2_(a, n)

Expand 2D array in its last dimension until it has a size of at least n

subroutine

Parameters

• a(:,:) – the array to expand – real(WP), allocatable, intent(inout)

• n – the minimum size of the second dimension of the expanded array – integer, intent(in)

Module mag_field_line_bin

Module : mag_field_line_bin

Purpose : single field line

class field_line_t

A field line object

type

Parameters

• vr(:,:) – xyz position along the field line; index 1: x, y, or z dimension, so values are 1:3, index 2: s dimension, so values are 1:n – real(WP), allocatable

• s(:) – the length along the field line – real(WP), allocatable

• vB(:,:) – magnetic field along the field line; index 1: x, y, or z dimension, so values are 1:3, index 2: s dimension, so values are 1:n – real(WP), allocatable

• n – number of grids along field line – integer

• i_0 – zero-point index where forwards and backwards tracing along a field meet – integer

• foot_N – boolean for the north magnetic foot point being on the star – integer

• foot_S – boolean for the south magnetic foot point being on the star – integer

field_line_t_(n) result (fl)

Construct a field line

space for type variables vr, s, vB is allocated; type variable n is set

type variables foot_N and foot_S are initialized to .FALSE.

function

Parameters

n – number of points on the field line – integer, intent(in)

Rtype fl

returned field line with vr, s, vB, and n initialized – field_line_t

field_line_t_trace_point_(pf, st, vr_0, R_outer, ds, tol, max_steps, move_s0_foot) result (fl)

Construct a field line by tracing from an arbitrary specified point

calls trace_point

function

Parameters

• pf – potential field – pot_field_t, target, intent(in)

• st – star – star_t, target, intent(in)

• vr_0(:) – the specified point – real(WP), intent(in)

• R_outer – outer radius for field-line calculation – real(WP), intent(in)

• ds – step size along the field line – real(WP), intent(in)

• tol – tolerance – real(WP), intent(in)

• max_steps – maximum steps along the field line – integer, optional, intent(in)

• move_s0_foot – enforce s=0 at northern end – logical, optional, intent(in)

Rtype fl

computed and returned field line – field_line_t

field_line_t_trace_star_(pf, st, theta_0, phi_0, R_outer, ds, tol, max_steps) result (fl)

Construct a field line by tracing from a specified point on the star

function

Parameters

• pf – potential field – pot_field_t, target, intent(in)

• st – star – star_t, target, intent(in)

• theta_0 – polar coordinate for field line tracing to start – real(WP), intent(in)

• phi_0 – azimuthal coordinate for field line tracing to start – real(WP), intent(in)

• R_outer – outer radius for field-line calculation – real(WP), intent(in)

• ds – step size along the field line – real(WP), intent(in)

• tol – tolerance – real(WP), intent(in)

• max_steps – maximum steps along the field line – integer, intent(in), optional

Rtype fl

computed and returned field line – field_line_t

discrim_star_(vr) result (D)

Calculate the discriminant for r being outside the star

D = st_m%D_surf(vr)

function

Parameters

vr(:) – position of discriminant calcualtion – real(WP), intent(in)

Rtype D

calculated and returned discrimant – real(WP)

discrim_source_(vr) result (D)

Calculate the discriminant for r being outside the source surface

D = NORM2(vr) - R_source_m

function

Parameters

vr(:) – position of discriminant calculation – real(WP), intent(in)

Rtype D

calculated and returned discrimant – real(WP)

discrim_outer_(vr) result (D)

Calculate the discriminant for r being outside the outer boundary

D = NORM2(vr) - R_outer_m

function

Parameters

vr(:) – position of discriminant calculation – real(WP), intent(in)

Rtype D

calculated and returned discriminant – real(WP)

read_(hg, fl)

Read various attributes of a field line

reads n, i_0, foot_N, foot_S, vr, s, vB

only if hdf5

subroutine

Parameters

• hg – hdf5 data set – hgroup_t, intent(inout)

• fl – field line – field_line_t

write_(hg, fl)

Write various assets of a field line

writes n, i_0, foot_N, foot_S, vr, s, vB

only if hdf5

subroutine

Parameters

• hg – hdf5 data set – hgroup_t, intent(inout)

• fl – field line – field_line_t, intent(in)

bcast_(fl, root_rank)

Broadcast a field line

vr, s, vB, n, i_0, foot_N, foot_S are broadcasted

only if MPI

subroutine

Parameters

• fl – field line to broadcast – field_line_t, intent(inout)

• root_rank – rank of root processor – integer, intent(in)

trace_point_(pf, st, vr_0, R_outer, ds, tol, fl, max_steps, move_s0_foot)

Construct a field line by tracing from a specified point

does the calculation here; traces forwards and backwards, then puts the results together

computes vr, s, vB, n, i_0, foot_N, foot_S for field line class

subroutine

Parameters

• pf – potential field – pot_field_t, target, intent(in)

• st – star – star_t, target, intent(in)

• vr_0(:) – the specified point – real(WP), intent(in)

• R_outer – outer radius for field-line calculation – real(WP), intent(in)

• ds – step size along the field line – real(WP), intent(in)

• tol – tolerance – real(WP), intent(in)

• max_steps – maximum steps along the field line – integer, optional, intent(in)

• move_s0_foot – enforce s=0 at northern end – logical, optional, intent(in)

Rtype fl

computed and returned field line – field_line_t, intent(out)

trace_star_(pf, st, theta_0, phi_0, R_outer, ds, tol, max_steps, fl)

Construct a field line by tracing from a specified point on the star

does the calculation here; traces forwards only since starting from the star

computes vr, s, vB, n, i_0, foot_N, foot_S for field line class

subroutine

Parameters

• pf – potential field – pot_field_t, target, intent(in)

• st – star – star_t, target, intent(in)

• theta_0 – polar coordinate for field line tracing to start – real(WP), intent(in)

• phi_0 – azimuthal coordinate for field line tracing to start – real(WP), intent(in)

• R_outer – outer radius for field-line calculation – real(WP), intent(in)

• ds – step size along the field line – real(WP), intent(in)

• tol – tolerance – real(WP), intent(in)

• max_steps – maximum steps along the field line – integer, optional, intent(in)

Rtype fl

computed and returned field line – field_line_t, intent(out)

trace_1_(s, vr, bound, vr_0, del_s, tol, max_steps)

Trace from the specified point in one direction

called by both trace_point and trace_star

subroutine

Rtype s(:)

position along ray in ray coordinate system – real(WP), allocatable, intent(out)

Rtype vr(:,:)

3D position of loop; index 1 is dimension, index 2 is loop point – real(WP), allocatable, intent(out)

Rtype bound

notes whether inside the star, outside the calculation domain, or in a region to continue computing the loop – integer, intent(out)

Parameters

• vr_0(:) – initial point – real(WP), intent(in)

• del_s(:) – change in physical distance along the loop – real(WP), intent(in)

• tol – tolerance – real(WP), intent(in)

• max_steps – maximum steps along loop – integer, optional, intent(in)

trace_1_inside_()

Trace inside the source surface using ODEPACK

part of trace_1 subroutine

subroutine

trace_1_outside_()

Trace outside the source surface using radial extrapolation

part of trace_1 subroutine

subroutine

trace_1_dipole_()

Trace a dipole field

part of trace_1 subroutine

subroutine

odepack_rhs_(neq, s, vr, vdr_ds)

Calculate the rhs vector for ODEPACK

subroutine

Parameters

• neq – number of first-order ODEs; hardwired to 3 – integer, intent(in)

• s – initial value of the independent variable – real(WP), intent(in)

• vr(neq) – array of initial values – real(WP), intent(in)

Rtype vdr_ds(neq)

v*dr/ds; computed from vB of potential field – real(WP), intent(out)

odepack_dummy_()

Dummy subroutine

subroutine

odepack_discrim_(neq, s, vr, ng, g_out)

Calculate the root discriminant for ODEPACK

subroutine

Parameters

• neq – number of first-order ODEs; hardwired to 3 – integer, intent(in)

• s – initial value of the independent variable – real(WP), intent(in)

• vr(neq) – array of initial values – real(WP), intent(in)

• ng – number of constraint functions; hardwired to 2 – integer, intent(in)

Rtype g_out(ng)

output of root information – real(WP), intent(out)

nudge_(vr, discrim, outside)

Nudge r in the radial direction, so it lies inside or outside the surface represented by the discriminant function discrim

subroutine

Parameters

• vr(:) – point from where the nudge occurs – real(WP), intent(inout)

• discrim – evaluate the discriminant – function discrim (vr) result (D)

• vr(:) – point for evaluating the discriminant; within funciton discrim – real(WP), intent(in)

• D – discriminant; within function discrim – real(WP)

• outside – outside the surface (true) or not (false) – logical, intent(in)

expand_1_(a, n)

Expand 1D array until it has a size of at least n

subroutine

Parameters

• a(:) – the array to expand – real(WP), allocatable, intent(inout)

• n – the minimum size of the expanded array – integer, intent(in)

expand_2_(a, n)

Expand 2D array in its last dimension until it has a size of at least n

subroutine

Parameters

• a(:,:) – the array to expand – real(WP), allocatable, intent(inout)

• n – the minimum size of the second dimension of the expanded array – integer, intent(in)

Module mag_field_vol

Module : mag_field_vol

Purpose : magnetosphere field data

class field_vol_t

A field volume object

type with contains that adds procedures

type, extends (volume_t)

Parameters

• pf – potential field – pot_field_t

• st – star – star_t

• field_mask(:,:,:) – mask for field nodes; true if field line goes through the particular – logical, allocatable

• star_mask(:,:,:) – mask for star nodes; true if particular node is in the star – logical allocatable

• build – loops over building, processing, and broadcasting nodes – procedure

• build_node – build a single node – procedure

• process_node – process a single node – procedure

• bcast-nodes – broadcast nodes if MPI – procedure

field_vol_t_(vl, pf, st) result (fv)

Construct the field_vol_t

sets volume, potential field, and star; allocates space for field_mask and star_mask

function

Parameters

• vl – volume — volume_t, intent(in)

• pf – potential field — pot_field_t, intent(in)

• st – star — star_t, intent(in)

Rtype fv

field volume — field_vol_t

read_(hg, fv)

Read the field_vol_t

read variables are volume, potential field, star, field_mask, and star_mask

only if HDF5

subroutine

Parameters

hg – hdf5 data set – hgroup_t, intent(inout)

Rtype fv

field volume – field_vol_t, intent(out)

write_(hg, fv)

Write the field_vol_t

written variables are volume, potential field, star, field_mask, and star_mask

only if HDF5

subroutine

Parameters

• hg – hdf5 data set – hgroup_t, intent(inout)

• fv – field volume – field_vol_t, intent(in)

build(this, R_outer, ds, tol, max_steps)

Process, build, and broadcast the nodes

subroutine

Parameters

• this – field volume – field_vol_t, intent(inout)

• R_outer – outer radius – real(WP), intent(in)

• ds – step size along field line – real(WP), intent(in)

• tol – tolerance – real(WP), intent(in)

• max_steps – maximum steps along field line – integer, optional, intent(in)

build_node(this, vi, R_outer, ds, tol, max_steps)

Build the node

subroutine

Parameters

• this – field volume – field_vol_t, intent(inout)

• vi(:) – node index – integer, intent(in)

• R_outer – outer radius – real(WP), intent(in)

• ds – step size along field line – real(WP), intent(in)

• tol – tolerance – real(WP), intent(in)

• max_steps – maximum steps along field line – integer, optional, intent(in)

process_node(this, vi, fl)

Process the node

checks that node index vi has size of 3

subroutine

Parameters

• this – field volume – field_vol_t, intent(inout)

• vi(:) – node index – integer, intent(in)

• fl – field volume – field_line_t, intent(in)

bcast_(fv, root_rank)

Broadcast the field_vol_t

only if MPI

subroutine

Parameters

• fv – field volume – :class:`field_vol_t), intent(inout)

• root_rank – rank of root processor – integer, intent(in)

bcast_nodes(this, vi_a, vi_b, root_rank)

Broadcast the nodes with indices between vi_a and vi_b

only if MPI

subroutine

Parameters

• this – field volume – field_vol_t, intent(inout)

• vi_a(:) – lower limit of node indices – integer, intent(in)

• vi_b(:) – upper limit of node indices – integer, intent(in)

• root_rank – rank of root processor – integer, intent(in)

Module mag_field_vol_bin

Module : mag_field_vol_bin

Purpose : magnetosphere field data

class field_vol_t

A field volume object

type with contains that adds procedures

type, extends (volume_t)

Parameters

• pf – potential field – pot_field_t

• st – star – star_t

• field_mask(:,:,:) – mask for field nodes; true if field line goes through the particular – logical, allocatable

• star_mask(:,:,:) – mask for star nodes; true if particular node is in the star – logical allocatable

• build – loops over building, processing, and broadcasting nodes – procedure

• build_node – build a single node – procedure

• process_node – process a single node – procedure

• bcast-nodes – broadcast nodes if MPI – procedure

field_vol_t_(vl, pf, st) result (fv)

Construct the field_vol_t

sets volume, potential field, and star; allocates space for field_mask and star_mask

function

Parameters

• vl – volume — volume_t, intent(in)

• pf – potential field — pot_field_t, intent(in)

• st – star — star_t, intent(in)

Rtype fv

field volume — field_vol_t

read_(hg, fv)

Read the field_vol_t

read variables are volume, potential field, star, field_mask, and star_mask

only if HDF5

subroutine

Parameters

hg – hdf5 data set – hgroup_t, intent(inout)

Rtype fv

field volume – field_vol_t, intent(out)

write_(hg, fv)

Write the field_vol_t

written variables are volume, potential field, star, field_mask, and star_mask

only if HDF5

subroutine

Parameters

• hg – hdf5 data set – hgroup_t, intent(inout)

• fv – field volume – field_vol_t, intent(in)

build(this, R_outer, ds, tol, max_steps)

Process, build, and broadcast the nodes

subroutine

Parameters

• this – field volume – field_vol_t, intent(inout)

• R_outer – outer radius – real(WP), intent(in)

• ds – step size along field line – real(WP), intent(in)

• tol – tolerance – real(WP), intent(in)

• max_steps – maximum steps along field line – integer, optional, intent(in)

build_node(this, vi, R_outer, ds, tol, max_steps)

Build the node

subroutine

Parameters

• this – field volume – field_vol_t, intent(inout)

• vi(:) – node index – integer, intent(in)

• R_outer – outer radius – real(WP), intent(in)

• ds – step size along field line – real(WP), intent(in)

• tol – tolerance – real(WP), intent(in)

• max_steps – maximum steps along field line – integer, optional, intent(in)

process_node(this, vi, fl)

Process the node

checks that node index vi has size of 3

subroutine

Parameters

• this – field volume – field_vol_t, intent(inout)

• vi(:) – node index – integer, intent(in)

• fl – field volume – field_line_t, intent(in)

bcast_(fv, root_rank)

Broadcast the field_vol_t

only if MPI

subroutine

Parameters

• fv – field volume – field_vol_t, intent(inout)

• root_rank – rank of root processor – integer, intent(in)

bcast_nodes(this, vi_a, vi_b, root_rank)

Broadcast the nodes with indices between vi_a and vi_b

only if MPI

subroutine

Parameters

• this – field volume – field_vol_t, intent(inout)

• vi_a(:) – lower limit of node indices – integer, intent(in)

• vi_b(:) – upper limit of node indices – integer, intent(in)

• root_rank – rank of root processor – integer, intent(in)

Module mag_harmonic

Module : mag_harmonic

Purpose : spherical harmonics

factorial(a) result (af)

Calculate the factorial a!

function

Parameters

a – input variable – integer, intent(in)

Rtype af

factorial of input variable – real(WP)

Y_lm_tableaux(theta, phi, Y_lm, grad_Y_lm_theta, grad_Y_lm_phi)

Create a tableaux of spherical harmonics Y_lm(theta, phi) for m >= 0

subroutine

Parameters

• theta – polar coordinate – real(WP), intent(in)

• phi – azimuthal coordinate – real(WP), intent(in)

Rtype Y_lm(0:,0:)

spherical harmonic table – complex(WP), intent(out)

Rtype grad_Y_lm_theta(0:,0:)

gradients in the theta direction – complex(WP), intent(out), optional

Rtype grad_Y_lm_phi(0:,0:)

gradients in the phi direction – complex(WP), intent(out), optional

Module mag_pot_field

Module : mag_pot_field

Purpose : force-free potential fields

class pot_field_t

pot_field_t_(l_max) result (pf)

Construct the pot_field_t

allocates G_lm, a_lm, and b_lm in pf class

function

Parameters

l_max – truncate G_lm to level l_max; array size is {0:l_max,-l_max:l_max} – integer, intent(in)

Rtype pf

potential field – pot_field_t

pot_field_t_coeffs_(G_lm, va) result (pf)

Construct the pot_field from the expansion coefficients

function

Parameters

• G_lm(:,:) – spherical harmonic coefficients to set – complex(WP), intent(in)

• va(:) – center of magnetic-centered frame – real(WP), intent(in)

Rtype pf

potential field – pot_field_t

is_dipole_(this) result (is_dipole)

Determine whether the potential represents a pure dipole

function

Parameters

• this – potential field – pot_field_t, intent(in)

• is_dipole – is the field a dipole or not – logical

vB_(this, vr, outside_source) result (vB)

Evaluate the magnetic field at vr

Calculate the spherical-polar coordinates in the magnetic-centered frame

function

Parameters

• this – potential field – pot_field_t, intent(in)

• vr(:) – location of magnetice-field evaluation – real(WP), intent(in)

• outside_source – outside the source or not – logical, intent(in), optional

Rtype vB(3)

magnetic field – real(WP)

read_(hg, pf)

Read the pot_field_t

read variables are l_max, R_source, va, G_lm

subroutine

Parameters

hg – hdf5 data set – hgroup_t, intent(inout)

Rtype pf

potential field – pot_field_t, intent(out)

write_(hg, pf)

Write the pot_field_t

written variables are l_max, R_source, va, G_lm

subroutine

Parameters

• hg – hdf5 data set – hgroup_t, intent(inout)

• pf – potential field – pot_field_t, intent(in)

get_R_source_(this, R_source)

Get the source-surface radius

subroutine

Parameters

this – potential field – pot_field_t, intent(in)

Rtype R_source

source radius – real(WP), intent(out)

set_R_source_(this, R_source)

Set the source-surface radius to R_source

subroutine

Parameters

• this – potential field – pot_field_t, intent(inout)

• R_source – source radius – real(WP), intent(in)

dipole_params_(this, B_pole, beta, gamma, va)

Calculate the parameters of the dipole component of the field

subroutine

Parameters

this – potential field – pot_field_t, intent(in)

Rtype B_pole

magnetic field at the pole – real(WP), optional, intent(out)

Rtype beta

angle between rotation axis and magnetic axis; rotation axis is z axis – real(WP), optional, intent(out)

Rtype gamma

azimuthal angle of magnetic axis; measured from x-axis to y-axis – real(WP), optional, intent(out)

Rtype va(:)

magnetic center of star – real(WP), optional, intent(out)

bcast_(pf, root_rank)

Broadcast the pot_field_t

only if MPI

subroutine

Parameters

• pf – potential field to broadcast – pot_field_t, intent(inout)

• root_rank – rank of root processor – integer, intent(in)

Module build_field_line

Module build_field_lines

Program : build_field_lines

Purpose : build field_lines

random()

Calculates a random number from [0,1) via the built-in fortran function RANDOM_NUMBER

Rtype real(WP) random

computed and returned random number

Module build_field_map

Program : build_field_map

Purpose : build & analyze a surface map of the field

Module build_pot_field

Program : build_pot_field

Purpose : build force-free potential fields

pf_oblique_dipole(beta, gamma, va, B_d_pole) result (pf)

pf_oblique_diquad(beta, gamma, va, B_d_pole, B_q_pole) result (pf)

pf_invers10(map_file, l_max, flip_lat, flip_lon) result (pf)

pf_donati(map_file, l_max, flip_lat, flip_lon) result (pf)

pf_invers10_read(map_file, n_lat, n_lon, lat, lon, B_r)

pf_donati_read(map_file, n_lat, n_lon, lat, lon, B_r)

pf_lat_lon_expand(pf, l_max, n_lat, n_lon, lat, lon, B_r)

Module calc_b_z

Program : calc_b_z

Purpose : calculate longitudinal field strength

init_pot_field(unit, pf)

init_star(unit, st, inc, u_limb, grav_dark)

init_geom(unit, x, y, phase)

init_output(unit, map_prefix, int_filename)

Module dipole_params

Program : dipole_params

Purpose : extract dipole parameters from a potential field

Module measure_loops

Program : measure_loops

Purpose : measure properties of closed field loops

random()

Module test_mag_harmonic

Module : test_mag_harmonic

Purpose : test mag_harmonic module