3D magnetic field with tricubic spline interpolation More...

#include <stdlib.h>
#include <stdio.h>
#include <math.h>
#include "../ascot5.h"
#include "../error.h"
#include "../print.h"
#include "B_3DS.h"
#include "../spline/interp.h"

Functions
int	B_3DS_init (B_3DS_data data, int p_n_r, real p_r_min, real p_r_max, int p_n_z, real p_z_min, real p_z_max, int b_n_r, real b_r_min, real b_r_max, int b_n_phi, real b_phi_min, real b_phi_max, int b_n_z, real b_z_min, real b_z_max, real axis_r, real axis_z, real psi0, real psi1, real psi, real B_r, real B_phi, real *B_z)
	Initialize magnetic field data.

void	B_3DS_free (B_3DS_data *data)
	Free allocated resources.

void	B_3DS_offload (B_3DS_data *data)
	Offload data to the accelerator.

a5err	B_3DS_eval_psi (real psi, real r, real phi, real z, B_3DS_data Bdata)
	Evaluate poloidal flux psi.

a5err	B_3DS_eval_psi_dpsi (real psi_dpsi[4], real r, real phi, real z, B_3DS_data *Bdata)
	Evaluate poloidal flux psi and its derivatives.

a5err	B_3DS_eval_rho_drho (real rho_drho[4], real r, real phi, real z, B_3DS_data *Bdata)
	Evaluate normalized poloidal flux rho and its derivatives.

a5err	B_3DS_eval_B (real B[3], real r, real phi, real z, B_3DS_data *Bdata)
	Evaluate magnetic field.

a5err	B_3DS_eval_B_dB (real B_dB[12], real r, real phi, real z, B_3DS_data *Bdata)
	Evaluate magnetic field and its derivatives.

a5err	B_3DS_get_axis_rz (real rz[2], B_3DS_data *Bdata)
	Return magnetic axis R-coordinate.

Variables
int	psigrid_n_r

int	psigrid_n_z

real	psigrid_r_min

real	psigrid_r_max

real	psigrid_z_min

real	psigrid_z_max

int	Bgrid_n_r

int	Bgrid_n_z

real	Bgrid_r_min

real	Bgrid_r_max

real	Bgrid_z_min

real	Bgrid_z_max

int	Bgrid_n_phi

real	Bgrid_phi_min

real	Bgrid_phi_max

real	psi0

real	psi1

real	axis_r

real	axis_z

Detailed Description

3D magnetic field with tricubic spline interpolation

This module represents a magnetic field where data is given in $R\phi z$ - grid from which it is interpolated with tricubic splines.

The magnetic field is evaluated from magnetic field strength $\mathbf{B}$ which may not be divergence free. However, $B_R$ and $B_z$ components are also evaluated from poloidal magnetic flux $\psi(R,z)$ as

$\begin{align*} B_R &= -\frac{1}{R}\frac{\partial\psi}{\partial z}\\ B_z &= \frac{1}{R}\frac{\partial\psi}{\partial R} \end{align*}$

The total field is then a sum of components interpolated directly from $\mathbf{B}$ and components calculated via interpolated $\psi$ . Note that $\psi$ is assumed to be axisymmetric and is interpolated with bicubic splines. $\psi$ and $\mathbf{B}$ are given in separate grids.

This module does no extrapolation so if queried value is outside the $Rz$ -grid an error is thrown.

The toroidal angle phi is treated as a periodic coordinate meaning that B(phi) = B(phi + N*(b_phimax - b_phimin)) being N the periodic number. Do note that to avoid duplicate data, the last points in phi axis in B data are not at b_phimax, i.e. br[:,-1,:] != BR(phi=b_phimax). It is user's responsibility to provide input whose $\phi$ -grid makes sense (in that it actually represents a periodic field).

Definition in file B_3DS.c.

Function Documentation

◆ B_3DS_init()

int B_3DS_init	(	B_3DS_data *	data,
		int	p_n_r,
		real	p_r_min,
		real	p_r_max,
		int	p_n_z,
		real	p_z_min,
		real	p_z_max,
		int	b_n_r,
		real	b_r_min,
		real	b_r_max,
		int	b_n_phi,
		real	b_phi_min,
		real	b_phi_max,
		int	b_n_z,
		real	b_z_min,
		real	b_z_max,
		real	axis_r,
		real	axis_z,
		real	psi0,
		real	psi1,
		real *	psi,
		real *	B_r,
		real *	B_phi,
		real *	B_z )

Initialize magnetic field data.

The offload array must contain the following data:

offload_array[ j*Bn_r*Bn_phi + z*Bn_r + i] = B_R(R_i, phi_z, z_j) [T]
offload_array[ Bn_r*Bn_z*Bn_phi + j*Bn_r*Bn_phi + z*Bn_r + i] = B_phi(R_i, phi_z, z_j) [T]
offload_array[2*Bn_r*Bn_z*Bn_phi + j*Bn_r*Bn_phi + z*Bn_r + i] = B_z(R_i, phi_z, z_j) [T]
offload_array[3*Bn_r*Bn_z*Bn_phi + j*n_r + i] = psi(R_i, z_j) [V*s*m^-1]

Parameters

data	pointer to the data struct
p_n_r	number of r grid points in psi data
p_r_min	minimum R coordinate in psi data grid [m]
p_r_max	maximum R coordinate in psi data grid [m]
p_n_z	number of z grid points in psi data
p_z_min	minimum z coordinate in psi data grid [m]
p_z_max	maximum z coordinate in psi data grid [m]
p_n_r	number of r grid points in B data
b_r_min	minimum R coordinate in B data grid [m]
b_r_max	maximum R coordinate in B data grid [m]
b_n_phi	number of phi grid points in B data
b_phi_min	minimum phi coordinate in B data grid [rad]
b_phi_max	maximum phi coordinate in B data grid [rad]
b_n_z	number of z grid points in B data
b_z_min	minimum z coordinate in B data grid [m]
b_z_max	maximum z coordinate in B data grid [m]
axis_r	R coordinate of magnetic axis [m]
axis_z	z coordinate of magnetic axis [m]
psi0	poloidal flux at magnetic axis [Vs/m]
psi1	poloidal flux at separatrix [Vs/m]
psi	poloidal flux psi(R_i,z_j) = arr[j*n_r + i] [Vs/m]
B_r	Magnetic field R component B_r(R_i,phi_j,z_k) = arr[kb_n_rb_n_phi + j*b_n_r + i] [T]
B_phi	Magnetic field phi component B_phi(R_i,phi_j,z_k) = arr[kb_n_rb_n_phi + j*b_n_r + i] [T]
B_z	Magnetic field z component B_z(R_i,phi_j,z_k) = arr[kb_n_rb_n_phi + j*b_n_r + i] [T]

Returns: zero if initialization succeeded

Definition at line 106 of file B_3DS.c.

◆ B_3DS_free()

void B_3DS_free ( B_3DS_data * data )

Free allocated resources.

Parameters

data	pointer to the data struct

Definition at line 191 of file B_3DS.c.

◆ B_3DS_offload()

void B_3DS_offload ( B_3DS_data * data )

Offload data to the accelerator.

Parameters

data	pointer to the data struct

Definition at line 203 of file B_3DS.c.

◆ B_3DS_eval_psi()

a5err B_3DS_eval_psi	(	real *	psi,
		real	r,
		real	phi,
		real	z,
		B_3DS_data *	Bdata )

Evaluate poloidal flux psi.

Parameters

psi	pointer where psi [Vsm^-1] value will be stored
r	R coordinate [m]
phi	phi coordinate [rad]
z	z coordinate [m]
Bdata	pointer to magnetic field data struct

Returns: Non-zero a5err value if evaluation failed, zero otherwise

Definition at line 224 of file B_3DS.c.

◆ B_3DS_eval_psi_dpsi()

a5err B_3DS_eval_psi_dpsi	(	real	psi_dpsi[4],
		real	r,
		real	phi,
		real	z,
		B_3DS_data *	Bdata )

Evaluate poloidal flux psi and its derivatives.

Parameters

psi_dpsi	pointer for storing psi [Vsm^-1] and its derivatives
r	R coordinate [m]
phi	phi coordinate [rad]
z	z coordinate [m]
Bdata	pointer to magnetic field data struct

Returns: Non-zero a5err value if evaluation failed, zero otherwise

Definition at line 248 of file B_3DS.c.

◆ B_3DS_eval_rho_drho()

a5err B_3DS_eval_rho_drho	(	real	rho_drho[4],
		real	r,
		real	phi,
		real	z,
		B_3DS_data *	Bdata )

Evaluate normalized poloidal flux rho and its derivatives.

Parameters

rho_drho	pointer where rho and its derivatives will be stored
r	R coordinate [m]
phi	phi coordinate [rad]
z	z coordinate [m]
Bdata	pointer to magnetic field data struct

Returns: Non-zero a5err value if evaluation failed, zero otherwise

Definition at line 279 of file B_3DS.c.

◆ B_3DS_eval_B()

a5err B_3DS_eval_B	(	real	B[3],
		real	r,
		real	phi,
		real	z,
		B_3DS_data *	Bdata )

Evaluate magnetic field.

Parameters

B	pointer to array where magnetic field values are stored
r	R coordinate [m]
phi	phi coordinate [deg]
z	z coordinate [m]
Bdata	pointer to magnetic field data struct

Returns: Non-zero a5err value if evaluation failed, zero otherwise

Definition at line 317 of file B_3DS.c.

◆ B_3DS_eval_B_dB()

a5err B_3DS_eval_B_dB	(	real	B_dB[12],
		real	r,
		real	phi,
		real	z,
		B_3DS_data *	Bdata )

Evaluate magnetic field and its derivatives.

Parameters

B_dB	pointer to array where the field and its derivatives are stored
r	R coordinate [m]
phi	phi coordinate [deg]
z	z coordinate [m]
Bdata	pointer to magnetic field data struct

Returns: Non-zero a5err value if evaluation failed, zero otherwise

Definition at line 364 of file B_3DS.c.

◆ B_3DS_get_axis_rz()

a5err B_3DS_get_axis_rz	(	real	rz[2],
		B_3DS_data *	Bdata )

Return magnetic axis R-coordinate.

Parameters

rz	pointer where axis R and z [m] values will be stored
Bdata	pointer to magnetic field data struct

Returns: Zero a5err value as this function can't fail.

Definition at line 428 of file B_3DS.c.

Variable Documentation

◆ psigrid_n_r

int psigrid_n_r

Number of R grid points in psi data

Definition at line 42 of file B_3DS.c.

◆ psigrid_n_z

int psigrid_n_z

Number of z grid points in psi data

Definition at line 43 of file B_3DS.c.

◆ psigrid_r_min

real psigrid_r_min

Minimum R grid point in psi data [m]

Definition at line 44 of file B_3DS.c.

◆ psigrid_r_max

real psigrid_r_max

Maximum R grid point in psi data [m]

Definition at line 45 of file B_3DS.c.

◆ psigrid_z_min

real psigrid_z_min

Minimum z grid point in psi data [m]

Definition at line 46 of file B_3DS.c.

◆ psigrid_z_max

real psigrid_z_max

Maximum z grid point in psi data [m]

Definition at line 47 of file B_3DS.c.

◆ Bgrid_n_r

int Bgrid_n_r

Number of R grid points in B data

Definition at line 49 of file B_3DS.c.

◆ Bgrid_n_z

int Bgrid_n_z

Number of z grid points in B data

Definition at line 50 of file B_3DS.c.

◆ Bgrid_r_min

real Bgrid_r_min

Minimum R coordinate in the grid in B data [m]

Definition at line 51 of file B_3DS.c.

◆ Bgrid_r_max

real Bgrid_r_max

Maximum R coordinate in the grid in B data [m]

Definition at line 52 of file B_3DS.c.

◆ Bgrid_z_min

real Bgrid_z_min

Minimum z coordinate in the grid in B data [m]

Definition at line 53 of file B_3DS.c.

◆ Bgrid_z_max

real Bgrid_z_max

Maximum z coordinate in the grid in B data [m]

Definition at line 54 of file B_3DS.c.

◆ Bgrid_n_phi

int Bgrid_n_phi

Number of phi grid points in B data

Definition at line 55 of file B_3DS.c.

◆ Bgrid_phi_min

real Bgrid_phi_min

Minimum phi grid point in B data [rad]

Definition at line 56 of file B_3DS.c.

◆ Bgrid_phi_max

real Bgrid_phi_max

Maximum phi grid point in B data [rad]

Definition at line 57 of file B_3DS.c.

◆ psi0

real psi0

Poloidal flux value at magnetic axis [V*s*m^-1]

Definition at line 59 of file B_3DS.c.

◆ psi1

real psi1

Poloidal flux value at separatrix [V*s*m^-1]

Definition at line 60 of file B_3DS.c.

◆ axis_r

real axis_r

R coordinate of magnetic axis [m]

Definition at line 61 of file B_3DS.c.

◆ axis_z

real axis_z

z coordinate of magnetic axis [m]

Definition at line 62 of file B_3DS.c.

Functions

Variables

Detailed Description

Function Documentation

◆ B_3DS_init()

◆ B_3DS_free()

◆ B_3DS_offload()

◆ B_3DS_eval_psi()

◆ B_3DS_eval_psi_dpsi()

◆ B_3DS_eval_rho_drho()

◆ B_3DS_eval_B()

◆ B_3DS_eval_B_dB()

◆ B_3DS_get_axis_rz()

Variable Documentation

◆ psigrid_n_r

◆ psigrid_n_z

◆ psigrid_r_min

◆ psigrid_r_max

◆ psigrid_z_min

◆ psigrid_z_max

◆ Bgrid_n_r

◆ Bgrid_n_z

◆ Bgrid_r_min

◆ Bgrid_r_max

◆ Bgrid_z_min

◆ Bgrid_z_max

◆ Bgrid_n_phi

◆ Bgrid_phi_min

◆ Bgrid_phi_max

◆ psi0

◆ psi1

◆ axis_r

◆ axis_z