Analytic magnetic field. More...

#include <stdlib.h>
#include <stdio.h>
#include <math.h>
#include "../ascot5.h"
#include "../consts.h"
#include "../print.h"
#include "../error.h"
#include "B_GS.h"

Functions
int	B_GS_init_offload (B_GS_offload_data offload_data, real *offload_array)
	Initialize magnetic field offload data.

void	B_GS_free_offload (B_GS_offload_data offload_data, real *offload_array)
	Free offload array.

void	B_GS_init (B_GS_data Bdata, B_GS_offload_data offload_data, real *offload_array)
	Initialize magnetic field data struct on target.

a5err	B_GS_eval_psi (real psi, real r, real phi, real z, B_GS_data Bdata)
	Evaluate poloidal flux psi.

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

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

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

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

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

Detailed Description

Analytic magnetic field.

This module implements a toroidal magnetic field based on an analytical solution to the Grad-Shafranov equation [1].

In this model, the poloidal flux psi is calculated as

$\begin{align*} \psi(R,Z) = &\psi_c [(1-A) (r^4/8) \\ &+ A (r^2\log(r)/2) \\ &+ c_0 \\ &+ c_1 (r^2) \\ &+ c_2 (r^2\log(r) - z^2) \\ &+ c_3 (r^4 - 4r^2z^2) \\ &+ c_4 (3r^4\log(r) - 9r^2z^2 - 12r^2\log(r)z^2 + 2z^4) \\ &+ c_5 (r^6 - 12r^4z^2 + 8r^2z^4) \\ &+ c_6 (8z^6 - 140r^2z^4 - 120r^2\log(r)z^4 + 180r^4\log(r)z^2 + 75r^4z^2 - 15r^6\log(r)) \\ &+ c_7 (z) \\ &+ c_8 (zr^2) \\ &+ c_9 (z^3 - 3zr^2\log(r)) \\ &+ c_{10} (3zr^4 - 4z^3r^2) \\ &+ c_{12} (8z^5 - 45zr^4 - 80z^3r^2\log(r) + 60zr^4\log(r)) ] \end{align*}$

where $c_i$ and $A$ are pre-calculated coefficients which can be chosen so that realistic equilibria resembling different machines are produced. The equilibrium can be non-symmetric with respect to magnetic plane, and can have zero, one, or two X-points. $\psi_c$ is a scaling constant, and $r = R/R_0$ $z = Z/R_0$ . From $\psi$ the poloidal magnetic field components can be evaluated from Grad-Shafranov relations

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

and toroidal field is evaluated as

$\begin{equation*} B_\phi = \frac{B_0R_0}{R} \end{equation*}$

This module also includes the possibility to have an analytical model for toroidal field ripple, which is used if ripple period $N>0$ . The rippled toroidal field is

$\begin{equation*} \tilde{B}_\phi = B_\phi( 1 + \delta\cos(N\phi) ) \end{equation*}$

where

$\begin{equation*} \delta = \delta_0 \frac{r'}{a_0}^{\alpha_0} e^{-\theta^2} \end{equation*}$

and $\theta = \arctan(Z - z_0, R- R_0)$ and $r' = \sqrt{(R-R_0)^2 + (Z-Z_0)^2}$ .

[1] A.J. Cerfon, J.P. Freidberg. "One size fits all" analytic solutions to the Grad-Shafranov equation. Physics of Plasmas 17 (3) (2010) 032502. http://scitation.aip.org/content/aip/journal/pop/17/3/10.1063/1.3328818

Definition in file B_GS.c.

Function Documentation

◆ B_GS_init_offload()

int B_GS_init_offload	(	B_GS_offload_data *	offload_data,
		real **	offload_array )

Initialize magnetic field offload data.

The offload data struct is very simple and contains only the necessary fields which are all initialized when the data is read (except B_GS.offload_array_length). The offload array is not required at all. Therefore, this function only sets the offload_array_length to zero, assigns a NULL pointer to offload_array, and prints sanity checks so that user may verify that data was initialized succesfully.

Parameters

offload_data	pointer to offload data struct
offload_array	pointer to offload array

Returns: zero to indicate success

Definition at line 91 of file B_GS.c.

◆ B_GS_free_offload()

void B_GS_free_offload	(	B_GS_offload_data *	offload_data,
		real **	offload_array )

Free offload array.

Parameters

offload_data	pointer to offload data struct
offload_array	pointer to pointer to offload array

Definition at line 131 of file B_GS.c.

◆ B_GS_init()

void B_GS_init	(	B_GS_data *	Bdata,
		B_GS_offload_data *	offload_data,
		real *	offload_array )

Initialize magnetic field data struct on target.

Parameters

Bdata	pointer to data struct on target
offload_data	pointer to offload data struct
offload_array	offload array

Definition at line 144 of file B_GS.c.

◆ B_GS_eval_psi()

a5err B_GS_eval_psi	(	real *	psi,
		real	r,
		real	phi,
		real	z,
		B_GS_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: zero to indicate success

Definition at line 174 of file B_GS.c.

◆ B_GS_eval_psi_dpsi()

a5err B_GS_eval_psi_dpsi	(	real	psi_dpsi[4],
		real	r,
		real	phi,
		real	z,
		B_GS_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: zero to indicate success

Definition at line 227 of file B_GS.c.

◆ B_GS_eval_rho_drho()

a5err B_GS_eval_rho_drho	(	real	rho_drho[4],
		real	r,
		real	phi,
		real	z,
		B_GS_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: zero to indicate success

Definition at line 296 of file B_GS.c.

◆ B_GS_eval_B()

a5err B_GS_eval_B	(	real	B[3],
		real	r,
		real	phi,
		real	z,
		B_GS_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: zero to indicate success

Definition at line 327 of file B_GS.c.

◆ B_GS_eval_B_dB()

a5err B_GS_eval_B_dB	(	real	B_dB[12],
		real	r,
		real	phi,
		real	z,
		B_GS_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: zero to indicate success

Definition at line 406 of file B_GS.c.

◆ B_GS_get_axis_rz()

a5err B_GS_get_axis_rz	(	real	rz[2],
		B_GS_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 557 of file B_GS.c.

Functions

Detailed Description

Function Documentation

◆ B_GS_init_offload()

◆ B_GS_free_offload()

◆ B_GS_init()

◆ B_GS_eval_psi()

◆ B_GS_eval_psi_dpsi()

◆ B_GS_eval_rho_drho()

◆ B_GS_eval_B()

◆ B_GS_eval_B_dB()

◆ B_GS_get_axis_rz()