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B_GS.c File Reference

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"

Go to the source code of this file.

Functions

int B_GS_init (B_GS_data *data, real R0, real z0, real raxis, real zaxis, real B_phi0, real psi0, real psi1, real psi_mult, real c[14], int Nripple, real a0, real alpha0, real delta0)
 Initialize magnetic field data.
 
void B_GS_free (B_GS_data *data)
 Free allocated resources.
 
void B_GS_offload (B_GS_data *data)
 Offload data to the accelerator.
 
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()

int B_GS_init ( B_GS_data * data,
real R0,
real z0,
real raxis,
real zaxis,
real B_phi0,
real psi0,
real psi1,
real psi_mult,
real c[14],
int Nripple,
real a0,
real alpha0,
real delta0 )

Initialize magnetic field data.

Parameters
datapointer to the data struct
R0major radius R coordinate [m]
z0midplane z coordinate [m]
raxismagnetic axis R coordinate [m]
zaxismagnetic axis z coordinate [m]
B_phi0on-axis toroidal field [T]
psi0poloidal flux at axis [Vs/m]
psi1poloidal flux at separatrix [Vs/m]
psi_multpsi multiplier
psi_coeffcoefficients for evaluating psi
Nripplenumber of toroidal field coils
a0minor radius
alpha0ripple r-dependency delta ~ (r/a0)^alpha0
delta0ripple strength
Returns
zero to indicate success

Definition at line 96 of file B_GS.c.

◆ B_GS_free()

void B_GS_free ( B_GS_data * data)

Free allocated resources.

Parameters
datapointer to the data struct

Definition at line 150 of file B_GS.c.

◆ B_GS_offload()

void B_GS_offload ( B_GS_data * data)

Offload data to the accelerator.

Parameters
datapointer to the data struct

Definition at line 159 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
psipointer where psi [V*s*m^-1] value will be stored
rR coordinate [m]
phiphi coordinate [rad]
zz coordinate [m]
Bdatapointer 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_dpsipointer for storing psi [V*s*m^-1] and its derivatives
rR coordinate [m]
phiphi coordinate [rad]
zz coordinate [m]
Bdatapointer 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_drhopointer where rho and its derivatives will be stored
rR coordinate [m]
phiphi coordinate [rad]
zz coordinate [m]
Bdatapointer 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
Bpointer to array where magnetic field values are stored
rR coordinate [m]
phiphi coordinate [deg]
zz coordinate [m]
Bdatapointer 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_dBpointer to array where the field and its derivatives are stored
rR coordinate [m]
phiphi coordinate [deg]
zz coordinate [m]
Bdatapointer 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
rzpointer where axis R and z [m] values will be stored
Bdatapointer to magnetic field data struct
Returns
Zero a5err value as this function can't fail.

Definition at line 557 of file B_GS.c.

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