dg::Vortex Struct Reference

\(f(x,y) =\begin{cases} \frac{u_d}{1.2965125} \left( r\left(1+\frac{\beta_i^2}{g_i^2}\right) - R \frac{\beta_i^2}{g_i^2} \frac{J_1(g_ir/R)}{J_1(g_i)}\right)\cos(\theta) \text{ if } r < R \\ \frac{u_d}{1.2965125} R \frac{K_1(\beta_i {r}/{R})}{K_1(\beta)} \cos(\theta) \text{ else } \end{cases} \) More...

Public Member Functions
	Vortex (double x0, double y0, unsigned state, double R, double u_dipole, double kz=0)
DG_DEVICE double	operator() (double x, double y) const
	\(f(x,y) =\begin{cases} \frac{u_d}{1.2965125} \left( r\left(1+\frac{\beta_i^2}{g_i^2}\right) - R \frac{\beta_i^2}{g_i^2} \frac{J_1(g_ir/R)}{J_1(g_i)}\right)\cos(\theta) \text{ if } r < R \\ \frac{u_d}{1.2965125} R \frac{K_1(\beta_i {r}/{R})}{K_1(\beta)} \cos(\theta) \text{ else } \end{cases} \) More...
DG_DEVICE double	operator() (double x, double y, double z) const
	\(f(x,y,z) =\cos(k_z z)\begin{cases} \frac{u_d}{1.2965125} \left( r\left(1+\frac{\beta_i^2}{g_i^2}\right) - R \frac{\beta_i^2}{g_i^2} \frac{J_1(g_ir/R)}{J_1(g_i)}\right)\cos(\theta) \text{ if } r < R \\ \frac{u_d}{1.2965125} R \frac{K_1(\beta_i {r}/{R})}{K_1(\beta)} \cos(\theta) \text{ else } \end{cases} \) More...

Detailed Description

\(f(x,y) =\begin{cases} \frac{u_d}{1.2965125} \left( r\left(1+\frac{\beta_i^2}{g_i^2}\right) - R \frac{\beta_i^2}{g_i^2} \frac{J_1(g_ir/R)}{J_1(g_i)}\right)\cos(\theta) \text{ if } r < R \\ \frac{u_d}{1.2965125} R \frac{K_1(\beta_i {r}/{R})}{K_1(\beta)} \cos(\theta) \text{ else } \end{cases} \)

Return a 2d vortex function where \( i\in \{0,1,2\}\) is the mode number and r and \(\theta\) are poloidal coordinates with \( r = \sqrt{(x-x_0)^2 + (y-y_0)^2}\), \( \theta = \arctan_2( (y-y_), (x-x_0))\), \( g_0 = 3.831896621 \), \( g_1 = -3.832353624 \), \( g_2 = 7.016\), \( \beta_0 = 0.03827327723\), \( \beta_1 = 0.07071067810 \), \( \beta_2 = 0.07071067810 \) \( K_1\) is the modified and \( J_1\) the Bessel function

Constructor & Destructor Documentation

Vortex()

dg::Vortex::Vortex ( double  x0, double  y0, unsigned  state, double  R, double  u_dipole, double  kz = 0  )

inline

Parameters

x0	X position
y0	Y position
state	mode 0,1, or 2
R	characteristic radius of dipole
u_dipole	u_drift/u_dipole = \( u_d\)
kz	multiply by \( \cos(k_z z) \) in three dimensions

Member Function Documentation

operator()() [1/2]

DG_DEVICE double dg::Vortex::operator() ( double  x, double  y  ) const

inline

\(f(x,y) =\begin{cases} \frac{u_d}{1.2965125} \left( r\left(1+\frac{\beta_i^2}{g_i^2}\right) - R \frac{\beta_i^2}{g_i^2} \frac{J_1(g_ir/R)}{J_1(g_i)}\right)\cos(\theta) \text{ if } r < R \\ \frac{u_d}{1.2965125} R \frac{K_1(\beta_i {r}/{R})}{K_1(\beta)} \cos(\theta) \text{ else } \end{cases} \)

Evaluate the vortex where \( i\in \{0,1,2\}\) is the mode number and r and \(\theta\) are poloidal coordinates

Parameters

x	value
y	value

Returns

the above function value

operator()() [2/2]

DG_DEVICE double dg::Vortex::operator() ( double  x, double  y, double  z  ) const

inline

\(f(x,y,z) =\cos(k_z z)\begin{cases} \frac{u_d}{1.2965125} \left( r\left(1+\frac{\beta_i^2}{g_i^2}\right) - R \frac{\beta_i^2}{g_i^2} \frac{J_1(g_ir/R)}{J_1(g_i)}\right)\cos(\theta) \text{ if } r < R \\ \frac{u_d}{1.2965125} R \frac{K_1(\beta_i {r}/{R})}{K_1(\beta)} \cos(\theta) \text{ else } \end{cases} \)

Evaluate the vortex modulated by a sine wave in z where \( i\in \{0,1,2\}\) is the mode number and r and \(\theta\) are poloidal coordinates

Parameters

x	value
y	value
z	value

Returns

the above function value

---

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

• functors.h