dg::BathRZ Struct Reference

\(f(R,Z) = A B \sum_\vec{k} \sqrt{E_k} \alpha_k \cos{\left(k \kappa_k + \theta_k \right)} \) More...

Public Member Functions
	BathRZ (unsigned N_kR, unsigned N_kZ, double R_min, double Z_min, double gamma, double L_E, double amp)
	Functor returning a random field in the RZ-plane or in the first RZ-plane. More...
double	operator() (double R, double Z) const
	Return the value of the Bath. More...
double	operator() (double R, double Z, double phi) const
	Return the value of the Bath. More...

Detailed Description

\(f(R,Z) = A B \sum_\vec{k} \sqrt{E_k} \alpha_k \cos{\left(k \kappa_k + \theta_k \right)} \)

A random bath in the R-Z plane with

\[ B := \sqrt{\frac{2}{N_{k_R} N_{k_Z}}} \\ k:=\sqrt{k_R^2 + k_Z^2} \\ k_R:=2 \pi \left( i -N_{k_R}/2\right)/N_{k_R} \\ k_Z:=2 \pi \left( j -N_{k_Z}/2\right)/N_{k_Z} \\ k_0:=2 \pi L_E / N_k\\ N_k := \sqrt{N_{k_R}^2 + N_{k_Z}^2} \\ E_k:=\left(4 k k_0/(k+k_0)^2\right)^{\gamma} \\ \alpha_k := \sqrt{\mathcal{N}_1^2 + \mathcal{N}_2^2} \\ \theta_k := \arctan{\left(\mathcal{N}_2/\mathcal{N}_1\right)} \\ \kappa_k(R,Z) := (R-R_{min}) \mathcal{U}_1 + (Z-Z_{min}) \mathcal{U}_2 \\ \]

where \(\mathcal{N}_{1,2}\) are random normal distributed real numbers with a mean of \(\mu = 0\) and a standard deviation of \(\sigma=1 \), \(\mathcal{U}_{1,2}\) are random uniformly distributed real numbers \(\in \left[0, 2 \pi \right) \) and \( A \) is the amplitude.

Constructor & Destructor Documentation

BathRZ()

dg::BathRZ::BathRZ ( unsigned  N_kR, unsigned  N_kZ, double  R_min, double  Z_min, double  gamma, double  L_E, double  amp  )

inline

Functor returning a random field in the RZ-plane or in the first RZ-plane.

Parameters

N_kR	Number of Fourier modes in R direction
N_kZ	Number of Fourier modes in Z direction
R_min	Minimal R (in units of rho_s)
Z_min	Minimal Z (in units of rho_s)
gamma	exponent in the energy function \(E_k\) (typically around 30)
L_E	is the typical eddysize (typically around 5)
amp	Amplitude

Member Function Documentation

operator()() [1/2]

double dg::BathRZ::operator() ( double  R, double  Z  ) const

inline

Return the value of the Bath.

\[f(R,Z) = A B \sum_\vec{k} \sqrt{E_k} \alpha_k \cos{\left(k \kappa_k + \theta_k \right)} \]

with

\[ \mathcal{N} := \sqrt{\frac{2}{N_{k_R} N_{k_Z}}} \\ k:=\sqrt{k_R^2 + k_Z^2} \\ k_R:=2 \pi \left( i -N_{k_R}/2\right)/N_{k_R} \\ k_Z:=2 \pi \left( j -N_{k_Z}/2\right)/N_{k_Z} \\ k_0:=2 \pi L_E / N_k\\ N_k := \sqrt{N_{k_R}^2 + N_{k_Z}^2} \\ E_k:=\left(4 k k_0/(k+k_0)^2\right)^{\gamma} \\ \alpha_k := \sqrt{\mathcal{N}_1^2 + \mathcal{N}_2^2} \\ \theta_k := \arctan{\left(\mathcal{N}_2/\mathcal{N}_1\right)} \\ \kappa_k(R,Z) := (R-R_{min}) \mathcal{U}_1 + (Z-Z_{min}) \mathcal{U}_2 \\ \]

where \(\mathcal{N}_{1,2}\) are random normal distributed real numbers with a mean of \(\mu = 0\) and a standard deviation of \(\sigma=1 \), \(\mathcal{U}_{1,2}\) are random uniformly distributed real numbers \(\in \left[0, 2 \pi \right) \) and \( A \) is the amplitude

Parameters

R	R - coordinate
Z	Z - coordinate

Returns

the above function value

operator()() [2/2]

double dg::BathRZ::operator() ( double  R, double  Z, double  phi  ) const

inline

Return the value of the Bath.

\[f(R,Z) = A B \sum_\vec{k} \sqrt{E_k} \alpha_k \cos{\left(k \kappa_k + \theta_k \right)} \]

with

\[ \mathcal{N} := \sqrt{\frac{2}{N_{k_R} N_{k_Z}}} \\ k:=\sqrt{k_R^2 + k_Z^2} \\ k_R:=2 \pi \left( i -N_{k_R}/2\right)/N_{k_R} \\ k_Z:=2 \pi \left( j -N_{k_Z}/2\right)/N_{k_Z} \\ k_0:=2 \pi L_E / N_k\\ N_k := \sqrt{N_{k_R}^2 + N_{k_Z}^2} \\ E_k:=\left(4 k k_0/(k+k_0)^2\right)^{\gamma} \\ \alpha_k := \sqrt{\mathcal{N}_1^2 + \mathcal{N}_2^2} \\ \theta_k := \arctan{\left(\mathcal{N}_2/\mathcal{N}_1\right)} \\ \kappa_k(R,Z) := (R-R_{min}) \mathcal{U}_1 + (Z-Z_{min}) \mathcal{U}_2 \\ \]

where \(\mathcal{N}_{1,2}\) are random normal distributed real numbers with a mean of \(\mu = 0\) and a standard deviation of \(\sigma=1 \), \(\mathcal{U}_{1,2}\) are random uniformly distributed real numbers \(\in \left[0, 2 \pi \right) \) and \( A \) is the amplitude

Parameters

R	R - coordinate
Z	Z - coordinate
phi	phi - coordinate

Returns

the above function value

---

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

• functors.h