Base Classes#
- class gcmotion.tokamak.qfactor.QFactor#
q Factor base class
Methods
- abstract psipNU(psi: float | ndarray) float | ndarray#
Calculates \(\psi_p(\psi)\). Input and output are both floats or np.ndarrays, in [NU].
- Parameters:
- psifloat | np.ndarray
Value(s) of \(\psi\) in NU.
- Returns:
- float | np.ndarray
Calculated \(\psi_p(\psi)\) in NU.
- abstract solverqNU(psi: float | ndarray) float | ndarray#
Calculates \(q(\psi)\). Input and output are both floats or np.ndarrays, in [NU].
Used inside the solver.
- Parameters:
- psifloat | np.ndarray
Value(s) of \(\psi\) in NU.
- Returns:
- float | np.ndarray
Calculated \(\psi_p(\psi)\) in NU.
- class gcmotion.tokamak.qfactor.NumericalQFactor(filename: str)#
Numerical QFactor base class.
Opens the dataset and creates the splines needed for the querry methods.
solverqandpsipNUwork identically to the analytic QFactor methods.- Parameters:
- filenamestr
The “*.nc” file located at gcmotion/tokamak/reconstructed.
Methods
psipNU(psi)Calculates \(\psi_p(\psi)\).
solverqNU(psi)Calculates \(q(\psi)\).
- class gcmotion.tokamak.bfield.MagneticField#
Magnetic field base class
Methods
bigNU(phi, theta)Calculates \(B(\psi, \theta), I(\psi, \theta), g(\psi,\ \theta)\).
solverbNU(psi, theta)Calculates all the values needed by the solver: \(B,I,g\) (by calling
self.bigNU()) and the derivatives \(\dfrac{\partial B}{\partial \psi}, \dfrac{\partial B}{\partial\ \theta}\ \dfrac{\partial I}{\partial \psi}\) and \(\dfrac{\partial\ g}{\partial \psi}\).- abstract bigNU(phi: float | ndarray, theta: float | ndarray) float | ndarray#
Calculates \(B(\psi, \theta), I(\psi, \theta), g(\psi,\ \theta)\). Input and output must be both floats or np.ndarrays, in [NU].
Used in energy contour plots.
- Parameters:
- psifloat | np.ndarray
The \(\psi\) value(s) in [NU].
- thetafloat | np.ndarray
The \(\theta\) value(s).
- Returns:
- float | np.ndarray
The Calculated \(B(\psi, \theta), I(\psi, \theta), g(\psi,\ \theta)\) value(s) in [NU].
- abstract solverbNU(psi: float, theta: float) tuple[float]#
Calculates all the values needed by the solver: \(B,I,g\) (by calling
self.bigNU()) and the derivatives \(\dfrac{\partial B}{\partial \psi}, \dfrac{\partial B}{\partial\ \theta}\ \dfrac{\partial I}{\partial \psi}\) and \(\dfrac{\partial\ g}{\partial \psi}\).Input and output must be floats, in [NU].
Used inside the solver.
Warning
The derivatives are calculated with respect to \(\psi\), and not \(\psi_p\), which appear in the differential equations. This is accounted for inside the solver by multiplying by \(q(\psi)\), since \(\dfrac{\partial f}{\partial \psi_p}\ =\dfrac{\partial f}{\partial \psi}\ \dfrac{\partial \psi}{\partial\ \psi_p} = q\dfrac{\partial f}{\partial \psi}\)
- Parameters:
- psifloat
Value of \(\psi\) in [NU].
- thetafloat
Value of \(\theta\) in [NU].
- Returns:
- 3-tuple of floats
Calculated values and derivatives in [NU].
- class gcmotion.tokamak.bfield.NumericalMagneticField(filename: str)#
Numerical Magnetic field base class
Opens the dataset and creates the splines needed for the querry methods. Also defines Bmin and Bmax, used in the parabolas.
solverBandbigNUwork identically to the analytic Magnetic field methods.- Parameters:
- filenamestr
The “*.nc” file located at gcmotion/tokamak/reconstructed.
- Attributes:
- Bmin, BmaxQuantities
The minimum and maximum magnetic field values.
- theta_min, theta_maxQuantities
The \(\theta\) coordinates where the magnetic field takes its minimum/maximum value.
- psi_min, psi_maxQuantities
The \(\psi\) coordinates where the magnetic field takes its minimum/maximum value.
Methods
bigNU(psi, theta)Calculates \(B(\psi, \theta), I(\psi, \theta), g(\psi,\ \theta)\).
solverbNU(psi, theta)Calculates all the values needed by the solver: \(B,I,g\) (by calling
self.bigNU()) and the derivatives \(\dfrac{\partial B}{\partial \psi}, \dfrac{\partial B}{\partial\ \theta}\ \dfrac{\partial I}{\partial \psi}\) and \(\dfrac{\partial\ g}{\partial \psi}\).
- class gcmotion.tokamak.efield.ElectricField#
Electric field base class.
Methods
Er(psi, theta)Calculates the electric field strength in [NU].
PhiNU(psi, theta)Calculates \(\Phi(\psi, \theta)\).
solverPhiderNU(psi, theta)Calculates the derivatives of \(\Phi\) with respect to \(\psi_p\) and \(\theta\).
- abstract Er(psi: ndarray, theta: ndarray) ndarray#
Calculates the electric field strength in [NU].
Used for plotting.
- Parameters:
- psinp.ndarray
The \(\psi\) values.
- Returns:
- np.ndarray
1D numpy array with calculated \(E\) values.
- abstract PhiNU(psi: float | ndarray, theta: float | ndarray) float | ndarray#
Calculates \(\Phi(\psi, \theta)\). Input can be either a float or a np.ndarray, but output is always np.ndarray, in [NU].
Used in energy contour plots.
- Parameters:
- psifloat | np.ndarray
The \(\psi\) value(s) in [NU].
- thetafloat | np.ndarray
The \(\psi\) value(s).
- Returns:
- np.ndarray
The Calculated \(\Phi\) value(s).
- abstract solverPhiderNU(psi: float, theta: float) tuple[float]#
Calculates the derivatives of \(\Phi\) with respect to \(\psi_p\) and \(\theta\). Input and output must be floats, in [NU].
Used inside the solver.
Important
The derivatives are calculated with respect to \(\psi\), and not \(\psi_p\), which appear in the differential equations. This is accounted for inside the solver by multiplying by \(q(\psi)\), since \(\dfrac{\partial f}{\partial \psi_p}=\ \dfrac{\partial f}{\partial \psi}\ \dfrac{\partial \psi}{\partial\ \psi_p} = q\dfrac{\partial f}{\partial \psi}\)
- Parameters:
- psifloat
Value of \(\psi\) in [NU].
- thetafloat
Value of \(\theta\) in [NU].
- Returns:
- 2-tuple of floats
Calculated derivatives in [NU].