gcmotion.qfactor#
Here is a list of the availiable q-factor configurations:
Unity q-factor |
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Parabolic q-factor |
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Hypergeometric q-factor |
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PrecomputedHypergeometric q-factor |
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(Numerical) SmartPositive |
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(Numerical) SmartNegative |
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(Numerical) SmartNegative2 |
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(Numerical) DTTPositive |
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(Numerical) DTTNegative |
Their parameters are documented below.
Examples#
>>> import gcmotion as gcm
>>>
>>> # Quantity Constructor
>>> Rnum = 1.6
>>> anum = 0.5
>>> B0num = 1
>>> species = "p"
>>> Q = gcm.QuantityConstructor(R=Rnum, a=anum, B0=B0num, species=species)
>>>
>>> # Intermediate values
>>> a = Q(anum, "meters")
>>> B0 = Q(B0num, "Tesla")
>>>
>>> # Some qfactors
>>> qfactor1 = gcm.qfactor.Unity()
>>> qfactor3 = gcm.qfactor.Parabolic(a, B0, q0=1.1, q_wall=3.8)
>>> qfactor3 = gcm.qfactor.Hypergeometric(a, B0, q0=1.1, q_wall=3.8, n=2)
Creating a numerical Qfactor. Use the respective Initializer to grab the normalization constants from the dataset automatically. See Initializers
>>> import gcmotion as gcm
>>>
>>> # Quantity Constructor
>>> species = "p"
>>> smart_init = gcm.SmartNegativeInit(species)
>>> Q = smart_init.QuantityConstructor()
>>>
>>> # Intermediate Quantities
>>> R = smart_init.R
>>> a = smart_init.a
>>> B0 = smart_init.B0
>>>
>>> qfactor=gcm.qfactor.SmartNegative(),
Note
The values of a and B0 are necessary whenever we define the qfactor with reference to its value at the wall.
Methods#
The functions solverqNU and psipNU work identically in every class, so I list their methods here.
- gcmotion.qfactor.QFactor.solverqNU(self, 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.
- gcmotion.qfactor.QFactor.psipNU(self, 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.
Available q-factors#
Unity
- class gcmotion.qfactor.Unity#
Initializes an object q with \(q(\psi) = 1\) and \(\psi_p=\psi\).
Methods
psipNU(psi)Always returns psi.
solverqNU(psi)Always returns 1.
Parabolic
- class gcmotion.qfactor.Parabolic(a: Quantity, B0: Quantity, q0: float, q_wall: float)#
Initializes an object q with
\[q(\psi) = q_0 + (q_{wall}-q_0)\bigg(\dfrac{\psi}{\psi_{wall}}\ \bigg)^2\]\(\psi_p(\psi)\) is calculated from:
\[\psi_p(\psi) = \dfrac{\psi_{wall}}{\sqrt{q_0 (q_{wall}-q_0)}}\ \arctan\bigg( \dfrac{\psi\sqrt{q_{wall}-q_0}}{\psi_{wall}\sqrt{q_0}}\ \bigg)\]- Parameters:
- aQuantity
float The tokamak’s minor radius in [m].
- B0Quantity
The Magnetic field’s strength in [T]
- q0float
q-value at the magnetic axis.
- q_wallfloat
q_value at the wall.
Methods
psipNU(psi)Calculates \(\psi_p(\psi)\).
solverqNU(psi)Calculates \(q(\psi)\).
Hypergeometric
- class gcmotion.qfactor.Hypergeometric(a: Quantity, B0: Quantity, q0: float, q_wall: float, n: int)#
Initializes an object q with:
\[q(\psi) = q_0\bigg\{ 1 + \bigg[ \bigg(\dfrac{q_{wall}}{q_0}\ \bigg)^n -1 \bigg] \ \bigg( \dfrac{\psi}{\psi_{wall}} \bigg)^n \bigg\}^{1/n}\]\(\psi_p(\psi)\) is calculated from:
\[\psi_p(\psi) = \dfrac{\psi}{q_0} \phantom{1}_2 F_1\ \bigg[ \dfrac{1}{n}, \dfrac{1}{n}, 1+\dfrac{1}{n}, \bigg(1 - \bigg( \dfrac{q_{wall}}{q_0} \bigg)^n\bigg) \bigg( \dfrac{\psi}{\psi_{wall}} \bigg)^n \bigg]\]where \(\phantom{1}_2 F_1\) the hypergeometric function.
- Parameters:
- aQuantity
float The tokamak’s minor radius in [m].
- B0Quantity
The Magnetic field’s strength in [T].
- q0float
q-value at the magnetic axis.
- q_wallfloat
q_value at the wall.
- nint
Order of equillibrium (1: peaked, 2: round, 4: flat).
Methods
psipNU(psi)Calculates \(\psi_p(\psi)\).
solverqNU(psi)Calculates \(q(\psi)\).
PrecomputedHypergeometric
- class gcmotion.qfactor.PrecomputedHypergeometric(a: Quantity, B0: Quantity, q0: float, q_wall: float, n: int)#
Same as the Hypergeometric qfactor but with precomputed hyp2f1.
Since the calculation of hyp2f1 is by a lot slower than any other calculation, it makes sense to precompute an array with all the needed values and make a spline on it.
Methods
psipNU(psi)Calculates \(\psi_p(\psi)\).
solverqNU(psi)Calculates \(q(\psi)\).
SmartPositive
- class gcmotion.qfactor.SmartPositive#
Initializes an object q with numerical data from the Smart Tokamak with Positive Triangularity.
The dataset must be stored in ./gcmotion/tokamak/reconstructed/smart_positive.nc.
Methods
psipNU(psi)Calculates \(\psi_p(\psi)\).
solverqNU(psi)Calculates \(q(\psi)\).
SmartNegative
- class gcmotion.qfactor.SmartNegative#
Initializes an object q with numerical data from the Smart Tokamak with Negative Triangularity.
The dataset must be stored in ./gcmotion/tokamak/reconstructed/smart_negative.nc.
Methods
psipNU(psi)Calculates \(\psi_p(\psi)\).
solverqNU(psi)Calculates \(q(\psi)\).
SmartNegative2
- class gcmotion.qfactor.SmartNegative2#
Initializes an object q with numerical data from the Smart Tokamak with Negative Triangularity.
The dataset must be stored in ./gcmotion/tokamak/reconstructed/smart_negative2.nc.
Methods
psipNU(psi)Calculates \(\psi_p(\psi)\).
solverqNU(psi)Calculates \(q(\psi)\).
DTTPositive
- class gcmotion.qfactor.DTTPositive#
Initializes an object q with numerical data from the Divertor Test Tokamak with Positive Triangularity.
The dataset must be stored in ./gcmotion/tokamak/reconstructed/dtt_positive.nc.
Methods
psipNU(psi)Calculates \(\psi_p(\psi)\).
solverqNU(psi)Calculates \(q(\psi)\).
DTTNegative
- class gcmotion.qfactor.DTTNegative#
Initializes an object q with numerical data from the Divertor Test Tokamak with Negative Triangularity.
The dataset must be stored in ./gcmotion/tokamak/reconstructed/dtt_negative.nc.
Methods
psipNU(psi)Calculates \(\psi_p(\psi)\).
solverqNU(psi)Calculates \(q(\psi)\).