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Efield Objects

dexter.EfieldObject: TypeAlias = NoEfield | GaussianEfield module-attribute

Available Efield objects.

dexter.NoEfield()

Bases: MachineObject, Efield

No electric field.

You shouldn't have to use this type; It is created when no efield parameter is passed to Machine.

No $\psi$ bounds checks are performed in evaluations.

Example 
>>> efield = dex.NoEfield()

dexter.GaussianEfield(strength: PlainQuantity[float] | float, mean: MagneticFlux, width: float)

Bases: MachineObject, Efield

Radial-Gaussian electric field.

Parameters:

  • strength (PlainQuantity[float] | float) –

    The electric field strength at the curve's peak. If float then it must be in Normalized Units. If Quantity then it must have the dimensionality of $[V/m]$. Defining it through an existing Machine's quantity method is necessary to properly convert to Normalized Units (see example). The machine's GeometryObject must be defined.

  • mean (MagneticFlux) –

    The magnetic flux surface where the peak is located.

  • width (float) –

    The standard deviation or root mean square width of the 'bell'.

Attributes:

  • strength (float) –

    The electric field strength at the curve's peak, in Normalized Units.

  • mean (MagneticFlux) –

    The magnetic flux surface where the peak is located.

  • width (float) –

    The standard deviation or root mean square width of the 'bell'.

Example
Electric Field in Normalized Units
>>> lcfs = dex.MagneticFlux.Toroidal(0.05)
>>>
>>> strength = 1e-4
>>> mean = lcfs / 2
>>> width = lcfs.value / 50
>>>
>>> efield = dex.GaussianEfield(strength, mean, width)
Electric Field from `machine`
>>> geometry=dex.LarGeometry(baxis=2, raxis=2.75, rlast=0.5)
>>> lcfs = geometry.psit_last
>>> machine = dex.Machine(
...     geometry=geometry,
...     qfactor=dex.UnityQfactor(lcfs),
...     current=dex.LarCurrent(),
...     bfield=dex.LarBfield(),
...     perturbation=dex.Perturbation(
...          [
...             dex.FluteMode(1e-5, lcfs, 2, 1, 0),
...             dex.FluteMode(1e-5, lcfs, 3, 1, 0),
...          ]
...     ),
... )
>>>
>>> strength = machine.quantity(50, "kiloVolt / meter")
>>> mean = lcfs / 2
>>> width = lcfs.value / 50
>>>
>>> # Now we can set the machine's electric field
>>> machine.efield = dex.GaussianEfield(strength, mean, width)

The GaussianEfield's profile is described by the following formulas (with $\psi$ being either the toroidal or the poloidal flux):

$$ E(\psi) = E\cdot\exp \bigg[-\dfrac{(\psi-\mu)^2}{2\sigma^2}\bigg], $$

$$ \Phi(\psi) = -\int_0^\psi E(\psi)d\psi = E \sigma \sqrt{\dfrac{\pi}{2}} \bigg[\text{erf} \bigg( \dfrac{\sqrt{2}(\psi-\mu)}{2\sigma} \bigg) + \text{erf} \bigg( \dfrac{\mu}{\sigma\sqrt{2}} \bigg) \bigg], \qquad \text{with} \quad \Phi(0) = 0 $$

$$ \dfrac{d\Phi}{d\psi} = - E(\psi), $$

$$ \dfrac{d^2\Phi}{d\psi^2} = \dfrac{\psi - \mu}{\sigma^2}E(\psi) $$