gcmotion.efield

Here is a list of the availiable efield configurations:

No Electric field	Nofield
Cosine Potential Electric field	CosinePotential
Radial Electric field	Radial

Their parameters are documented below.

Example

>>> 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")
>>> Ea = Q(75, "kiloVolts/meter")
>>>
>>> # Some qfactors
>>> efield1 = gcm.efield.Nofield()
>>> efield2 = gcm.efield.Radial(a=a, B0=B0, Ea=Ea, peak=0.98, rw=1/50)

Note

The values of a and B0 are necessary whenever we define the electric field with reference to its value at the wall.

Methods

The functions PhiNU, Er and solverPhiderNU work identically in every class, so I list their methods here.

Available electric fields

Nofield

class gcmotion.efield.Nofield

Initializes an electric field of 0

Exists to avoid compatibility issues.

Methods

Er(psi, theta)	Always returns a zero array in the same shape as psi.
PhiNU(psi, theta)	Always returns a zero array in the same shape as psi.
solverPhiderNU(psi, theta)	Always returns (0,0).

CosinePotential

class gcmotion.efield.CosinePotential(V0: Quantity, f: float)

Initializes a cosine-like radial electric field of the form:

\[E(r) = V_0f\pi\sin(f\pi\psi)\]

with

\[\Phi(\psi) = V_0 + V_0\cos(f\pi\psi)\]

Important

This Electric field is defined through its Potential.

Parameters:

V0: Quantity

The Electric Potential amplitude.

f: float

The “frequency” factor of the cosine term.

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 \(\theta\).

Radial

class gcmotion.efield.Radial(a: Quantity, Ea: Quantity, B0: Quantity, peak: float, rw: float)

Initializes an electric field of the form:

\[E(r) = -E_{peak}\exp\bigg[-\dfrac{(r-r_{peak})^2}{r_{w}^2})\bigg]\]

with

\[\Phi(\psi) = E_{peak} \sqrt{\dfrac{\pi\psi_{wall}}{2}}\ \bigg[ \text{erf} \bigg( \ \dfrac{\sqrt{\psi} - \sqrt{\psi_{peak}}}{\sqrt{\psi_w}}\bigg) \ + \text{erf} \bigg( \sqrt{\dfrac{\psi_{peak}}{\psi_w}} \bigg) \ \bigg]\]

where \(\psi_w = r_w^2/2\) and \(\psi_{peak} = r_{peak}^2/2\)

Parameters:

aQuantity

The tokamak’s minor radius in [m].

EaQuantity

The Electric field magnitude in [V/m].

B0Quantity

The Magnetic field’s strength in [T].

peakfloat

The Electric field’s peak point with respect to \(\psi_{wall}\).

rwfloat

The Electric field’s waist width relative to \(r_{wall}\), defined as: \(r_{waist} = \alpha\cdot \text{rw}\).

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 \(\theta\).