wellbalanced.spatial.coupling

The coil current and the plasma together: a power-dependent plasma in the RF field.

For a prescribed plasma the field is linear in the coil current, so the absorbed power fixes the current (:meth:~wellbalanced.spatial.inductive.InductiveSolution.for_power). A real plasma depends on the power it absorbs; :class:DriverCoupling closes the loop between a field model and a plasma model, each a callable:

• plasma(P): the plasma absorbing P W, as a :class:PlasmaProfile (and anything else to keep, e.g. a global model’s state);
• field(profile): the :class:~wellbalanced.spatial.inductive.InductiveField2D of that plasma.

:meth:DriverCoupling.at_absorbed_power sets the power the plasma absorbs (one pass, the coil current follows). :meth:DriverCoupling.at_rf_power sets the generator power, as Zielke et al. (PSST 31, 035019, 2022) do with their integral controller: the plasma absorbs P = eta P_RF with eta = R_p / (R_p + R_net), and R_p depends on the plasma, so P is the fixed point of P -> eta(P) P_RF, iterated (with relaxation) to a relative tolerance.

:func:global_model_plasma makes the plasma model of an :class:~wellbalanced.driver.RFDriver’s global model: its electron density, temperature and momentum-transfer frequency on a fixed spatial shape. With it the 0D plasma sits in the real 2D (or r–z) field instead of the transformer model, which the returned :class:~wellbalanced.driver.DriverState still gives for comparison. A fluid model (Fluid2D) will replace the fixed shape.

Classes

Name	Description
CoupledState	A plasma and its field at one operating point.
DriverCoupling	A field model and a power-dependent plasma model, solved together.
PlasmaProfile	A plasma for the field model: electron density, collision frequency, temperature.

Functions

Name	Description
global_model_plasma	The plasma model of driver's global model, on a fixed spatial shape.

CoupledStateclassdataclass#

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class CoupledState(solution: InductiveSolution, plasma: Any, rf_power: float, absorbed_power: float, network_resistance: float, depth: float | None, iterations: int = 1, converged: bool = True, history: list[float] = list())

A plasma and its field at one operating point.

Attributes

Name	Type	Description
solution	InductiveSolution	The field, scaled to the coil current of the operating point.
plasma	Any	What the plasma model returned besides the profile (a :class:~wellbalanced.driver.DriverState for :func:global_model_plasma).
rf_power	float	The generator power P + R_net I^2 / 2 [W].
absorbed_power	float	The power the plasma absorbs [W].
network_resistance	float	R_net [Ohm].
depth	float | None	The effective depth of a cut [m]; None in r–z.
iterations	int	The passes of the fixed point (1 at a set absorbed power).
converged	bool	Whether the fixed point reached the tolerance.
history	list[float]	The absorbed power after each pass [W].

absorbed_powerattributeinstance attribute#

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absorbed_power: float

convergedattributeclass attributeinstance attribute#

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converged: bool = True

depthattributeinstance attribute#

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depth: float | None

historyattributeclass attributeinstance attribute#

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history: list[float] = field(default_factory=list)

iterationsattributeclass attributeinstance attribute#

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iterations: int = 1

network_resistanceattributeinstance attribute#

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network_resistance: float

plasmaattributeinstance attribute#

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plasma: Any

rf_powerattributeinstance attribute#

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rf_power: float

solutionattributeinstance attribute#

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solution: InductiveSolution

coil_currentproperty#

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coil_current: float

The coil current amplitude [A].

efficiencyproperty#

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efficiency: float

The RF power transfer efficiency P / P_RF.

plasma_resistanceproperty#

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plasma_resistance: float

R_p [Ohm].

DriverCouplingclassdataclass#

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class DriverCoupling(field: Callable[[PlasmaProfile], InductiveField2D], plasma: Callable[[float], tuple[PlasmaProfile, Any]], network_resistance: float, depth: float | None = None)

A field model and a power-dependent plasma model, solved together.

Attributes

Name	Type	Description
field	Callable[[PlasmaProfile], InductiveField2D]	profile -> InductiveField2D.
plasma	Callable[[float], tuple[PlasmaProfile, Any]]	absorbed power [W] -> (PlasmaProfile, anything).
network_resistance	float	R_net [Ohm].
depth	float | None	The effective depth of a cut [m]; None in r–z.

depthattributeclass attributeinstance attribute#

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depth: float | None = None

fieldattributeinstance attribute#

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field: Callable[[PlasmaProfile], InductiveField2D]

network_resistanceattributeinstance attribute#

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network_resistance: float

plasmaattributeinstance attribute#

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plasma: Callable[[float], tuple[PlasmaProfile, Any]]

at_absorbed_powermethod#

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def at_absorbed_power(power: float) -> CoupledState

The operating point where the plasma absorbs power W.

at_rf_powermethod#

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def at_rf_power(rf_power: float, *, guess: float | None = None, tolerance: float = 1e-06, max_iterations: int = 50, relaxation: float = 1.0) -> CoupledState

The operating point at the generator power rf_power W.

Iterates P <- P + relaxation (eta(P) P_RF - P) from guess (half the generator power by default) until |eta P_RF - P| < tolerance P_RF.

PlasmaProfileclassdataclass#

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class PlasmaProfile(electron_density: CellField, collision_frequency: CellField, electron_temperature: CellField | None = None)

A plasma for the field model: electron density, collision frequency, temperature.

Attributes

Name	Type	Description
electron_density	CellField	n_e [m^-3].
collision_frequency	CellField	nu [1/s].
electron_temperature	CellField | None	T_e [eV], for viscous electrons; None: cold.

collision_frequencyattributeinstance attribute#

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collision_frequency: CellField

electron_densityattributeinstance attribute#

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electron_density: CellField

electron_temperatureattributeclass attributeinstance attribute#

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electron_temperature: CellField | None = None

settingsmethod#

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def settings() -> dict[str, Any]

The keyword arguments of :class:InductiveField2D this plasma sets.

global_model_plasmafunction#

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def global_model_plasma(driver: RFDriver, shape: CellField = 1.0, *, viscous: bool = False, guess: GlobalState | Mapping[str, float] | None = None) -> Callable[[float], tuple[PlasmaProfile, DriverState]]

The plasma model of driver’s global model, on a fixed spatial shape.

n_e = shape * <n_e> with the global model’s <n_e> (scale shape to a volume average of 1 over the plasma), and its T_e (if viscous) and momentum-transfer frequency uniform; shape is zero outside the plasma or the field model’s plasma region does it. Each call continues from the last state. Returns (profile, DriverState): the driver state is the transformer model’s view of the same plasma.