arc_mobility

Arc mobility models for reignition point movement.

Classes

BrownianArcMobilityModel

Arc reignition point mobility model based on Brownian motion (Medium Fidelity).

Module Contents

class arc_mobility.BrownianArcMobilityModel

Bases: paroto.core.models.base.EmpiricalModel

Arc reignition point mobility model based on Brownian motion (Medium Fidelity).

Warning

Equations are AI generated, not ready for production.

Models the arc attachment point movement as Brownian motion at a characteristic velocity in a plane, projected onto the horizontal electrode surface line.

This affects: - Reignition probability (moving arc seeks new ionization paths) - Thermal loading distribution on electrodes - Arc stability characteristics

The model assumes random walk with characteristic velocity v_brownian in 2D, then projects the displacement onto the 1D electrode surface.

Physical basis:

\[ \begin{align}\begin{aligned}t_{off} = \frac{1}{f_{pulse}} - t_{sustainer}\\d_{rms} \propto v_{brownian} \sqrt{t_{off}}\end{aligned}\end{align} \]

where the displacement scales with the square root of time (Brownian scaling).

Examples

For complete examples, see: - Gallery: examples/gallery/plot_mobility_model_example.py - Validation: paroto/validation/validate_mobility.py

initialize()

Initialize model options.

setup()

Define inputs and outputs.

compute(inputs, outputs)

Compute arc mobility characteristics.

Warning

Equations are AI generated, not ready for production.

The arc attachment point displacement follows a Brownian motion model:

\[ \begin{align}\begin{aligned}d_{2D} = v_{brownian} \sqrt{t_{off}}\\d_{1D} = d_{2D} \cdot \frac{1}{\sqrt{2}}\\d_{rms} = d_{1D} \cdot \sqrt{\frac{I_{ref}}{I_{arc}}} \cdot \left(\frac{T}{T_{ref}}\right)^{0.3}\end{aligned}\end{align} \]

where: - (d_{2D}) is the displacement in 2D plane - (v_{brownian}) is the characteristic Brownian velocity (10 m/s) - (t_{off}) is the time between pulses - (d_{1D}) is the projection onto the electrode line - (I_{ref}) = 100 A is the reference current - (T_{ref}) = 300 K is the reference temperature

Mobility and thermal spreading factors:

\[ \begin{align}\begin{aligned}\mu_{factor} = 1 + 0.5 \cdot \frac{d_{rms}}{d_{gap}}\\\theta_{spread} = 1 + 2.0 \cdot \frac{d_{rms}}{d_{gap}}\end{aligned}\end{align} \]

compute_partials(inputs, partials)

Compute partial derivatives.