arc_mobility
============

.. py:module:: arc_mobility

.. autoapi-nested-parse::

   Arc mobility models for reignition point movement.



Classes
-------

.. autoapisummary::

   arc_mobility.BrownianArcMobilityModel


Module Contents
---------------

.. py:class:: BrownianArcMobilityModel

   Bases: :py:obj:`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:

   .. math::

      t_{off} = \frac{1}{f_{pulse}} - t_{sustainer}

      d_{rms} \propto v_{brownian} \sqrt{t_{off}}

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

   .. rubric:: Examples

   .. minigallery:: paroto.core.models.arc_mobility.BrownianArcMobilityModel
       :add-heading: Examples using this model

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


   .. py:method:: initialize()

      Initialize model options.



   .. py:method:: setup()

      Define inputs and outputs.



   .. py:method:: 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:

      .. math::

         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}

      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:

      .. math::

         \mu_{factor} = 1 + 0.5 \cdot \frac{d_{rms}}{d_{gap}}

         \theta_{spread} = 1 + 2.0 \cdot \frac{d_{rms}}{d_{gap}}



   .. py:method:: compute_partials(inputs, partials)

      Compute partial derivatives.