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+# Sphinx build info version 1
+# This file hashes the configuration used when building these files. When it is not found, a full rebuild will be done.
+config: 1ae37ff3f3b799b63f140f358f9b932e
+tags: 645f666f9bcd5a90fca523b33c5a78b7

_sources/index.rst.txt

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+NESO-Tokamak
+=========================
+
+NESO-Tokamak documentation
+
+.. toctree::
+   :maxdepth: 3
+   :caption: Contents:
+   :glob:
+
+   static_rst/*
+
+Indices and tables
+==================
+
+* :ref:`genindex`
+* :ref:`modindex`
+* :ref:`search`

_sources/static_rst/reactions_minimal_coupling.rst.txt

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+=================================================
+NESO-Tokamak-Reactions coupling minimal equations
+=================================================
+
+Single field anisotropic diffusion with sources and outflow
+-----------------------------------------------------------
+
+This can be in 2D or 3D.
+
+.. math:: \frac{\partial n}{\partial t} + \nabla \cdot \vec{\Gamma} = S_n
+
+with the diffusive flux given by :math:`\vec{\Gamma} = D \cdot \nabla n`
+with D being the anisotropic diffusion tensor
+:math:`D = \vec{b}\vec{b} k_\parallel + (I - \vec{b}\vec{b}) k_\perp`
+where the :math:`k_\parallel` and :math:`k_\perp` should have the option
+of being functions of fields, and :math:`\vec{b}` is the local unit
+vector tangential to the magnetic field.
+
+The source :math:`S_n` should be given by Reactions, with the idea of
+starting off with ionisation only, so it would always be positive in
+this example. For the purpose of Reactions and the Bohm BC, we will
+assume an isothermal plasma here.
+
+The boundary condition should be set to Neumann in the directions
+perpendicular to the magnetic field, while the parallel component of the
+flux at the boundary
+
+.. math:: \vec{\Gamma}\cdot \vec{b} = n c_s
+
+where :math:`c_s` in this case is a constant (isothermal Bohm speed
+:math:`c_s = \sqrt{kT/m_i}`).
+
+Once basic coupling has been done with this, we can add another field.
+
+Two diffusive fields with particle and energy coupling with Reactions
+---------------------------------------------------------------------
+
+Same as above for :math:`n`-field, with the addition of non-constant
+:math:`T`.
+
+We will ignore all advective and field terms for the first pass, and
+write a pressure equation as
+
+.. math:: \frac{3}{2} \frac{\partial p}{\partial t} + \nabla \cdot \vec{q} = S_E + Q,
+
+where :math:`p = nkT` and
+
+.. math:: \vec{q} = \kappa \cdot \nabla T
+
+with the conductivity tensor given as
+
+.. math:: \kappa =  \kappa_\parallel(T) \vec{b}\vec{b} + \kappa_\perp(T) (I-\vec{b}\vec{b})
+
+with parallel and perpendicular conductivities being functions of
+temperature to start off with.
+
+Energy sinks :math:`S_E` should again be supplied by Reactions, with
+some heating :math:`Q` in the core being an input parameter.
+
+At the parallel boundaries, we set the energy outflow to
+
+.. math:: \vec{q}\cdot \vec{b} = \gamma nkTc_s,
+
+where now :math:`c_s=\sqrt{kT/m_i}` for both this and the particle BC,
+and :math:`\gamma \approx 7`. No outflow/Neumann at perpendicular
+boundaries.
+
+Only after both of these models have been tested with Reactions coupling
+does it make sense to move towards a model with an explicit momentum
+equation, such as a reduced version of Hermes-3 mean-field equations.