From f7dd6a9bc8bb1cfe863409fcf0451b020e99509e Mon Sep 17 00:00:00 2001 From: Johannes van de Wetering <92386744+johvandewetering@users.noreply.github.com> Date: Mon, 16 Sep 2024 19:21:59 -0700 Subject: [PATCH] [Hackathon] Ionization docs fixes (#5270) * Fixed typos in generalized Ohm's law * Fixed Testing link * Removed minus sign from BTO equation (Zhang eq 8 is wrong) * Clarify comment about difference to published equation. Co-authored-by: Axel Huebl --------- Co-authored-by: Johannes Van de Wetering Co-authored-by: Roelof Groenewald <40245517+roelof-groenewald@users.noreply.github.com> Co-authored-by: Axel Huebl --- Docs/source/theory/kinetic_fluid_hybrid_model.rst | 4 ++-- Docs/source/theory/multiphysics/ionization.rst | 6 +++--- 2 files changed, 5 insertions(+), 5 deletions(-) diff --git a/Docs/source/theory/kinetic_fluid_hybrid_model.rst b/Docs/source/theory/kinetic_fluid_hybrid_model.rst index b4f494d8382..f764ce4e02b 100644 --- a/Docs/source/theory/kinetic_fluid_hybrid_model.rst +++ b/Docs/source/theory/kinetic_fluid_hybrid_model.rst @@ -46,7 +46,7 @@ integrating over velocity), also called the generalized Ohm's law, is given by: .. math:: - en_e\vec{E} = \frac{m}{e}\frac{\partial \vec{J}_e}{\partial t} + \frac{m}{e^2}\left( \vec{U}_e\cdot\nabla \right) \vec{J}_e - \nabla\cdot {\overleftrightarrow P}_e - \vec{J}_e\times\vec{B}+\vec{R}_e + en_e\vec{E} = \frac{m}{e}\frac{\partial \vec{J}_e}{\partial t} + \frac{m}{e}\left( \vec{U}_e\cdot\nabla \right) \vec{J}_e - \nabla\cdot {\overleftrightarrow P}_e - \vec{J}_e\times\vec{B}+\vec{R}_e where :math:`\vec{U}_e = \vec{J}_e/(en_e)` is the electron fluid velocity, :math:`{\overleftrightarrow P}_e` is the electron pressure tensor and @@ -64,7 +64,7 @@ Plugging this back into the generalized Ohm' law gives: \left(en_e +\frac{m}{e\mu_0}\nabla\times\nabla\times\right)\vec{E} =& - \frac{m}{e}\left( \frac{\partial\vec{J}_{ext}}{\partial t} + \sum_{s\neq e}\frac{\partial\vec{J}_s}{\partial t} \right) \\ - &+ \frac{m}{e^2}\left( \vec{U}_e\cdot\nabla \right) \vec{J}_e - \nabla\cdot {\overleftrightarrow P}_e - \vec{J}_e\times\vec{B}+\vec{R}_e. + &+ \frac{m}{e}\left( \vec{U}_e\cdot\nabla \right) \vec{J}_e - \nabla\cdot {\overleftrightarrow P}_e - \vec{J}_e\times\vec{B}+\vec{R}_e. If we now further assume electrons are inertialess (i.e. :math:`m=0`), the above equation simplifies to, diff --git a/Docs/source/theory/multiphysics/ionization.rst b/Docs/source/theory/multiphysics/ionization.rst index 11abea386c8..5003872b1a1 100644 --- a/Docs/source/theory/multiphysics/ionization.rst +++ b/Docs/source/theory/multiphysics/ionization.rst @@ -56,18 +56,18 @@ where :math:`\mathrm{d}\tau` is the simulation timestep, which is divided by the Empirical Extension to Over-the-Barrier Regime for Hydrogen ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ -For hydrogen, WarpX offers the modified empirical ADK extension to the Over-the-Barrier (OTB) published in :cite:t:`mpion-zhang_empirical_2014` Eq. (8). +For hydrogen, WarpX offers the modified empirical ADK extension to the Over-the-Barrier (OTB) published in :cite:t:`mpion-zhang_empirical_2014` Eq. (8) (note there is a typo in the paper and there should not be a minus sign in Eq. 8). .. math:: - W_\mathrm{M} = \exp\left[ -\left( a_1 \frac{E^2}{E_\mathrm{b}} + a_2 \frac{E}{E_\mathrm{b}} + a_3 \right) \right] W_\mathrm{ADK} + W_\mathrm{M} = \exp\left[ a_1 \frac{E^2}{E_\mathrm{b}} + a_2 \frac{E}{E_\mathrm{b}} + a_3 \right] W_\mathrm{ADK} The parameters :math:`a_1` through :math:`a_3` are independent of :math:`E` and can be found in the same reference. :math:`E_\mathrm{b}` is the classical Barrier Suppresion Ionization (BSI) field strength :math:`E_\mathrm{b} = U_\mathrm{ion}^2 / (4 Z)` given here in atomic units (AU). For a detailed description of conversion between unit systems consider the book by :cite:t:`mpion-Mulser2010`. Testing ^^^^^^^ -* `Testing the field ionization module <../../../../Examples/Tests/field_ionization/README.rst>`_. +* `Testing the field ionization module <../../../../en/latest/usage/examples/field_ionization/README.html>`_. .. bibliography:: :keyprefix: mpion-