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73 changes: 48 additions & 25 deletions README.rst
Original file line number Diff line number Diff line change
Expand Up @@ -9,61 +9,84 @@ Stellarator Optimization Package

|Docs| |UnitTests| |RegressionTests| |Codecov|

DESC solves for and optimizes 3D MHD equilibria using pseudo-spectral numerical methods and automatic differentiation.
DESC solves for and optimizes 3D MHD equilibria using pseudo-spectral numerical methods
and automatic differentiation.

The theoretical approach and implementation details used by DESC are presented in the
following papers and documented at Theory_. Please cite our work if you use DESC!

- Dudt, D. & Kolemen, E. (2020). DESC: A Stellarator Equilibrium Solver.
[`Physics of Plasmas <https://doi.org/10.1063/5.0020743>`__]
[`pdf <https://github.com/PlasmaControl/DESC/blob/master/publications/dudt2020/dudt2020desc.pdf>`__]
- Panici, D. et al (2023). The DESC Stellarator Code Suite Part I: Quick and accurate equilibria computations.
[`Journal of Plasma Physics <https://doi.org/10.1017/S0022377823000272>`__]
[`pdf <https://github.com/PlasmaControl/DESC/blob/master/publications/panici2022/Panici_DESC_Stellarator_suite_part_I_quick_accurate_equilibria.pdf>`__]
- Conlin, R. et al. (2023). The DESC Stellarator Code Suite Part II: Perturbation and continuation methods.
[`Journal of Plasma Physics <https://doi.org/10.1017/S0022377823000399>`__]
[`pdf <https://github.com/PlasmaControl/DESC/blob/master/publications/conlin2022/conlin2022perturbations.pdf>`__]
- Dudt, D. et al. (2023). The DESC Stellarator Code Suite Part III: Quasi-symmetry optimization.
[`Journal of Plasma Physics <https://doi.org/10.1017/S0022377823000235>`__]
[`pdf <https://github.com/PlasmaControl/DESC/blob/master/publications/dudt2022/dudt2022optimization.pdf>`__]

The theoretical approach and implementation details used by DESC are presented in these papers [1]_ [2]_ [3]_ [4]_ and documented at Theory_.
Please cite our work if you use DESC!

.. [1] Dudt, D. & Kolemen, E. (2020). DESC: A Stellarator Equilibrium Solver. [`Physics of Plasmas <https://doi.org/10.1063/5.0020743>`__] [`pdf <https://github.com/PlasmaControl/DESC/blob/master/publications/dudt2020/dudt2020desc.pdf>`__]
.. [2] Panici, D. et al (2023). The DESC Stellarator Code Suite Part I: Quick and accurate equilibria computations. [`JPP <https://doi.org/10.1017/S0022377823000272>`__] [`pdf <https://github.com/PlasmaControl/DESC/blob/master/publications/panici2022/Panici_DESC_Stellarator_suite_part_I_quick_accurate_equilibria.pdf>`__]
.. [3] Conlin, R. et al. (2023). The DESC Stellarator Code Suite Part II: Perturbation and continuation methods. [`JPP <https://doi.org/10.1017/S0022377823000399>`__] [`pdf <https://github.com/PlasmaControl/DESC/blob/master/publications/conlin2022/conlin2022perturbations.pdf>`__]
.. [4] Dudt, D. et al. (2023). The DESC Stellarator Code Suite Part III: Quasi-symmetry optimization. [`JPP <https://doi.org/10.1017/S0022377823000235>`__] [`pdf <https://github.com/PlasmaControl/DESC/blob/master/publications/dudt2022/dudt2022optimization.pdf>`__]
.. _Theory: https://desc-docs.readthedocs.io/en/latest/theory_general.html

Quick Start
===========

.. role:: console(code)
:language: console

The easiest way to install DESC is from pypi: :console:`pip install desc-opt`
The easiest way to install DESC is from PyPI: ``pip install desc-opt``

For more detailed instructions on installing DESC and its dependencies, see Installation_.
The code is run using the syntax :console:`desc <path/to/inputfile>` and the full list of command line options are given in `Command Line Interface`_. (Note that you may have to prepend the command with :console:`python -m`)

DESC can be ran in two ways:
The best place to start learning about DESC is our tutorials:

The first is through an input file specifying the equilibrium and solver options, this way can also can also accept VMEC input files.
- `Basic fixed boundary equilibrium`_: running from a VMEC input, creating an equilibrium from scratch
- `Advanced equilibrium`_: continuation and perturbation methods.
- `Free boundary equilibrium`_: vacuum and or finite beta with external field.
- `Using DESC outputs`_: analysis, plotting, saving to VMEC format.
- `Basic optimization`_: specifying objectives, fixing degrees of freedom.
- `Advanced optimization`_: advanced constraints, precise quasi-symmetry, constrained optimization.
- `Near axis constraints`_: loading solutions from QSC/QIC and fixing near axis expansion.

The second is through a python script, where the equilibrium and solver options are specified programmatically, this method offers much more flexibility over what types of equilibrium solution, optimization and analysis can be performed.
See the tutorial `Script Interface`_ for more detailed information.
For details on the various objectives, constraints, optimizable objects and more, see
the full `api documentation`_.

Refer to `Inputs`_ for documentation on how to format the input file.
The equilibrium solution is output in a HDF5 binary file, whose format is detailed in `Outputs`_.
If all you need is an equilibrium solution, the simplest method is through the command
line by giving an input file specifying the equilibrium and solver options, this
way can also can also accept VMEC input files.

As an example usage of the input file method, to use DESC to solve for the equilibrium of the high-beta, D-shaped plasma described with the DSHAPE input file, the command from the :console:`DESC` directory is
:console:`desc -p desc/examples/DSHAPE`, where the :console:`-p` flag tells DESC to plot the results once it finishes.
The code is run using the syntax ``desc <path/to/inputfile>`` and the full list
of command line options are given in `Command Line Interface`_. (Note that you may have
to prepend the command with ``python -m``)

An example of the script usage to solve and optimize an equilibrium, refer to the python script `desc/examples/precise_QA.py`, which can be run from the :console:`DESC` directory from the command line with :console:`python3 desc/examples/precise_QA.py`
Refer to `Inputs`_ for documentation on how to format the input file.

The equilibrium solution is output in a HDF5 binary file, whose format is detailed in `Outputs`_.

.. _Installation: https://desc-docs.readthedocs.io/en/latest/installation.html
.. _Command Line Interface: https://desc-docs.readthedocs.io/en/latest/command_line.html
.. _Inputs: https://desc-docs.readthedocs.io/en/latest/input.html
.. _Outputs: https://desc-docs.readthedocs.io/en/latest/output.html
.. _Script Interface: https://desc-docs.readthedocs.io/en/latest/notebooks/tutorials/02_Script_Interface.html
.. _Basic fixed boundary equilibrium: https://desc-docs.readthedocs.io/en/latest/notebooks/tutorials/basic_equilibrium.html
.. _Advanced equilibrium: https://desc-docs.readthedocs.io/en/latest/notebooks/tutorials/advanced_equilibrium_continuation.html
.. _Free boundary equilibrium: https://desc-docs.readthedocs.io/en/latest/notebooks/tutorials/free_boundary_equilibrium.html
.. _Using DESC outputs: https://desc-docs.readthedocs.io/en/latest/notebooks/tutorials/use_outputs.html
.. _Basic optimization: https://desc-docs.readthedocs.io/en/latest/notebooks/tutorials/basic_optimization.html
.. _Advanced optimization: https://desc-docs.readthedocs.io/en/latest/notebooks/tutorials/advanced_optimization.html
.. _Near axis constraints: https://desc-docs.readthedocs.io/en/latest/notebooks/tutorials/nae_constraint.html
.. _api documentation: https://desc-docs.readthedocs.io/en/latest/api.html

Repository Contents
===================

- desc_ contains the source code including the main script and supplemental files. Refer to the API_ documentation for details on all of the available functions and classes.
- docs_ contains the documentation files.
- examples_ contains example input files along with corresponding DESC solutions, which are also accessible using the `desc.examples.get` function.
- tests_ contains routines for automatic testing.
- publications_ contains PDFs of publications by the DESC group, as well as scripts and data to reproduce the results of these papers.

.. _desc: https://github.com/PlasmaControl/DESC/tree/master/desc
.. _docs: https://github.com/PlasmaControl/DESC/tree/master/docs
.. _examples: https://github.com/PlasmaControl/DESC/tree/master/desc/examples
.. _tests: https://github.com/PlasmaControl/DESC/tree/master/tests
.. _publications: https://github.com/PlasmaControl/DESC/tree/master/publications
.. _API: https://desc-docs.readthedocs.io/en/latest/api.html

Contribute
Expand Down
42 changes: 22 additions & 20 deletions desc/magnetic_fields/_current_potential.py
Original file line number Diff line number Diff line change
Expand Up @@ -16,14 +16,14 @@
class CurrentPotentialField(_MagneticField, FourierRZToroidalSurface):
"""Magnetic field due to a surface current potential on a toroidal surface.

surface current K is assumed given by
K = n x ∇ Φ
where:
n is the winding surface unit normal.
Phi is the current potential function,
which is a function of theta and zeta.
This function then uses biot-savart to find the
B field from this current density K on the surface.
Surface current K is assumed given by K = n x ∇ Φ
where:

- n is the winding surface unit normal.
- Phi is the current potential function, which is a function of theta and zeta.

This function then uses biot-savart to find the B field from this current
density K on the surface.

Parameters
----------
Expand Down Expand Up @@ -159,7 +159,7 @@ def potential_dzeta(self, new):
def save(self, file_name, file_format=None, file_mode="w"):
"""Save the object.

**Not supported for this object!
**Not supported for this object!**

Parameters
----------
Expand Down Expand Up @@ -275,19 +275,21 @@ class FourierCurrentPotentialField(
):
"""Magnetic field due to a surface current potential on a toroidal surface.

surface current K is assumed given by
Surface current K is assumed given by

K = n x ∇ Φ

Φ(θ,ζ) = Φₛᵥ(θ,ζ) + Gζ/2π + Iθ/2π

where:

K = n x ∇ Φ
Φ(θ,ζ) = Φₛᵥ(θ,ζ) + Gζ/2π + Iθ/2π
- n is the winding surface unit normal.
- Phi is the current potential function, which is a function of theta and zeta,
and is given as a secular linear term in theta/zeta and a double Fourier
series in theta/zeta.

where:
n is the winding surface unit normal.
Phi is the current potential function,
which is a function of theta and zeta,
and is given as a secular linear term in theta/zeta
and a double Fourier series in theta/zeta.
This function then uses biot-savart to find the
B field from this current density K on the surface.
This function then uses biot-savart to find the B field from this current
density K on the surface.

Parameters
----------
Expand Down
14 changes: 14 additions & 0 deletions docs/Makefile
Original file line number Diff line number Diff line change
Expand Up @@ -18,9 +18,23 @@ variables.csv:
optimizers.csv:
python write_optimizers.py

clean:
# generated by sphinx
rm -rf _build/
rm -rf _api/
# generated by us
rm -f desc*.csv
rm -f optimizers.csv
rm -f variables.csv
rm -f variables.rst

.PHONY: help Makefile variables.csv optimizers.csv

# Catch-all target: route all unknown targets to Sphinx using the new
# "make mode" option. $(O) is meant as a shortcut for $(SPHINXOPTS).
%: Makefile variables.csv optimizers.csv
@$(SPHINXBUILD) -M $@ "$(SOURCEDIR)" "$(BUILDDIR)" $(SPHINXOPTS) $(O)
rm -f desc*.csv
rm -f optimizers.csv
rm -f variables.csv
rm -f variables.rst
10 changes: 6 additions & 4 deletions docs/api.rst
Original file line number Diff line number Diff line change
@@ -1,6 +1,6 @@
=================
API Documentation
=================
====================
Alphabetical Listing
====================

Basis
*****
Expand Down Expand Up @@ -123,7 +123,6 @@ IO
:recursive:
:template: class.rst

desc.io.InputReader
desc.io.load

Magnetic Fields
Expand All @@ -134,6 +133,8 @@ Magnetic Fields
:recursive:
:template: class.rst

desc.magnetic_fields.CurrentPotentialField
desc.magnetic_fields.FourierCurrentPotentialField
desc.magnetic_fields.ScaledMagneticField
desc.magnetic_fields.SumMagneticField
desc.magnetic_fields.ToroidalMagneticField
Expand Down Expand Up @@ -188,6 +189,7 @@ Objective Functions
desc.objectives.GoodCoordinates
desc.objectives.HelicalForceBalance
desc.objectives.Isodynamicity
desc.objectives.LinearObjectiveFromUser
desc.objectives.MagneticWell
desc.objectives.MeanCurvature
desc.objectives.MercierStability
Expand Down
31 changes: 31 additions & 0 deletions docs/api_continuation.rst
Original file line number Diff line number Diff line change
@@ -0,0 +1,31 @@
======================
Solving and Perturbing
======================

Continuation
************
``desc.continuation`` contains the methods used for solving equilibrium problems.
``solve_continuation_automatic`` is usually the easiest method, users desiring more
control over the process can also use ``solve_continuation``.

.. autosummary::
:toctree: _api/continuation
:recursive:

desc.continuation.solve_continuation_automatic
desc.continuation.solve_continuation


Perturbations
*************
``desc.perturbations.perturb`` is used inside of the continuation methods but can
also be used alone to perform sensitivity analysis or perform parameter scans.
``optimal_perturb`` is effectively a single step of a constrained optimization solver.

.. autosummary::
:toctree: _api/perturbations
:recursive:

desc.perturbations.perturb
desc.perturbations.optimal_perturb
desc.perturbations.get_deltas
69 changes: 69 additions & 0 deletions docs/api_equilibrium.rst
Original file line number Diff line number Diff line change
@@ -0,0 +1,69 @@
==========================================
Equilibrium, Surfaces, and Profile classes
==========================================


Equilibrium
***********
The ``Equilibrium`` is the core class representing an MHD equilibrium configuration.
An ``EquilibriaFamily`` is a ``list`` like object for storing multiple equilibria.

.. autosummary::
:toctree: _api/equilibrium
:recursive:
:template: class.rst

desc.equilibrium.Equilibrium
desc.equilibrium.EquilibriaFamily


Geometry
********
The ``desc.geometry`` module contains important classes such as ``FourierRZToroidalSurface``
for representing the shape of the plasma boundary, as well as classes for representing
the magnetic axis, cross section, and various space curves.

.. autosummary::
:toctree: _api/geometry/
:recursive:
:template: class.rst

desc.geometry.FourierRZToroidalSurface
desc.geometry.FourierRZCurve
desc.geometry.FourierXYZCurve
desc.geometry.FourierPlanarCurve
desc.geometry.SplineXYZCurve
desc.geometry.ZernikeRZToroidalSection


Profiles
********
``desc.profiles`` contains objects representing 1-D flux functions such as pressure,
current, rotational transform, temperature, or density. It is also possible to combine
profiles together by addition, multiplication, or scaling.

.. autosummary::
:toctree: _api/profiles
:recursive:
:template: class.rst

desc.profiles.PowerSeriesProfile
desc.profiles.SplineProfile
desc.profiles.MTanhProfile
desc.profiles.ScaledProfile
desc.profiles.SumProfile
desc.profiles.ProductProfile


Utilities
*********
``desc.compat`` has utility functions for enforcing sign conventions or rescaling
equilibria to a given size and/or field strength.

.. autosummary::
:toctree: _api/compat
:recursive:

desc.compat.ensure_positive_jacobian
desc.compat.flip_helicity
desc.compat.rescale
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