VMEC++

VMEC++ is a Python-friendly, from-scratch reimplementation in C++ of the Variational Moments Equilibrium Code (VMEC), a free-boundary ideal-MHD equilibrium solver for stellarators and tokamaks.

The original version was written by Steven P. Hirshman and colleagues in the 1980s and 1990s. The latest version of the original code is called PARVMEC and is available here.

Compared to its Fortran predecessors, VMEC++:

• has a zero-crash policy and reports issues via standard Python exceptions
• allows hot-restarting a run from a previous converged state (see Hot restart)
• supports inputs in the classic INDATA format as well as simpler-to-parse JSON files; it is also simple to construct input objects programmatically in Python
• typically runs faster
• comes with substantial documentation of its internal numerics

VMEC++ can run on a laptop, but it is a suitable component for large-scale stellarator optimization pipelines.

On the other hand, some features of the original Fortran VMEC are not available in VMEC++. See below for more details.

Table of Contents

• Usage
  • As a Python package
  • With SIMSOPT
  • As a command line tool
  • As a Docker image
• Installation
  • Ubuntu
  • Arch
  • Fedora
  • MacOS
  • With Nix
  • As part of a conda environment
  • C++ build from source
• Hot restart
• Differences with respect to PARVMEC/VMEC2000
• Roadmap
• Related repositories
• License

Usage

This is a quick overview of the three main ways in which you can use VMEC++. See examples/ for some actual example scripts. Suitable input files are found in examples/data. If unsure where to start, we suggest giving the w7x case a try, which is a five-field-period stellarator case for the Wendelstein 7-X stellarator.

For example examples/force_residual_convergence.py runs fixed-boundary VMEC++ on the W7-X case and plots the convergence of the force residuals.

As a Python package

VMEC++ offers a simple Python API:

import vmecpp

# Construct a VmecInput object, e.g. from a classic Fortran input file
vmec_input = vmecpp.VmecInput.from_file("input.w7x")  # or VMEC++'s w7x.json format
# This is a normal Python object: it can be constructed and modified programmatically
vmec_input.rbc[0, 0] *= 1.1

# Run VMEC++
vmec_output = vmecpp.run(vmec_input)

# Inspect the results programmatically or save them as a classic wout file
print(vmec_output.mercier.iota)
vmec_output.wout.save("wout_w7x.nc")

All other output files are accessible via members of the vmec_output object called threed1_volumetrics, jxbout and mercier.

An optional iteration_callback is available to investigate the progress of the solver. It can be used to interactively debug and interact with vmecpp's state from a Python repl, or generate animations of the convergence progress like in examples/watch_solve.py.

With SIMSOPT

SIMSOPT is a popular stellarator optimization framework. VMEC++ implements a SIMSOPT-friendly wrapper that makes it easy to use it with SIMSOPT.

import vmecpp.simsopt_compat

vmec = vmecpp.simsopt_compat.Vmec("input.w7x")
print(f"Computed plasma volume: {vmec.volume()}")

As a command line tool

You can use VMEC++ directly as a CLI tool. In a terminal in which Python has access to the VMEC++ package:

# run on a given input file -> produce corresponding wout_w7x.nc
# vmecpp is a python module and can be either run with `python -m` or directly as a script
vmecpp examples/data/input.w7x

# check all options
vmecpp --help

As a Docker image

A pre-built Docker image is available at https://github.com/proximafusion/vmecpp/pkgs/container/vmecpp. Note that at present it is only updated occasionally.

See docker/README.md for more information and instructions on how to build a new image.

Installation

The easiest method for installing vmecpp is using pip:

pip install vmecpp

For usage as part of MPI-parallelized SIMSOPT applications, you might want to also install MPI on your machine and pip install mpi4py.

Alternatively you can build the latest vmecpp directly from source according to the appropriate instructions below.

Ubuntu/Debian

Ubuntu 22.04 and 24.04, as well as Debian 12 are officially supported.

1. Install required system packages:

sudo apt-get install -y build-essential cmake gfortran libnetcdf-dev libomp-dev libhdf5-dev python3-dev

2. Install VMEC++ as a Python package (possibly after creating a dedicated virtual environment):

pip install git+https://github.com/proximafusion/vmecpp

The procedure will take a few minutes as it will build VMEC++ and some dependencies from source.

A common issue on Ubuntu is a build failure due to no python executable being available in PATH, since on Ubuntu the executable is called python3. When installing in a virtual environment (which is always a good idea anyways) python will be present. Otherwise the Ubuntu package python-is-python3 provides the python alias.

Arch Linux

1. Install required system packages:

pacman -Sy --noconfirm python-pip gcc gcc-fortran openmp hdf5 netcdf

2. Install VMEC++ as a Python package (possibly after creating a virtual environment):

python -m pip install git+https://github.com/proximafusion/vmecpp

Fedora

Fedora 41 is officially supported.

1. Install required system packages:

dnf install -y python3.10-devel cmake g++ gfortran libomp-devel hdf5-devel netcdf-devel

2. Install VMEC++ as a Python package (possibly after creating a virtual environment):

# If you are installing with MPI support, remember to source the mpi compiler first
. /etc/profile.d/modules.sh
python3.10 -m pip install git+https://github.com/proximafusion/vmecpp

MacOS

1. Install dependencies via Homebrew:

brew install python@3.10 ninja libomp netcdf-cxx git
# And if they aren't pre-installed already:
brew install gcc cmake

2. Install VMEC++ as a Python package (possibly after creating a virtual environment):

# tell cmake where to find gfortran and gcc as they have non-standard names
export FC=$(which gfortran-14)
# OpenMP headers live under a different path on newer OS-X versions, so CMake can't find them
export OpenMP_ROOT=$(brew --prefix)/opt/libomp
export HDF5_ROOT=$(brew --prefix hdf5)
python3.10 -m pip install git+https://github.com/proximafusion/vmecpp

With Nix (Community support)

For a Linux development shell with the latest supported Python version:

nix develop
python --version
python -m pip install -e .[test]

The shell provides Python 3.13 together with the native build dependencies needed to build and test VMEC++, including CMake, GCC, GFortran, HDF5, NetCDF, OpenMPI, and Git LFS.

As part of a conda environment

VMEC++ is currently not packaged for conda, but all its dependencies are and VMEC++ can be installed inside a conda environment. An example environment.yml file is provided here that can be used, after cloning the vmecpp repository, as:

git clone https://github.com/proximafusion/vmecpp.git
cd vmecpp
# this creates a "vmecpp" conda environment
conda env create --file environment.yml
# use the environment as usual
conda activate vmecpp

C++ build from source

After having installed the build dependencies as shown above, you can compile the C++ core of VMEC++ via CMake or Bazel. E.g. with CMake:

git clone https://github.com/proximafusion/vmecpp.git
cd vmecpp
cmake -B build  # create and configure build directory
cmake --build build --parallel  # build VMEC++
# you can now use the vmec_standalone C++ executable to run VMEC on a VMEC++ input JSON file, e.g.
./build/vmec_standalone ./examples/data/solovev.json

The main C++ source code tree is located at src/vmecpp/cpp/vmecpp.

Hot restart

By passing the output of a VMEC++ run as initial state for a subsequent one, VMEC++ is initialized using the previously converged equilibrium. This can dramatically decrease the number of iterations to convergence when running VMEC++ on a configuration that is very similar to the converged equilibrium.

Example

import vmecpp

vmec_input = vmecpp.VmecInput.from_file("w7x.json")

# Base run
vmec_output = vmecpp.run(vmec_input)

# Now let's perturb the plasma boundary a little bit...
vmec_input.rbc[0, 0] *= 0.8
vmec_input.rbc[1, 0] *= 1.2
# ...and fix up the multigrid steps: hot-restarted runs only allow a single step
vmec_input.ns_array = vmec_input.ns_array[-1:]
vmec_input.ftol_array = vmec_input.ftol_array[-1:]
vmec_input.niter_array = vmec_input.niter_array[-1:]

# We can now run with hot restart:
# passing the previously obtained vmec_output ensures that
# the run starts already close to the equilibrium, so it will take
# very few iterations to converge this time!
hot_restarted_output = vmecpp.run(vmec_input, restart_from=vmec_output)

Differentiable runs

The wout quantities support autodiff with JAX. jax.grad can differentiate objectives written in terms of wout quantities with respect to the boundary coefficients rbc, zbs. When they are JAX tracers, vmecpp.run solves through the implicit adjoint of the force residual, which needs a build with -DVMECPP_ENABLE_ENZYME=ON. Otherwise it returns NumPy arrays as before.

Leaves that change shape depending on iteration progress (fsqt trace for example) are treated as aux data to support differentiability. jxbout, mercier and threed1 tables are also treated as non-differentiable aux data. Under jax.jit these tables and diagnostics are None.

import jax
import jax.numpy as jnp
import vmecpp

vmec_input = vmecpp.VmecInput.from_file("cth_like_fixed_bdy.json")


def aspect(rbc, zbs):
    boundary = vmec_input.model_copy(update={"rbc": rbc, "zbs": zbs})
    return vmecpp.run(boundary, verbose=False).wout.aspect


rbc = jnp.asarray(vmec_input.rbc)
zbs = jnp.asarray(vmec_input.zbs)
d_aspect_d_rbc, d_aspect_d_zbs = jax.grad(aspect, argnums=(0, 1))(rbc, zbs)

Full tests and validation against the reference Fortran VMEC v8.52

When developing the C++ core, it's advisable to locally run the full C++ tests for debugging or to validate changes before submitting them. The full C++ tests live in src/vmecpp/cpp/vmecpp_large_cpp_tests and use Git LFS for large test data files. To run them locally (after cloning with git lfs pull to fetch the LFS objects):

cd src/vmecpp/cpp
bazel test --config=opt //vmecpp/... //vmecpp_large_cpp_tests/...

The CI of this repo runs these tests automatically.

The single-thread runtimes as well as the contents of the "wout" file produced by VMEC++ can be compared with those of Fortran VMEC v8.52. The full validation test can be found at https://github.com/proximafusion/vmecpp-validation, including a set of sensible input configurations, parameter scan values and tolerances that make the comparison pass. See that repo for more information.

This full validation (~219 input configurations) is run against every commit to main and can also be triggered on demand from the Full V&V against reference VMEC workflow (click "Run workflow"). It builds vmecpp from the corresponding commit rather than using the version pinned by vmecpp-validation.

Differences with respect to PARVMEC/VMEC2000

VMEC++:

• reports issues via standard Python exceptions and has a zero crash policy
• allows hot-restarting a run from a previous converged state (see Hot restart)
• supports inputs in the classic INDATA format as well as simpler-to-parse JSON files; it is also simple to construct input objects programmatically in Python
• The Fortran version falls back to fixed-boundary computation if the mgrid file cannot be found; VMEC++ (gracefully) errors out instead.
• The Fortran version accepts both the full path or filename of the input file as well as the "extension", i.e., the part after input.; VMEC++ only supports a valid filename or full path to an existing input file.
• employs the same parallelization strategy as Fortran VMEC, but VMEC++ leverages OpenMP for a multi-thread implementation rather than Fortran VMEC's MPI parallelization: as a consequence it cannot parallelize over multiple nodes, but can utilize shared caches between threads
• Reduces the force spikes between multi-grid stages in free-boundary, which should lead to faster and more robust free-boundary convergence (for details see https://github.com/proximafusion/vmecpp/releases/tag/v0.7.0)
• Stable recurrence for Neumann kernel integrals enables convergence of free-boundary solves at high mpol, ntor (see https://github.com/proximafusion/vmecpp/releases/tag/v0.5.3)
• Uses FFT kernels optimized for small mode numbers generated using FFTX instead of DFT for supported resolutions. They give a 10-20% speedup relative to the DFT counterparts.
• implements the iteration algorithm of Fortran VMEC 8.52, which sometimes has different convergence behavior from (PAR)VMEC 9.0: some configurations might converge with VMEC++ and not with (PAR)VMEC 9.0, and vice versa. One deliberate exception: at multigrid grid transitions, the rollback backup of the state vector is taken after the radial interpolation of the coarse-grid solution (matching PARVMEC/VMEC2000 since 2017-01-24, "SPH 012417"), not before it as in VMEC 8.52 -- with the 8.52 ordering, the first restart of a stage silently discards the interpolated state and the finer stages effectively re-solve from a cold start

Limitations with respect to the Fortran implementations

• lrfp flag is available for wout compatibility, but RFP-specific physics is not implemented yet - only stellarators/Tokamaks for now
• several profile parameterizations are not fully implemented yet:
  • sum_cossq_s
  • sum_cossq_sqrts
  • sum_cossq_s_free
• 2D preconditioning using block-tridiagonal solver (BCYCLIC) is not implemented; neither are the associated input fields precon_type and prec2d_threshold
• VMEC++ only computes the output quantities if the run converged (can be overridden via return_outputs_even_if_not_converged input)

Related repositories

• proximafusion/vmecpp-validation - Validation tests for VMEC++
• proximafusion/the_numerics_of_vmecpp - Documentation of the numerical details of VMEC++
• proximafusion/vmecpp-benchmarks - Performance benchmarks comparing VMEC++ and VMEC2000

License

vmecpp is distributed under the terms of the MIT license.