diff --git a/PAPER_JOSS/paper.bib b/PAPER_JOSS/paper.bib index 912f4dd..26b0590 100644 --- a/PAPER_JOSS/paper.bib +++ b/PAPER_JOSS/paper.bib @@ -316,3 +316,17 @@ @article{eder_integration_2021 pages = {P3.1059}, file = {Eder et al. - Integration of the guiding-center equations in tor.pdf:/Users/micheder/Zotero/storage/NKCA46JJ/Eder et al. - Integration of the guiding-center equations in tor.pdf:application/pdf}, } + +@article{kasilov_geometric_2016, +title = {Geometric integrator for charged particle orbits in axisymmetric fusion devices}, +journal = {Computer Physics Communications}, +volume = {207}, +pages = {282-286}, +year = {2016}, +issn = {0010-4655}, +doi = {10.1016/j.cpc.2016.07.019}, +url = {https://www.sciencedirect.com/science/article/pii/S0010465516302077}, +author = {S.V. Kasilov and A.M. Runov and W. Kernbichler}, +keywords = {Plasma physics, Kinetic modelling, Numerical integrators}, +abstract = {A semi-analytical geometric integrator of guiding centre orbits in an axisymmetric tokamak is described. The integrator preserves all three invariants of motion up to computer accuracy at the expense of reduced orbit accuracy and it is roughly an order of magnitude more efficient than a direct solution of the equations of guiding centre motion with a standard high order adaptive ODE integrator.} +} diff --git a/PAPER_JOSS/paper.md b/PAPER_JOSS/paper.md index f09e642..d56e6c9 100644 --- a/PAPER_JOSS/paper.md +++ b/PAPER_JOSS/paper.md @@ -23,7 +23,7 @@ authors: - name: Daniel Forstenlechner affiliation: 1 - name: Georg S. Graßler - affiliation: 1 + affiliation: 1 - name: Sergei V. Kasilov affiliation: "1, 2, 3" - name: Winfried Kernbichler @@ -48,33 +48,34 @@ bibliography: paper.bib --- # Introduction -Extremely hot plasmas with a temperature of the order of hundred million degrees Celsius are needed to produce energy from nuclear fusion. Under these conditions, hydrogen isotopes are fused, and energy is released. The energy release from 1 kg of fusion fuel corresponds approximately to that of 10000 tons of coal. A future use of this energy source is the subject of worldwide research projects. The confinement of such hot plasmas, however, poses major physical and technological problems for researchers. In particular, complex numerical methods are necessary to understand the physics of such plasmas in complicated toroidal magnetic fields. +Extremely hot plasmas with a temperature of the order of hundred million degrees Celsius are needed to produce energy from nuclear fusion. Under these conditions, hydrogen isotopes are fused, and energy is released. The energy release from 1 kg of fusion fuel corresponds approximately to that of 10000 tons of coal. This high energy density has made fusion the subject of worldwide research projects. The confinement of such hot plasmas, however, poses major physical and technological problems for researchers. In particular, complex numerical methods are necessary to understand the physics of such plasmas in complicated toroidal magnetic fields. -An important kinetic approach for simulating the collective behavior of a plasma utilizes direct modeling of particle orbits. A well-known approximation for computing the motion of electrically charged particles in slowly varying electromagnetic fields is to reduce the dynamical equations by separating the relatively fast circular motion around a point called the guiding-center, and primarily treat the relatively slow drift motion of this point. This drift motion is described by the guiding-center equations in non-canonical Hamiltonian form; see, e.g., [@boozer_guiding_1980], [@littlejohn_variational_1983] and [@cary_hamiltonian_2009]. +An important kinetic approach for simulating the collective behavior of a plasma uses direct modeling of particle orbits. A well-known approximation for computing the motion of electrically charged particles in slowly varying electromagnetic fields is to reduce the dynamical equations by separating the relatively fast circular motion around a point called the guiding-center, and primarily treat the relatively slow drift motion of this point. This drift motion is described by the guiding-center equations in non-canonical Hamiltonian form [@boozer_guiding_1980; @littlejohn_variational_1983; @cary_hamiltonian_2009]. -Here, we provide `GORILLA`: an efficient code for the purpose of solving the guiding-center equations. This code is a numerical implementation of the novel, quasi-geometric integration method described by @eder_quasi-geometric_2020. -There exists a variety of codes for tracing guiding-center drift motion including ORBIT [@white_hamiltonian_1984], DCOM [@wakasa2001monte], MOCA [@tribaldos_monte_2001], FORTEC-3D [@satake_non-local_2005], VENUS [@isaev_venusf_2006], NEO-MC [@allmaier_variance_2008], XGC [@ku_full-f_2009], ANTS [@drevlak_thermal_2009], ASCOT [@kurki-suonio_ascot_2009], VENUS-LEVIS [@pfefferle_venus-levis_2014], SIMPLE [@albert_symplectic_2020] etc; see also [@beidler_benchmarking_2011]. Most of these codes solve the guiding-center equations primarily in the plasma core of toroidal fusion devices. Due to its formulation in general curvilinear coordinates, `GORILLA` is not limited by the field topology. That means that the computation domain of `GORILLA` covers both the closed field line region (i.e. the plasma core) and the open field line region (i.e. the scrape-off layer). +Here, we provide `GORILLA`: an efficient code for the purpose of solving the guiding-center equations. This code is a numerical implementation of the novel, quasi-geometric integration method in 3D geometry described by @eder_quasi-geometric_2020. A related method for axisymmetric geometry has been realized in the code K2D [@kasilov_geometric_2016]. +Apart from this quasi-geometric approach there exists a variety of codes for tracing guiding-center drift motion including ORBIT [@white_hamiltonian_1984], DCOM [@wakasa2001monte], MOCA [@tribaldos_monte_2001], FORTEC-3D [@satake_non-local_2005], VENUS [@isaev_venusf_2006], NEO-MC [@allmaier_variance_2008], XGC [@ku_full-f_2009], ANTS [@drevlak_thermal_2009], ASCOT [@kurki-suonio_ascot_2009], VENUS-LEVIS [@pfefferle_venus-levis_2014], SIMPLE [@albert_symplectic_2020]; see also @beidler_benchmarking_2011. Most of these codes solve the guiding-center equations primarily in the plasma core of toroidal fusion devices. Due to its formulation in general curvilinear coordinates, `GORILLA` is not limited by the field topology. That means that the computation domain of `GORILLA` covers both the closed field line region (i.e., the plasma core) and the open field line region (i.e., the scrape-off layer). # Summary -`GORILLA` is a Fortran code that computes guiding-center orbits for charged particles of given mass, charge and energy in toroidal fusion devices with three-dimensional field geometry. -Conventional methods for integrating the guiding-center equations utilize high order interpolation of the electromagnetic field in space. -In `GORILLA`, a special linear interpolation employing a spatial mesh is used for the discretization of the electromagnetic field. -This leads to locally linear equations of motion with piecewise constant coefficients. +`GORILLA` is a Fortran code that computes guiding-center orbits for charged particles of given mass, charge and energy in toroidal fusion devices with three-dimensional field geometry. +Conventional methods for integrating the guiding-center equations use high order interpolation of the electromagnetic field in space. +In `GORILLA`, a linear interpolation of a specific representation of quantities in the guiding-center system employing a spatial mesh is used for the discretization of the electromagnetic field. +This leads to locally linear equations of motion with piecewise constant coefficients. As shown by @eder_quasi-geometric_2020, this local linearization approach retains the Hamiltonian structure of the guiding-center equations. For practical purposes this means that the total energy, the magnetic moment and the phase-space volume are conserved. -Furthermore, the approach reduces computational effort and sensitivity to noise in the electromagnetic field. In `GORILLA`, guiding-center orbits are computed without taking into account collisions between particles. Such exemplary guiding-center orbits obtained with `GORILLA` can be seen in \autoref{fig:example} where the magnetic field of a real-world fusion device is used, specifically the tokamak “ASDEX Upgrade”. +Furthermore, the approach reduces computational effort and sensitivity to noise in the electromagnetic field. In `GORILLA`, guiding-center orbits are computed without taking into account collisions between particles. Two examples of guiding-center orbits obtained with `GORILLA` can be seen in \autoref{fig:example} where the magnetic field of a real-world fusion device is used, specifically the tokamak “ASDEX Upgrade”. # Statement of need -`GORILLA` is designed to be used by researchers in scientific plasma physics simulations in the field of magnetic confinement fusion. -In such complex simulations, a simple interface for the efficient integration of the guiding-center equations is needed. Specifically, the initial set of coordinates in five-dimensional phase-space is provided (i.e. guiding-center position, parallel and perpendicular velocity) and the main interest is to retrieve the phase-space coordinates after a prescribed time step while the integration process itself is irrelevant. Such a pure “orbit time step routine” acting as an interface with a plasma physics simulation is provided. -The integration process itself, however, can also be of great interest. Therefore, a program allowing the detailed analysis of guiding-center orbits, the time evolution of their respective invariants of motion and Poincaré plots is also available. +`GORILLA` is designed to be used by researchers in scientific plasma physics simulations in the field of magnetic confinement fusion. +In such complex simulations, a simple interface for the efficient integration of the guiding-center equations is needed. Specifically, the initial position in five-dimensional phase-space is provided in terms of guiding-center coordinates (i.e., guiding-center position, parallel and perpendicular velocity) and the main interest is to retrieve the phase-space position after a prescribed time step. Such a pure “orbit time step routine” acting as an interface with a plasma physics simulation is provided. +The integration process itself, however, can also be of great interest. Therefore, a program allowing the detailed analysis of guiding-center orbits, the time evolution of their respective invariants of motion and Poincaré plots is also available. A unique feature of `GORILLA` is the direct way in which fluxes through cell boundaries can be directly obtained while conserving physical invariants. These properties result from the geometric approach of linear approximation in tetrahedal cells. Thus the computation of moments of the distribution function such as current densities from Monte-Carlo sampling can be much more efficient and stable than in usual orbit tracers. Furthermore, the mesh is agnostic to whether an orbit is inside or outside the magnetic separatrix, and does not rely on flux coordinates. Therefore `GORILLA` is a flexible tool that is useful in a variety of applications for non-axisymmetric devices, in particular stellarators and tokamaks with 3D perturbations. `GORILLA` has already been used by @eder_quasi-geometric_2020 for the application of collisionless guiding-center orbits in an axisymmetric tokamak and a realistic three-dimensional stellarator configuration. There, the code demonstrated stable long-term orbit dynamics conserving invariants. In the same publication, `GORILLA` was further applied to the Monte Carlo evaluation of transport coefficients. There, the computational efficiency of `GORILLA` was shown to be an order of magnitude higher than with a standard fourth order Runge–Kutta integrator. Currently, `GORILLA` is part of the “EUROfusion Theory, Simulation, Validation and Verification Task for Impurity Sources, Transport, and Screening”, where it is tested for the kinetic modelling of the impurity ion component. First results of this research project and, in addition, `GORILLA`'s application to the -computation of fusion alpha particle losses in a realistic stellarator configuration have been reported by @eder_integration_2021. -The source code for `GORILLA` has been archived on Zenodo with the linked DOI: [@eder_gorilla_2021] +computation of fusion alpha particle losses in a realistic stellarator configuration have been reported by @eder_integration_2021. +The source code for `GORILLA` has been archived on Zenodo [@eder_gorilla_2021]. + # Acknowledgements diff --git a/README.md b/README.md index e6ad741..c426935 100644 --- a/README.md +++ b/README.md @@ -1,5 +1,5 @@ [![DOI](https://zenodo.org/badge/343767192.svg)](https://zenodo.org/badge/latestdoi/343767192) -[![](https://img.shields.io/github/workflow/status/itpplasma/GORILLA/CI)](https://github.com/itpplasma/GORILLA/actions/workflows/build.yml) +[![](https://img.shields.io/github/actions/workflow/status/itpplasma/GORILLA/Ubuntu.yml?branch=main)](https://github.com/itpplasma/GORILLA/actions/workflows/Ubuntu.yml) [![GitHub](https://img.shields.io/github/license/itpplasma/GORILLA?style=flat)](https://github.com/itpplasma/GORILLA/blob/master/LICENCE) [![status](https://joss.theoj.org/papers/842b83a430e4c2985d202c79ed626587/status.svg)](https://joss.theoj.org/papers/842b83a430e4c2985d202c79ed626587)