GENE

GENE (Gyrokinetic Electromagnetic Numerical Experiment) is an open-source computer simulation code used to study plasma turbulence in magnetic confinement fusion devices. GENE solves the gyrokinetic equations to simulate electromagnetic turbulence in plasmas, which is critical for understanding energy confinement in fusion reactors like tokamaks and stellarators.

Overview

GENE is a gyrokinetic turbulence code that simulates plasma behavior at very small scales comparable to the ion and electron gyroradius. The code was originally developed at the Max Planck Institute for Plasma Physics in Garching, Germany, with the first version written by Frank Jenko in 1999.

GENE is widely used in the international fusion research community and is considered one of the leading codes for plasma turbulence simulations. The code has been continuously developed by an international team of researchers and is designed to run on high-performance supercomputers.

Purpose and Applications

The main purpose of GENE is to understand and predict turbulent transport in fusion plasmas. Plasma turbulence is one of the key factors limiting energy confinement in magnetic fusion devices, which directly affects the performance and efficiency of potential fusion power plants. By simulating this turbulence, GENE helps researchers:

• Predict energy confinement times in fusion experiments
• Understand heat and particle transport mechanisms
• Optimize plasma conditions for better performance
• Design future fusion devices including ITER
• Validate theoretical models against experimental data

The code has been successfully validated against experimental measurements from major fusion devices including ASDEX Upgrade and has shown excellent agreement with multiple simultaneous plasma observables.

Physical Model

GENE is based on gyrokinetic theory, which describes plasma behavior on spatial scales comparable to particle gyroradii and on time scales much slower than the cyclotron frequency. This approach reduces the complexity of the full kinetic description while retaining the essential physics of plasma turbulence.

Gyrokinetic Equations

The gyrokinetic model assumes that:

• The plasma is strongly magnetized
• Perpendicular spatial scales are comparable to the ion gyroradius
• Frequencies are much lower than the ion cyclotron frequency
• Perturbations are small compared to background quantities

The fundamental equations solved by GENE include:

Gyrokinetic Vlasov Equation

The gyrokinetic equation describes the evolution of the perturbed distribution function. In simplified form, it can be written as:

$\frac{\partial h_s}{\partial t}+{\mathbf{𝐯}}_{\text{gc}}\cdot \mathrm{\nabla }{h}_s+{\dot{v}}_{\parallel }\frac{\partial h_s}{\partial v_{\parallel }}=C(h_s)$

where:

• $h_s$ is the perturbed distribution function for species s
• ${\mathbf{𝐯}}_{\text{gc}}$ is the guiding center velocity
• $v_{\parallel }$ is the parallel velocity
• $C(h_s)$ represents collisional effects

Maxwell's Equations

GENE couples the gyrokinetic equation to Maxwell's equations to determine the electromagnetic fields. In the electrostatic approximation, this reduces to the quasineutrality condition:

$\sum _s{Z}_{s}eB\int d{v}_{\parallel }d\mu d\phi h_s(\mathbf{𝐑})=\sum _s\frac{Z_s^2{e}^2{n}_s\varphi }{T_s}$

For electromagnetic simulations, GENE also solves Ampère's law for the parallel magnetic field perturbations.

Turbulence Mechanisms

GENE can simulate various types of plasma turbulence, including:

• Ion Temperature Gradient (ITG) modes - driven by temperature gradients in the plasma
• Trapped Electron Modes (TEM) - caused by particles trapped in magnetic field variations
• Electron Temperature Gradient (ETG) modes - electron-scale turbulence
• Kinetic Ballooning Modes (KBM) - pressure-driven instabilities
• Microtearing modes - electromagnetic instabilities that can tear magnetic field lines

Numerical Methods

GENE is a Eulerian code, meaning it solves the gyrokinetic equations on a fixed grid in phase space rather than following individual particles. This approach has several advantages for turbulence simulations.

Discretization

The code uses a combination of numerical methods:

• Spectral methods in the perpendicular directions (for periodic boundary conditions)
• Finite differences in the radial direction (for global simulations)
• Upwind schemes along magnetic field lines
• Runge-Kutta methods for time integration

Coordinate Systems

GENE employs field-aligned coordinates that follow magnetic field lines, which is natural for strongly magnetized plasmas. Different versions of the code use different coordinate approaches:

• Standard GENE - uses flux-tube or radially global geometry in tokamaks
• GENE-3D - full three-dimensional geometry for stellarators
• GENE-X - flux-coordinate independent (FCI) approach for edge and scrape-off layer regions

Code Versions and Extensions

Local and Global Versions

GENE can operate in different spatial modes:

• Local (flux-tube) - simulates a small radial region with periodic boundary conditions; computationally efficient for core turbulence
• Radially global - includes variations across the plasma radius; necessary for edge effects and profile evolution

GENE-3D

GENE-3D is an extension that handles the complex three-dimensional geometry of stellarators. Development of GENE-3D took approximately five years and was presented by Maurice Maurer and colleagues. Unlike the original tokamak-oriented version, GENE-3D can simulate the full ion and electron dynamics in the complex magnetic field geometry of stellarators like Wendelstein 7-X.

GENE-X

GENE-X is a full-f gyrokinetic continuum code based on the flux-coordinate independent (FCI) approach. This version was developed specifically to handle:

• Edge and scrape-off layer turbulence
• Regions with magnetic X-points (where traditional field-aligned coordinates have singularities)
• Geometries without well-defined flux surfaces
• Transition regions between core and edge plasma

GENE-X uses unstructured, locally Cartesian grids that provide flexibility while maintaining computational efficiency. The code is capable of simulating regions from the magnetic axis, across the separatrix, and into the scrape-off layer.

Development and Community

History

Frank Jenko wrote the first version of GENE in 1999 during his early postdoctoral work. Since then, the code has been continuously developed and improved by an international team of researchers. Major development centers include:

• Max Planck Institute for Plasma Physics (IPP), Garching, Germany
• Max Planck Computing and Data Facility (MPCDF), Germany
• Technical University of Munich, Germany
• University of Texas at Austin, USA
• École Polytechnique Fédérale de Lausanne (EPFL), Switzerland
• Many other international institutions

International Collaboration

The GENE Development Team is an international collaboration that includes members from universities and research laboratories across the world. The project welcomes contributions from the global fusion community and maintains an open-source development model.

Institutions using GENE include research centers in Germany, USA, Switzerland, France, UK, Netherlands, Italy, Japan, India, China, South Korea, and many others.

High-Performance Computing

GENE has been at the forefront of high-performance computing in plasma physics since the 1960s. The code is designed to run efficiently on the world's largest supercomputers. In 2022, a major project was launched with €2.14 million in EU funding to develop an exascale version of GENE, pioneering the transition to exascale supercomputers.

The goal is to create "digital twins" of fusion experiments like ITER, allowing researchers to predict plasma behavior rather than just interpret experimental results.

Validation and Impact

GENE has been extensively validated against experimental measurements from major fusion devices. A landmark 2025 study demonstrated successful multi-channel validation of GENE against ASDEX Upgrade tokamak data, comparing simultaneous measurements of multiple plasma properties including turbulence amplitudes, wavenumber spectra, and cross phases.

The code has been used to:

• Explain turbulence suppression by fast ions in tokamak plasmas
• Predict similar effects in stellarators
• Understand energy confinement scaling
• Design optimal plasma scenarios for ITER
• Investigate the effects of different wall materials (like tungsten) on plasma performance

See also

• Gyrokinetic simulations
• Plasma Physics at the LNF
• Nuclear fusion
• Tokamak
• Stellarator
• ITER
• Plasma simulation
• MHD equilibrium

External links

• Official GENE website
• Max Planck Institute for Plasma Physics
• GENE license & how to obtain the source
• ITER Organization