User Guide

User Guide

• Installation
  • Prerequisites
  • Install GVEC with pip
    • Installing pre-releases
    • Configuring compilation options
    • Troubleshooting
  • Getting GVEC with git
    • Installing the python bindings manually
• Stages
  • Increasing resolution
  • Prescribing a toroidal current profile
    • Theory
      • The default approach
    • Basic control
    • Advanced control
• GVEC parameter list
  • Initialization parameters
  • Discretization parameters
  • Boundary and axis parameters
  • Profile parameters
  • Minimizer parameters
  • hmap parameters
  • Visualization and output parameters
• Theory
  • Continuous problem
    • Coordinate maps
      • A simple map: the torus
  • The magnetic field
  • The MHD energy functional
    • First variation of the energy functional
  • Discretization
    • Boundary conditions in radial direction
    • Approximation of the integrals
  • An equation for lambda
    • Solving the discrete equation
  • Transformation to Boozer coordinates
    • Computing \(|B|\) in Boozer coordinates
  • Other choices for hmap
    • Periodic Cylinder
    • The knot
    • Frenet-Serret frame of a closed curve
      • Curve evaluation
    • G-Frame: A generalized curve-following frame
  • References
• Coordinate conventions
  • GVEC coordinates
  • Different conventions
    • Geometric Quantities
      • reciprocal basis vectors
      • contravariant components of a vector \(\boldsymbol{Q}\)
      • Jacobian determinant
      • components of the metric tensor
    • components of the second fundamental form (of the fluxsurfaces)
• Quantities for Postprocessing
  • Solution variables
    • Additional solution variables for the Boozer transform
  • Curvilinear coordinates
    • Boozer coordinates
    • PEST coordinates
  • Reference coordinates
  • Geometric quantities
  • Magnetic flux
    • Current profiles
  • Pressure
  • Magnetic field
    • Boozer magnetic field
    • PEST magnetic field
  • Current density
    • Boozer current density
    • PEST current density
  • MHD Force
  • Derived quantities of interest
    • Mercier stability criterion
    • Geodesic curvature
  • Others

Tutorials

• Getting Started
  • Virtual Environments
  • Installing GVEC
  • On the tutorials
    • Running Jupyter notebooks
• Elliptic Tokamak
  • Setting up a GVEC run
  • Problem setup
    • Physics parameters
    • Boundary shape
    • Numerical setup
  • Running GVEC
  • Post-processing & Visualization
    • Visualize profiles
    • Visualize poloidal plane
  • pygvec command line interface
• Elliptic Stellarator
  • Setting up the GVEC run
    • Problem setup
  • Running GVEC
  • Post-processing
    • Loading the state
    • Visualize profiles
    • Visualize axis quantities
    • Plotting poloidal planes
    • Evaluating equilibrium quantities
    • Custom 3D visualization
  • Exporting data for visualization
• Boozer transform
  • Load previously computed state
  • Boozer transform
• Visualization in Boozer angles
• Radial grid refinement via stages
  • Add stages to parameter dictionary
  • Run without stages
• Prescribe a current profile
  • New parameters
  • Running GVEC with prescribed toroidal current
    • Understanding the diagnostics
  • Visualize the result
  • Summary
• Postprocessing
  • Derived Quantities
  • Computing integrals
  • Straight-fieldline coordinates
    • PEST transform
    • Boozer transform
    • Field-aligned grid
  • Available quantities for evaluation
• Plotting
• 1D plots
  • Radial profiles
  • Magnetic axis
• 2D plotting
  • Poloidal slice plots
  • Flux surface plots
• Help
• 3D plotting
• G-Frame feature
  • Idea of the G-Frame
  • Requirements for the G-Frame
  • Constructing a G-Frame from a simple curve
  • Using the G-Frame in a GVEC run
  • Rotate the G-Frame
    • Add boundary surface to G-Frame file
  • Compare cross-sections, G-Frame vs cylinder coordinates
  • Generate the G-Frame from a Frenet frame
    • Run in GVEC
  • Generate the G-Frame from a surface
    • Input surface
    • Construct the G-Frame
    • Cross-sections comparison
    • Run in GVEC
• Coils and fieldline tracing
  • Defining coils in GVEC
    • Extracting coils
    • Saving and loading coils
    • Accessing individual coils in a CoilSet
  • Visualizing coils
  • Evaluating the coil-field
  • Fieldline tracing in Cartesian coordinates
    • Defining starting positions
    • Terminating tracing early
    • Automatic event creation via planes
    • Start the fieldline tracing
  • Poincaré plots
    • Visualizing the fieldlines in 3D
• Frame aligned Poincaré plots
  • Setting up the quasr case
    • Visualizing the 3D geometry
  • Fieldline tracing
  • Frame aligned Poincaré plots
    • Visualizing fieldlines in 3D
  • Using equilibrium quantities with coil-fields
    • Visualizing \(\mathbf{B}_{\text{coils}}\cdot \mathbf{n}\)

CLI and Interfaces

• pygvec CLI
• QUASR and G-Frame
  • GVEC-QUASR interface
  • Construction from other surface data
  • Visualization of the G-Frame file
• CAS3D
  • Usage
  • Interface
    • Coordinates
    • field-periodic representation
• GENE-GIST
  • Usage
  • Derivations for GIST quantities
    • Boozer coordinates
    • changing coordinate directions
    • Fieldline coordinates
    • GIST quantities
    • coordinate directions
• Other Interfaces
  • VMEC