Skip to content

Model Overview

GUERNICA solves a deterministic kinetic model for atomic hydrogen neutrals in the edge and divertor regions of fusion plasmas. The purpose of this page is to define what is being solved and what physical processes are included, without deriving the governing equations in detail. Numerical discretization and implementation details are covered in the Numerics and Implementation sections.

Kinetic description

The neutral population is described by the phase-space distribution function

\[ f_n(\mathbf{x}, \mathbf{v}, t), \]

where \(\mathbf{x}\) denotes configuration space and \(\mathbf{v}\) denotes velocity space. GUERNICA evolves this distribution according to the Boltzmann equation,

\[ \frac{\partial f_n}{\partial t} + \mathbf{v} \cdot \nabla_{\mathbf{x}} f_n = C[f_n] + S_n, \]

where \(S_n\) represents explicit volumetric neutral sources and \(C[f_n]\) is a collision operator modeling plasma–neutral and neutral–neutral interactions.

Configuration space is treated in one or two spatial dimensions, while velocity space is fully three-dimensional.

Plasma background assumptions

Plasma quantities are treated as externally prescribed inputs and are not evolved self-consistently in GUERNICA. In particular:

  • Electron density \(n_e(\mathbf{x})\)
  • Ion density \(n_i(\mathbf{x})\)
  • Ion flow velocity \(\mathbf{u}_i(\mathbf{x})\)
  • Electron temperature \(T_e(\mathbf{x})\)
  • Ion temperature \(T_i(\mathbf{x})\)

are provided by a background plasma simulation or analytic model.

Electrons and ions are assumed Maxwellian when evaluating plasma–neutral collisions. This assumption is standard in edge-neutral modeling and enables closed-form or tabulated reaction rates.

Collision operator decomposition

The total collision operator is written as a sum of physical processes,

\[ C[f_n] = C_{\mathrm{iz}}[f_n] + C_{\mathrm{cx}}[f_n] + C_{\mathrm{bgk}}[f_n], \]

corresponding to ionization, charge exchange and neutral–neutral elastic collisions.

Macroscopic moments

Macroscopic neutral quantities are obtained as velocity moments of the distribution function. The primary moments of interest are:

  • Neutral density \(n_n\)
  • Bulk velocity \(\mathbf{u}_n\)
  • Temperature \(T_n\)

These moments are used for diagnostics, coupling and construction of collision operators. All moments are computed consistently with the discrete velocity quadrature used elsewhere in the solver.

Scope and limitations

GUERNICA is designed as a neutral-only kinetic solver. In its current form:

  • Plasma quantities are fixed inputs and not evolved dynamically.
  • Only atomic hydrogen is modeled.
  • Molecular processes, recombination and excited-state kinetics are not included.

These choices are deliberate and reflect a focus on high-fidelity modeling of plasma–neutral interactions in regimes where kinetic effects are important.

Relationship to the rest of the documentation

This page defines the physical model assumed throughout the documentation. Subsequent sections focus on:

  • Numerics: how the kinetic equation is discretized in configuration and velocity space.
  • Implementation: how these discretizations are realized efficiently in code.
  • Verification and Performance: how the solver is validated and how it scales.

Readers interested primarily in algorithmic or implementation details may proceed directly to the Numerics section.