VOSP — Vlasov Open Source Project

VOSP is an open-source Vlasov–Poisson solver developed in Rust and Tauri, designed with an emphasis on numerical correctness, physical generality, and accessibility. The solver supports multiple plasma species, configurable collision operators, and is particularly suited for simulating complex chemistry within a kinetic plasma framework.

Getting Started

Pre-built binaries are available under the Releases tab on GitHub, in the Assets section.

Platform	File
Debian-based Linux	vogui_0.1.0_amd64.deb
Linux (AppImage)	vogui_0.1.0_amd64.AppImage
Windows	vogui_0.1.0_x64-setup.exe

---

Graphical Interface

Solver Configuration Window

The solver window provides control over the physical and numerical parameters of the simulation.

Data Visualisation Window

The data window enables real-time and post-hoc visualisation of simulation outputs.

---

Solver Parameters

The solver is the central object of VOSP. It is configured through the following parameters:

Parameter	Description
DT	Simulation time step
End Time	The simulation runs until the physical time reaches this value
LX	Spatial domain length
NX	Number of grid points along the spatial axis
NV	Number of grid points along the velocity axis
Lambda	Ratio of simulation length to the Debye length
Save Every N Iterations	Frequency at which the electric potential and species data are written to an HDF5 file

---

Species (Elements)

Each plasma species is represented as an Element object. New species are added via the Add Element button and are automatically registered with the solver. The configurable parameters for each species are as follows:

Parameter	Description
Element Name	Identifier used to reference this species within the solver
Left / Right Boundary Condition	Boundary conditions applied at each end of the spatial domain
Initial Condition	Initial phase-space distribution function $f_s(x, v, t=0)$
Velocity Domain Length (Lv)	Half-width of the velocity domain; the velocity space spans $[-L_v, +L_v]$
Charge Number (Z)	Species charge in units of the elementary charge
Mass Ratio	Species mass relative to the electron mass $(m_e / m_i)$

---

Numerical Methods

Governing Equations

VOSP solves the Vlasov–Poisson system. For a species $s$, the system reads:

$$ \begin{cases} \partial_t f_s + v , \partial_x f_s + \dfrac{q_s}{m_s} E , \partial_v f_s = \displaystyle\sum_{s'} \hat{C}_{s,s'} \[10pt] \lambda^2 , \Delta \phi = -\displaystyle\sum_s q_s n_s \end{cases} $$

where $f_s(x, v, t)$ is the distribution function of species $s$, $E$ is the self-consistent electric field, $\phi$ is the electrostatic potential, $n_s$ is the number density, and $\hat{C}_{s,s'}$ denotes the collision operator between species $s$ and $s'$.

The phase space is $(x, v)$-dimensional. In its current version, VOSP operates in the 1D-1V configuration (one spatial dimension, one velocity dimension).

Operator Splitting

Operator splitting — referred to in the plasma physics literature as time splitting — decomposes the full Vlasov equation into a sequence of simpler sub-problems solved successively within each time step:

1. Spatial advection: $\partial_t f_s = -v , \partial_x f_s$
2. Velocity advection: $\partial_t f_s = -\frac{q_s}{m_s} E , \partial_v f_s$
3. Collision step: application of $\hat{C}_{s,s'}$

This decomposition introduces a time discretisation error of order $\mathcal{O}(\Delta t^2)$. Higher-order splitting schemes exist but are not currently implemented. The primary advantage of operator splitting lies in its modularity: each sub-step can be treated with a method tailored to its structure, and new collision operators can be incorporated without modifying the advection scheme.

Semi-Lagrangian Method

Each advection sub-step is solved using a Semi-Lagrangian (SL) method. Since $v$ and $E$ are constant along the $x$- and $v$-axes respectively within each sub-step, the advection equations admit exact characteristics. The solution satisfies:

$$ f_s(x, v, t) = f_s(x - v ,\Delta t,; v,; t - \Delta t) $$

Given a grid point $(x_i, v_j)$ at time $t$, the SL method traces the characteristic backwards to the foot $(x_i - v_j \Delta t, v_j)$ at time $t - \Delta t$, and reconstructs $f_s$ at that point by interpolation from the known grid values.

VOSP uses a CWENO-3.2 (Compact Weighted Essentially Non-Oscillatory) polynomial reconstruction, which provides third-order accuracy in smooth regions while suppressing the Gibbs phenomenon near discontinuities.

A key advantage of the SL method is that it is unconditionally stable with respect to the CFL condition, which is critical for Vlasov simulations where large disparities in thermal velocities between species would otherwise impose prohibitively small time steps.

Note: Although the scheme is CFL-unconditional, the time discretisation error remains $\mathcal{O}(\Delta t^2)$. Users should therefore select $\Delta t$ according to the required accuracy rather than stability constraints.