Fluid model

ColdPlasma

Cold plasma model: electron-fluid current coupled with Maxwell's equations via a cold-plasma Ohm's law.

Overview

This is a fluid electromagnetic model for a cold plasma response. The

electron fluid is represented only through its current, so thermal pressure and kinetic velocity-space effects are omitted. It is useful as a reduced model between vacuum Maxwell and fully kinetic Vlasov-Maxwell dynamics.

Use cases

This model is appropriate for:

cold-plasma wave propagation studies
electromagnetic benchmarks with a fluid current response
regimes where thermal pressure can be neglected
algorithm verification for Maxwell plus current coupling

Governing equations

PDEs solved by model:

Cold-plasma current:

\frac{1}{n _{0}} \frac{\partial j}{\partial t} = \frac{1}{ε} E + \frac{1}{ε n _{0}} j \times B_{0}

Faraday's law:

\frac{\partial B}{\partial t} + \nabla \times E = 0

Ampère's law:

- \frac{\partial E}{\partial t} + \nabla \times B = \frac{α ^{2}}{ε} j

where $(n_{0}, B_{0})$ denotes an inhomogeneous background.

Normalization

Velocities are normalized with the speed of light and the fields satisfy

v^= c, E^= c B^.

The dimensionless plasma parameters are the cold-species $α = Ω^_{p} / Ω^_{c}$ and $ε = 1/ (Ω^_{c} t^)$ .

Discretization

Time integration is performed by the following propagators (in sequence):

struphy.propagators.maxwell_weak_ampere.MaxwellWeakAmpere
struphy.propagators.ohm_cold.OhmCold
struphy.propagators.jxb_cold.JxBCold

Diagnostics

The following scalars are tracked during simulation:

Electric field energy: electric_energy
Magnetic field energy: magnetic_energy
Cold-current energy: kinetic_energy
Total energy: total_energy

Example

Create and initialize a cold-plasma model:

from struphy.models import ColdPlasma

model = ColdPlasma()
model.em_fields.e_field
model.em_fields.b_field

model.electrons.current