MANCHA-2F: Simulating Partially Ionized Solar Plasmas

• MANCHA-2F is a numerical simulation code that models waves, instabilities, and heating in partially ionized solar plasmas with explicit charge–neutral coupling and non-ideal effects.
• It implements both single-fluid (using ambipolar diffusion) and two-fluid (via elastic collisions) formulations to capture ion–neutral drift, frictional heating, and energy flux differences.
• Applications include comparing fast magneto-acoustic wave damping and Biermann battery magnetic-field generation, thereby testing reduced plasma closures in different coupling regimes.

Searching arXiv for MANCHA-2F and closely related work to ground the article in the relevant literature. MANCHA-2F is a numerical code for simulating waves, instabilities, and heating in the partially ionized solar atmosphere with both single-fluid and two-fluid formulations. It extends MANCHA3D to include explicit charge–neutral coupling through elastic collisions in a two-fluid description, while also retaining a single-fluid option based on ambipolar diffusion. In the literature summarized here, MANCHA-2F is used in two distinct but related contexts: the comparison of single-fluid and two-fluid treatments of fast magneto-acoustic waves in the solar chromosphere (Míguez et al., 22 Jul 2025), and the simulation of Biermann battery magnetic-field generation in partially ionised plasmas undergoing the Kelvin–Helmholtz instability (Martínez-Gómez et al., 2021). Across these applications, its defining role is to resolve the dynamical and thermodynamic consequences of ion–neutral drift, frictional coupling, and non-ideal induction terms in regimes where partial ionization is not a perturbative detail but a controlling aspect of the plasma dynamics.

1. Code framework and scope

MANCHA-2F is a two-fluid extension of the single-fluid MANCHA3D code. In the solar-chromospheric wave study, it is described as a numerical code designed to simulate waves, instabilities, and heating in the partially ionized solar atmosphere using both single-fluid (1F) and two-fluid (2F) formulations, built on MANCHA3D and extended to include explicit charge–neutral coupling via elastic collisions in a 2F description (Míguez et al., 22 Jul 2025). In the Biermann battery study, it is described as solving time-dependent two-fluid equations for a partially ionised plasma in SI units (Martínez-Gómez et al., 2021).

The code adopts a reduced species description in which ions and electrons are grouped into a charged fluid and neutrals form a separate neutral fluid. In the Biermann battery formulation, a strong ion–electron coupling is assumed and electrons are massless in the momentum balance, so the charged fluid satisfies $V_{\rm c}\equiv V_{\rm i}$, while electrons contribute pressure but not inertia (Martínez-Gómez et al., 2021). In the chromospheric wave study, the corresponding notation is “c” for charges $(i+e)$ and “n” for neutrals, with hydrogen as the plasma species and electrons strongly coupled to ions (Míguez et al., 22 Jul 2025).

A major implementation feature is the treatment of stiff collisional source terms. MANCHA-2F implements semi-implicit time-stepping for such terms, which enables chromospheric applications where collision frequencies vary by orders of magnitude (Míguez et al., 22 Jul 2025). The same study states that it can also solve linearized systems, allowing linear and nonlinear effects to be separated. This dual capability is important because the code is used not only for direct nonlinear time evolution but also for controlled comparisons with linear theory.

The code’s documented use spans chromospheric wave damping and heating, Kelvin–Helmholtz instability, Rayleigh–Taylor instability, and ion–neutral collisional and radiative effects. The summarized references attribute the 2F algorithm and semi-implicit collisional treatment to Popescu Braileanu et al. 2019a, chromospheric wave applications to Popescu Braileanu et al. 2019b, Rayleigh–Taylor applications to Popescu Braileanu et al. 2021, and ion–neutral collisional and radiative effects to Popescu Braileanu and Keppens 2024 (Míguez et al., 22 Jul 2025). The present sources do not state explicit public code availability, but they place MANCHA-2F within the MANCHA framework and note repeated use by the authors’ groups (Míguez et al., 22 Jul 2025, Martínez-Gómez et al., 2021).

2. Fluid models implemented in MANCHA-2F

A central feature of MANCHA-2F is its support for both two-fluid and single-fluid descriptions of partially ionized plasma. In the two-fluid approximation, charges and neutrals are evolved as separate fluids coupled by elastic collisions. Magnetic stresses act directly on the charge fluid, while neutrals feel the magnetic field indirectly through collisions. This formulation naturally captures the drift velocity

$\mathbf{w}=\mathbf{u}_{\rm c}-\mathbf{u}_{\rm n},$

frictional heating, thermal exchange between species, and inertial effects of the drift at all heights and frequencies (Míguez et al., 22 Jul 2025).

In the single-fluid approximation used in the chromospheric wave comparison, the state variables are center-of-mass quantities $\rho,\mathbf{u},p,e$, with

$$\mathbf{u}=\frac{\rho_{\rm n}\mathbf{u}_{\rm n}+\rho_{\rm c}\mathbf{u}_{\rm c}}{\rho}, \qquad \rho=\rho_{\rm c}+\rho_{\rm n}.$$

This 1F model assumes strong coupling, expressed as $\omega\ll \nu$, so that a single center-of-mass fluid is adequate, but it allows finite drift through ambipolar diffusion added to the induction and energy equations via the generalized Ohm’s law (Míguez et al., 22 Jul 2025). In the formulation examined there, only ambipolar diffusion is retained; Ohmic and Hall terms are neglected, along with viscosity, heat flux, and inelastic ionization/recombination, consistent with a five-moment closure (Míguez et al., 22 Jul 2025).

The distinction between the 1F and 2F formulations is not merely numerical. The wave-comparison study identifies two omissions in the 1F model as central to the observed discrepancies with 2F: the neglect of explicit frictional coupling terms and the omission of the center-of-mass heat-flux term that arises when transforming the 2F energy flux to the center-of-mass frame (Míguez et al., 22 Jul 2025). This makes MANCHA-2F not only a solver but also a framework for testing the validity domain of reduced partially ionized plasma closures.

The Biermann battery study uses the two-fluid formulation exclusively. There, gravity, resistivity, Hall term, and ionisation/recombination are neglected, while the generalized Ohm’s law retains the electron pressure-gradient term responsible for the Biermann battery and a collisional drift term proportional to $V_{\rm n}-V_{\rm c}$ (Martínez-Gómez et al., 2021). Elastic and charge-exchange momentum and energy exchange are included, and the collisional contribution to the induction equation is also retained and measured (Martínez-Gómez et al., 2021).

3. Governing equations and collisional physics

In the chromospheric wave application, MANCHA-2F solves five-moment equations for neutrals and charges. For each fluid, it evolves continuity, momentum, and total energy, together with an induction equation in which the magnetic field is advected by the charged fluid: $$\frac{\partial \mathbf{B}}{\partial t} +\nabla\cdot(\mathbf{u}_{\rm c}\otimes\mathbf{B}-\mathbf{B}\otimes\mathbf{u}_{\rm c})=0, \qquad \nabla\cdot\mathbf{B}=0.$$ The magnetic stress tensor is

$$\hat{p}_{\rm m}=p_{\rm m}\hat{I}-\frac{1}{\mu_0}\mathbf{B}\otimes\mathbf{B}, \qquad p_{\rm m}=\frac{B^2}{2\mu_0}, \qquad \nabla\cdot\hat{p}_{\rm m}=-\mathbf{J}\times\mathbf{B},$$

with current density

$\mathbf{J}=\frac{1}{\mu_0}\nabla\times\mathbf{B}.$

The equation of state is ideal-gas hydrogen, with

$(i+e)$0

the factor 2 reflecting electrons plus protons per unit mass (Míguez et al., 22 Jul 2025).

The collision model is based on elastic coupling. The friction force density on neutrals is

$(i+e)$1

with equal and opposite action on charges. The collisional energy exchange is

$(i+e)$2

and the total collisional heating in internal-energy form satisfies

$(i+e)$3

The collision parameter $(i+e)$4 is defined using hard-sphere elastic collisions with proton–neutral and electron–neutral channels and cross-sections $(i+e)$5. The collision frequencies are

$(i+e)$6

(Míguez et al., 22 Jul 2025).

In the 1F ambipolar-diffusion model, the induction equation is

$(i+e)$7

with non-ideal field

$(i+e)$8

where

$(i+e)$9

Since Ohmic diffusivity is neglected, the Cowling diffusivity reduces approximately to the ambipolar diffusivity, $\mathbf{w}=\mathbf{u}_{\rm c}-\mathbf{u}_{\rm n},$0. The corresponding ambipolar heating rate is

$\mathbf{w}=\mathbf{u}_{\rm c}-\mathbf{u}_{\rm n},$1

(Míguez et al., 22 Jul 2025).

The Biermann battery application uses a related but distinct two-fluid system. There, the generalized Ohm’s law is

$\mathbf{w}=\mathbf{u}_{\rm c}-\mathbf{u}_{\rm n},$2

with $\mathbf{w}=\mathbf{u}_{\rm c}-\mathbf{u}_{\rm n},$3 and $\mathbf{w}=\mathbf{u}_{\rm c}-\mathbf{u}_{\rm n},$4. The induction equation is decomposed as

$\mathbf{w}=\mathbf{u}_{\rm c}-\mathbf{u}_{\rm n},$5

The Biermann battery contribution is therefore

$\mathbf{w}=\mathbf{u}_{\rm c}-\mathbf{u}_{\rm n},$6

which, in the 2D configuration used there, generates only $\mathbf{w}=\mathbf{u}_{\rm c}-\mathbf{u}_{\rm n},$7 (Martínez-Gómez et al., 2021).

4. Chromospheric wave calculations and the 1F–2F comparison

In the wave-heating study, MANCHA-2F is applied to vertically propagating fast magneto-acoustic waves launched from the top of the photosphere into a vertically stratified chromosphere with a horizontal, homogeneous magnetic field. The model atmosphere extends from approximately 600 km above the photosphere to the base of the transition region, uses the VAL3C temperature profile, and assumes hydrogen only, with electrons provided by hydrogen ionization and no multi-species effects, molecules, or negative ions (Míguez et al., 22 Jul 2025).

The background magnetic field is homogeneous and horizontal, $\mathbf{w}=\mathbf{u}_{\rm c}-\mathbf{u}_{\rm n},$8 G along $\mathbf{w}=\mathbf{u}_{\rm c}-\mathbf{u}_{\rm n},$9, chosen so that $\rho,\mathbf{u},p,e$0 is near the middle of the computational domain (Míguez et al., 22 Jul 2025). Hydrostatic equilibrium is imposed separately for neutrals and charges, with scale heights

$\rho,\mathbf{u},p,e$1

The ionization fraction increases with height from $\rho,\mathbf{u},p,e$2 at the bottom to $\rho,\mathbf{u},p,e$3 at the top solely because of stratification; no non-equilibrium ionization or recombination is included (Míguez et al., 22 Jul 2025).

The bottom boundary injects a vertically propagating fast magneto-acoustic mode with small amplitude $\rho,\mathbf{u},p,e$4. In the 2F model, the charged and neutral vertical velocities are equal at the bottom, reflecting strong coupling. The periods explored are $\rho,\mathbf{u},p,e$5 s, chosen to sample frequencies close to collision frequencies in the upper chromosphere, approximately $\rho,\mathbf{u},p,e$6 (Míguez et al., 22 Jul 2025).

The numerical configuration uses the same time step for 1F and 2F runs. The 1F system is integrated with explicit fourth-order Runge–Kutta, whereas the 2F system uses a semi-implicit update for collisional source terms and was also tested in explicit mode with consistent results at the resolutions employed. The vertical grid spacing is $\rho,\mathbf{u},p,e$7 m for $\rho,\mathbf{u},p,e$8 s and $\rho,\mathbf{u},p,e$9 m for $$\mathbf{u}=\frac{\rho_{\rm n}\mathbf{u}_{\rm n}+\rho_{\rm c}\mathbf{u}_{\rm c}}{\rho}, \qquad \rho=\rho_{\rm c}+\rho_{\rm n}.$$0 s. A sixth-order low-pass filter is applied periodically, and the top boundary uses a Perfectly Matched Layer (Míguez et al., 22 Jul 2025).

The quantitative comparison shows systematic, though not large, differences. Heating profiles are compared using the factor

$$\mathbf{u}=\frac{\rho_{\rm n}\mathbf{u}_{\rm n}+\rho_{\rm c}\mathbf{u}_{\rm c}}{\rho}, \qquad \rho=\rho_{\rm c}+\rho_{\rm n}.$$1

to express rates in $$\mathbf{u}=\frac{\rho_{\rm n}\mathbf{u}_{\rm n}+\rho_{\rm c}\mathbf{u}_{\rm c}}{\rho}, \qquad \rho=\rho_{\rm c}+\rho_{\rm n}.$$2. Peaks of collisional heating in 2F and ambipolar heating in 1F occur above the heights where velocity amplitudes begin to decay, and the peak moves higher with increasing period (Míguez et al., 22 Jul 2025). The time-averaged temperature perturbation grows linearly with time for all periods. Above the heating peak, the 1F model yields slightly higher mean temperature than 2F, especially for $$\mathbf{u}=\frac{\rho_{\rm n}\mathbf{u}_{\rm n}+\rho_{\rm c}\mathbf{u}_{\rm c}}{\rho}, \qquad \rho=\rho_{\rm c}+\rho_{\rm n}.$$3 s, whereas below the peak the 2F model produces slightly larger increases (Míguez et al., 22 Jul 2025).

The total fast-mode energy flux $$\mathbf{u}=\frac{\rho_{\rm n}\mathbf{u}_{\rm n}+\rho_{\rm c}\mathbf{u}_{\rm c}}{\rho}, \qquad \rho=\rho_{\rm c}+\rho_{\rm n}.$$4 is consistently larger in the 1F runs along most of the domain. The study interprets positive 1F–2F residuals, whose envelope resembles the heating profiles, as evidence of a physical rather than numerical origin. The explanation advanced is that 2F dissipation is more efficient in deep layers, so less wave energy is transported upward and less heating occurs at high layers than in the 1F model (Míguez et al., 22 Jul 2025).

The drift velocity diagnostics further clarify the regime structure. The simulations show that $$\mathbf{u}=\frac{\rho_{\rm n}\mathbf{u}_{\rm n}+\rho_{\rm c}\mathbf{u}_{\rm c}}{\rho}, \qquad \rho=\rho_{\rm c}+\rho_{\rm n}.$$5 in most of the domain, but $$\mathbf{u}=\frac{\rho_{\rm n}\mathbf{u}_{\rm n}+\rho_{\rm c}\mathbf{u}_{\rm c}}{\rho}, \qquad \rho=\rho_{\rm c}+\rho_{\rm n}.$$6 in layers where damping is strongest. Longer-period waves reach higher layers where coupling is weaker, producing larger drift aloft than shorter-period waves, even though intrinsic friction is strongest at higher $$\mathbf{u}=\frac{\rho_{\rm n}\mathbf{u}_{\rm n}+\rho_{\rm c}\mathbf{u}_{\rm c}}{\rho}, \qquad \rho=\rho_{\rm c}+\rho_{\rm n}.$$7. Shorter-period waves damp earlier and therefore do not reach the heights where 1F–2F differences are greatest (Míguez et al., 22 Jul 2025).

5. Linear theory, drift physics, and the source of model discrepancies

The wave study supplements the simulations with linear theory in a vertically stratified atmosphere with a horizontal field $$\mathbf{u}=\frac{\rho_{\rm n}\mathbf{u}_{\rm n}+\rho_{\rm c}\mathbf{u}_{\rm c}}{\rho}, \qquad \rho=\rho_{\rm c}+\rho_{\rm n}.$$8. Using an Eikonal approximation, it derives fast magneto-acoustic dispersion relations for both the 2F and 1F systems. A key structural difference is that the 2F relation contains an $$\mathbf{u}=\frac{\rho_{\rm n}\mathbf{u}_{\rm n}+\rho_{\rm c}\mathbf{u}_{\rm c}}{\rho}, \qquad \rho=\rho_{\rm c}+\rho_{\rm n}.$$9 term absent in 1F. The stated reason is that the single-fluid approximation neglects drift inertia, represented by the term proportional to $\omega\ll \nu$0 (Míguez et al., 22 Jul 2025).

Damping is quantified through $\omega\ll \nu$1 and the quality factor

$\omega\ll \nu$2

with strong damping when $\omega\ll \nu$3 (Míguez et al., 22 Jul 2025). The linear analysis shows that in deep layers the 2F damping exceeds the 1F damping: waves propagate nearly acoustically at $\omega\ll \nu$4, exhibit weak stratification-modulated growth, but lose energy faster in 2F because friction is represented explicitly. In upper layers, where $\omega\ll \nu$5, 1F ambipolar damping increases and can exceed 2F damping for the fast branches, but by then the 2F waves already carry less energy because of stronger deep-layer losses (Míguez et al., 22 Jul 2025). This linear picture matches the numerical temperature and energy-flux trends.

The study identifies two specific physical reasons for the discrepancies between the models. The first is the contribution of pressure forces to the drift velocity. Combining the 2F momentum equations yields the approximate drift balance

$\omega\ll \nu$6

with thermal pressure function

$\omega\ll \nu$7

Neglecting inertia when $\omega\ll \nu$8 leads to the 1F drift closure

$\omega\ll \nu$9

This makes explicit that ambipolar diffusion represents the magnetic-force part of the drift, while $V_{\rm n}-V_{\rm c}$0 is the pressure-force contribution (Míguez et al., 22 Jul 2025). In the weakly ionized chromospheric atmosphere of the simulations, $V_{\rm n}-V_{\rm c}$1 is small in the deepest and very highest layers but contributes in intermediate layers, where it enhances 2F dissipation relative to the AD-only 1F model (Míguez et al., 22 Jul 2025).

The second cause is the omitted center-of-mass heat-flux term in the 1F energy equation. Transforming 2F energy fluxes to the center-of-mass frame produces a non-zero term

$V_{\rm n}-V_{\rm c}$2

and, neglecting quadratic and cubic terms in $V_{\rm n}-V_{\rm c}$3, an important piece is

$V_{\rm n}-V_{\rm c}$4

The 1F equations used in the study omit $V_{\rm n}-V_{\rm c}$5 (Míguez et al., 22 Jul 2025). The omission matters because, together with the pressure-force contribution $V_{\rm n}-V_{\rm c}$6, it is required to recover the exact 2F collisional heating in the high-coupling limit. The paper reports that adding $V_{\rm n}-V_{\rm c}$7 and $V_{\rm n}-V_{\rm c}$8 to an extended 1F dispersion relation largely removes deep-layer discrepancies, while the remaining high-layer differences are traced to drift inertia, which 1F still neglects (Míguez et al., 22 Jul 2025).

A plausible implication is that MANCHA-2F functions as a testing ground for asymptotic closure validity, not merely as a production solver. The documented comparisons show that disagreement between 1F and 2F is not reducible to numerical stiffness or resolution, but can arise from specific missing terms in the reduced formulation.

6. Biermann battery simulations and Kelvin–Helmholtz instability

In the Biermann battery study, MANCHA-2F is used to simulate magnetic-field generation in a 2D partially ionised plasma with no initial magnetic field and an unstable shear layer. The computational domain is rectangular, $V_{\rm n}-V_{\rm c}$9, with periodic boundaries in both directions and resolution $$\frac{\partial \mathbf{B}}{\partial t} +\nabla\cdot(\mathbf{u}_{\rm c}\otimes\mathbf{B}-\mathbf{B}\otimes\mathbf{u}_{\rm c})=0, \qquad \nabla\cdot\mathbf{B}=0.$$0 (Martínez-Gómez et al., 2021). The initial state consists of a denser central slab embedded in a lighter medium, with smooth hyperbolic-tangent transitions at two shear layers. Pressure is initially uniform for both fluids, so temperature varies inversely with density (Martínez-Gómez et al., 2021).

The ionisation degree

$$\frac{\partial \mathbf{B}}{\partial t} +\nabla\cdot(\mathbf{u}_{\rm c}\otimes\mathbf{B}-\mathbf{B}\otimes\mathbf{u}_{\rm c})=0, \qquad \nabla\cdot\mathbf{B}=0.$$1

is uniform initially and varied across simulations in the interval $$\frac{\partial \mathbf{B}}{\partial t} +\nabla\cdot(\mathbf{u}_{\rm c}\otimes\mathbf{B}-\mathbf{B}\otimes\mathbf{u}_{\rm c})=0, \qquad \nabla\cdot\mathbf{B}=0.$$2. The flow has a central region moving at $$\frac{\partial \mathbf{B}}{\partial t} +\nabla\cdot(\mathbf{u}_{\rm c}\otimes\mathbf{B}-\mathbf{B}\otimes\mathbf{u}_{\rm c})=0, \qquad \nabla\cdot\mathbf{B}=0.$$3 along $$\frac{\partial \mathbf{B}}{\partial t} +\nabla\cdot(\mathbf{u}_{\rm c}\otimes\mathbf{B}-\mathbf{B}\otimes\mathbf{u}_{\rm c})=0, \qquad \nabla\cdot\mathbf{B}=0.$$4, outer regions at rest, and a small incompressible vertical perturbation is imposed to seed the instability. The magnetic field is initially zero everywhere to isolate Biermann battery generation (Martínez-Gómez et al., 2021). The adopted parameters are representative of the solar chromosphere: $$\frac{\partial \mathbf{B}}{\partial t} +\nabla\cdot(\mathbf{u}_{\rm c}\otimes\mathbf{B}-\mathbf{B}\otimes\mathbf{u}_{\rm c})=0, \qquad \nabla\cdot\mathbf{B}=0.$$5 with subsonic Mach numbers $$\frac{\partial \mathbf{B}}{\partial t} +\nabla\cdot(\mathbf{u}_{\rm c}\otimes\mathbf{B}-\mathbf{B}\otimes\mathbf{u}_{\rm c})=0, \qquad \nabla\cdot\mathbf{B}=0.$$6 and $$\frac{\partial \mathbf{B}}{\partial t} +\nabla\cdot(\mathbf{u}_{\rm c}\otimes\mathbf{B}-\mathbf{B}\otimes\mathbf{u}_{\rm c})=0, \qquad \nabla\cdot\mathbf{B}=0.$$7 (Martínez-Gómez et al., 2021).

The study examines elastic collisions, charge exchange, and the collision-induced term in Ohm’s law. The effective friction coefficient is

$$\frac{\partial \mathbf{B}}{\partial t} +\nabla\cdot(\mathbf{u}_{\rm c}\otimes\mathbf{B}-\mathbf{B}\otimes\mathbf{u}_{\rm c})=0, \qquad \nabla\cdot\mathbf{B}=0.$$8

with elastic collision frequencies defined in momentum-transfer form and cross-sections $$\frac{\partial \mathbf{B}}{\partial t} +\nabla\cdot(\mathbf{u}_{\rm c}\otimes\mathbf{B}-\mathbf{B}\otimes\mathbf{u}_{\rm c})=0, \qquad \nabla\cdot\mathbf{B}=0.$$9 and $$\hat{p}_{\rm m}=p_{\rm m}\hat{I}-\frac{1}{\mu_0}\mathbf{B}\otimes\mathbf{B}, \qquad p_{\rm m}=\frac{B^2}{2\mu_0}, \qquad \nabla\cdot\hat{p}_{\rm m}=-\mathbf{J}\times\mathbf{B},$$0. Charge exchange is modelled באמצעות a velocity-dependent cross-section

$$\hat{p}_{\rm m}=p_{\rm m}\hat{I}-\frac{1}{\mu_0}\mathbf{B}\otimes\mathbf{B}, \qquad p_{\rm m}=\frac{B^2}{2\mu_0}, \qquad \nabla\cdot\hat{p}_{\rm m}=-\mathbf{J}\times\mathbf{B},$$1

in SI units (Martínez-Gómez et al., 2021).

The global magnetic field is diagnosed through the domain average

$$\hat{p}_{\rm m}=p_{\rm m}\hat{I}-\frac{1}{\mu_0}\mathbf{B}\otimes\mathbf{B}, \qquad p_{\rm m}=\frac{B^2}{2\mu_0}, \qquad \nabla\cdot\hat{p}_{\rm m}=-\mathbf{J}\times\mathbf{B},$$2

and its exponential growth rate in the linear phase is measured as

$$\hat{p}_{\rm m}=p_{\rm m}\hat{I}-\frac{1}{\mu_0}\mathbf{B}\otimes\mathbf{B}, \qquad p_{\rm m}=\frac{B^2}{2\mu_0}, \qquad \nabla\cdot\hat{p}_{\rm m}=-\mathbf{J}\times\mathbf{B},$$3

which is consistent with the finite-shear-layer prediction $$\hat{p}_{\rm m}=p_{\rm m}\hat{I}-\frac{1}{\mu_0}\mathbf{B}\otimes\mathbf{B}, \qquad p_{\rm m}=\frac{B^2}{2\mu_0}, \qquad \nabla\cdot\hat{p}_{\rm m}=-\mathbf{J}\times\mathbf{B},$$4 and below the sharp-interface estimate $$\hat{p}_{\rm m}=p_{\rm m}\hat{I}-\frac{1}{\mu_0}\mathbf{B}\otimes\mathbf{B}, \qquad p_{\rm m}=\frac{B^2}{2\mu_0}, \qquad \nabla\cdot\hat{p}_{\rm m}=-\mathbf{J}\times\mathbf{B},$$5 (Martínez-Gómez et al., 2021).

The reported results separate several effects. During the linear phase, $$\hat{p}_{\rm m}=p_{\rm m}\hat{I}-\frac{1}{\mu_0}\mathbf{B}\otimes\mathbf{B}, \qquad p_{\rm m}=\frac{B^2}{2\mu_0}, \qquad \nabla\cdot\hat{p}_{\rm m}=-\mathbf{J}\times\mathbf{B},$$6 increases by approximately four orders of magnitude between $$\hat{p}_{\rm m}=p_{\rm m}\hat{I}-\frac{1}{\mu_0}\mathbf{B}\otimes\mathbf{B}, \qquad p_{\rm m}=\frac{B^2}{2\mu_0}, \qquad \nabla\cdot\hat{p}_{\rm m}=-\mathbf{J}\times\mathbf{B},$$7 and $$\hat{p}_{\rm m}=p_{\rm m}\hat{I}-\frac{1}{\mu_0}\mathbf{B}\otimes\mathbf{B}, \qquad p_{\rm m}=\frac{B^2}{2\mu_0}, \qquad \nabla\cdot\hat{p}_{\rm m}=-\mathbf{J}\times\mathbf{B},$$8. In the nonlinear stage it continues to grow more slowly, peaks near $$\hat{p}_{\rm m}=p_{\rm m}\hat{I}-\frac{1}{\mu_0}\mathbf{B}\otimes\mathbf{B}, \qquad p_{\rm m}=\frac{B^2}{2\mu_0}, \qquad \nabla\cdot\hat{p}_{\rm m}=-\mathbf{J}\times\mathbf{B},$$9, and later decays due to numerical dissipation. The peak time and magnitude both increase with resolution, indicating reduced numerical diffusion at finer grids (Martínez-Gómez et al., 2021).

Without charge–neutral collisions, the generated magnetic field is independent of $\mathbf{J}=\frac{1}{\mu_0}\nabla\times\mathbf{B}.$0 over the range $\mathbf{J}=\frac{1}{\mu_0}\nabla\times\mathbf{B}.$1–$\mathbf{J}=\frac{1}{\mu_0}\nabla\times\mathbf{B}.$2. With elastic collisions only, the generated field increases as $\mathbf{J}=\frac{1}{\mu_0}\nabla\times\mathbf{B}.$3 decreases: relative to the uncoupled case, $\mathbf{J}=\frac{1}{\mu_0}\nabla\times\mathbf{B}.$4 increases by approximately $\mathbf{J}=\frac{1}{\mu_0}\nabla\times\mathbf{B}.$5 at $\mathbf{J}=\frac{1}{\mu_0}\nabla\times\mathbf{B}.$6 and approximately $\mathbf{J}=\frac{1}{\mu_0}\nabla\times\mathbf{B}.$7 at $\mathbf{J}=\frac{1}{\mu_0}\nabla\times\mathbf{B}.$8. Adding the collisional induction term $\mathbf{J}=\frac{1}{\mu_0}\nabla\times\mathbf{B}.$9 has negligible effect compared with the Biermann term, while including charge exchange yields a modest further enhancement, especially at low $(i+e)$00 (Martínez-Gómez et al., 2021).

For fixed ionisation degree, increasing the total density strengthens collisional coupling and drives the two-fluid results toward single-fluid predictions. At $(i+e)$01, the two-fluid curves nearly overlay the single-fluid scaling, whereas at $(i+e)$02 departures are larger (Martínez-Gómez et al., 2021). This supports the paper’s interpretation that convergence to single-fluid behavior is controlled by coupling strength rather than by ionisation fraction alone.

The physical mechanism proposed is that collisions modify the charged-fluid temperature $(i+e)$03 through drift heating and thermal exchange. In weakly ionised plasma, the charged fluid undergoes larger collisional temperature changes per particle because $(i+e)$04 is small, which steepens $(i+e)$05 and increases the charged-fluid baroclinic source that drives the Biermann battery (Martínez-Gómez et al., 2021). The paper makes this explicit by rewriting the battery term as

$(i+e)$06

The vorticity–battery correspondence is likewise emphasized through the proportionality

$(i+e)$07

while the corresponding ratio for the collisional induction source is much smaller,

$(i+e)$08

which explains the negligible role of $(i+e)$09 in the magnetic evolution (Martínez-Gómez et al., 2021).

7. Applicability, limitations, and methodological significance

The wave-comparison study states that 1F ambipolar diffusion is adequate when $(i+e)$10 and coupling is strong, especially in deep chromospheric layers or when energy deposition occurs mainly where the drift-inertia estimator

$(i+e)$11

is much less than unity (Míguez et al., 22 Jul 2025). In this regime, the 1F model captures magnetic-force-driven drift and ambipolar heating while remaining numerically simpler. By contrast, a 2F description is necessary when drift inertia is non-negligible, when pressure-force contributions to drift matter, or when the energy budget requires a consistent partition between charges and neutrals, including frictional heating and thermal exchange (Míguez et al., 22 Jul 2025).

The Biermann battery study reaches a conceptually similar conclusion from a different angle. Single-fluid battery scalings are recovered only when collisional coupling is strong enough that $(i+e)$12 and $(i+e)$13. At lower total density or weaker coupling, the two-fluid model departs from the single-fluid prediction, and single-fluid theory can overestimate the low-$(i+e)$14 enhancement (Martínez-Gómez et al., 2021). This suggests that MANCHA-2F is especially useful in regimes where the coupling time, mean free path, and macroscopic evolution time are comparable enough that interspecies relaxation cannot be assumed instantaneous.

Both studies also delimit the code’s modeled physics. The chromospheric wave calculations are restricted to elastic collisions and exclude Ohmic, Hall, viscosity, heat flux, and inelastic ionization/recombination; they consider hydrogen only and omit non-equilibrium ionization and helium effects (Míguez et al., 22 Jul 2025). The Biermann battery simulations are 2D, have no background magnetic field, neglect resistivity, Hall, ambipolar diffusion, physical viscosity, thermal conduction, radiation, gravity, and ionisation/recombination, and use periodic boundaries with isotropic scalar pressures (Martínez-Gómez et al., 2021). In both cases, these exclusions are not hidden assumptions but explicit constraints on interpretability.

A common misconception in partially ionized plasma modelling is that agreement between 1F and 2F descriptions is determined solely by small ionization fraction. The results summarized here do not support that simplification. In the chromospheric wave problem, discrepancies persist because of pressure-force contributions, omitted frame-change heat flux, and neglected drift inertia even in a weakly ionized atmosphere (Míguez et al., 22 Jul 2025). In the Biermann battery problem, the enhancement of magnetic-field generation depends not only on ionisation degree but also on collisional coupling strength and total density (Martínez-Gómez et al., 2021). This suggests that ionization fraction alone is not a sufficient criterion for model reduction.

Taken together, the documented applications define MANCHA-2F as a specialized framework for non-ideal, partially ionized solar and astrophysical plasma dynamics in which charge–neutral decoupling, drift-mediated heating, and multi-fluid induction physics are central. Its significance lies less in a single algorithmic novelty than in its ability to expose where reduced closures succeed, where they fail, and which specific terms are responsible for the difference.