Canonical Vorticity Perspective on Magnetogenesis: Unifying Weibel, Biermann, and Beyond

TL;DR

This work develops a canonical vorticity framework in which the dynamical variable ${\bf Q}_\sigma = m_\sigma {\boldsymbol\Omega}_\sigma + q_\sigma {\bf B}$ evolves under a convective term and a non-ideal canonical battery, unifying Biermann battery, Weibel instability, and pressure-tensor–driven seed-field generation. By extending to relativistic kinetics, it introduces a kineclinicity source ${\vec{\mathcal R}}$ that breaks the frozen-in constraint in a new way, and validates the theory with PIC simulations across 1D, 2D localized, axisymmetric, and relativistic pair-plasma scenarios. The framework predicts multiple pressure-tensor configurations as distinct magnetogenesis pathways and demonstrates kinetic-scale generalizations of classic mechanisms, with potential relevance to laboratory experiments and astrophysical plasmas. Limitations include the lack of a covariant formulation and the focus on linear growth in 2D, signaling the need for 3D nonlinear studies to fully map the role of kineclinicity in relativistic magnetogenesis.

Abstract

We briefly review the current status of magnetogenesis, a cross-disciplinary field that bridges cosmology and plasma physics, studying the origin of magnetic fields in the universe. We formulate a canonical vorticity framework to investigate kinetic plasma physics-based magnetogenesis processes in a collisionless plasma. By considering canonical vorticity, a weighted sum of the fluid vorticity and the magnetic field as the canonical variable, this framework unifies several magnetogenesis processes, including the Biermann battery, the Weibel instability, and predicts several new pressure tensorial configurations as the fundamental source of self-generated magnetic field and vorticity in plasma. The framework is further extended to relativistic regime where an additional source of canonical vorticity, termed as kineclinicity effect, is identified. The theoretical predictions are systematically validated using particle-in-cell simulations, highlighting their implications for laboratory and astrophysical plasma environments.

Figures (9)

• Figure 1: Distribution of particles in $(v_x, v_y)$ space at different times (a) $t\omega_p= 0$, (b) $t\omega_p= 47$, and (c) $t\omega_p= 98$. The distribution tries to isotropize the initial pressure anisotropy as the instability proceeds Yoon2025PoP.
• Figure 2: Streak plot of various quantities of the $z$-component of Eq. (\ref{['canonical_vorticity_eqn']}), namely (a) $B_z$, (b) $\Omega_{ez}$, (c) $Q_{ez}$, (d) $\partial Q_{ez}/\partial t$, (e) $\mathcal{C}_z$, and (f) $\mathcal{B}_z$ from the 1D PIC simulation. They are shown in units of (a) $m_e\omega_{pe}/e$, (b) $\omega_{pe}$, (c) $m_e\omega_{pe}$, and (d-f) $m_e\omega_{pe}^2$, where $\omega_{pe}=\sqrt{n_0e^2/m_e\epsilon_0}$.
• Figure 3: Time-dependent rms values of normalized $B_z$, $\Omega_{ez}$, and $Q_{ez}$.
• Figure 4: Streak plots of (a) $B_z [m_e\omega_{pe}/e]$, (b) $\omega_{ez} [\omega_{pe}]$, and (c) $Q_{ez} [m_e\omega_{pe}]$ with each panel corresponds to $t\omega_{pe}=33.89, 58.82,$ and $86.74$ from the 2D PIC simulation with uniform density and non-localized temperature anisotropy $T_{eyy}=T_{ezz}=10^{-4}m_ec^2$ and $T_{exx}=0.04 m_ec^2$.
• Figure 5: Streak plots of (a) $B_z$, (b) $\Omega_{ez}$, (c) $Q_{ez}$, (d) $\partial Q_{ez}/\partial t$, (e) $\mathcal{C}_z$, and (f) $\mathcal{B}_z$ the 2D PIC simulation with uniform density ($n_0$) and localized temperature anisotropy $T_{eyy}=T_{ezz}=10^{-4}m_ec^2$ and $T_{exx}=T_{eyy}+0.04m_ec^2\exp\left(-[(x-x_0)^2+(y-y_0)^2]/\delta^2\right)$. The units are the same as in Fig. \ref{['Spatiotemporal_all_By_case']}. The three slices in each panel correspond to $t\omega_{pe}=$ 0.19, 5.02, and 9.94.