From Weibel seeds to collisionless dynamos beyond pair-plasmas

TL;DR

This paper addresses how seed magnetic fields form and are amplified in weakly collisional plasmas, a problem central to intracluster medium magnetism. It adopts a 10-moment collisionless fluid model (Gkeyll) that evolves the full pressure tensor for ions and electrons and couples to Maxwell's equations, enabling electron Weibel seed generation and subsequent dynamo amplification at a mass ratio $m_i/m_e=100$. A local isotropization closure with parameters $k_{0,e}$ and $k_{0,i}$ sets effective damping and Reynolds-number analogs, allowing the exploration of regimes from Weibel-dominated to more MHD-like dynamos. Baseline simulations show a rapid Weibel-seeded growth followed by slow, turnover-time-scale dynamo growth that saturates near equipartition with the bulk flow, while increasing $k_{0,e}$ weakens the Weibel phase and boosts dynamo efficiency, illustrating how closure physics controls the transition between kinetic and fluid-like dynamos. These results provide a computationally efficient framework to connect seed-field generation to large-scale dynamo action in collisionless astrophysical plasmas, with implications for understanding magnetic field evolution in the intracluster medium and guiding closure improvements for more accurate kinetic-fluid modeling.

Abstract

Bridging the spatiotemporal scales of magnetic seed field generation and subsequent dynamo amplification in the weakly collisional intracluster medium presents an extreme numerical challenge. We perform collisionless turbulence simulations with initially unmagnetized electrons that capture both magnetic seed generation via the electron Weibel instability and the ensuing dynamo amplification. Going beyond existing pair-plasma studies, we use an ion-to-electron mass ratio of 100 for which we find electron and ion dynamics are sufficiently decoupled. These simulations are enabled by the 10-moment collisionless fluid solver of Gkeyll, which evolves the full pressure tensor for all species. The electron heat-flux closure regulates pressure isotropization and effectively sets the magnetic Reynolds number. We investigate how the strength of of the closure influences the transition between a regime reminiscent of previous kinetic pair-plasma simulations and a more MHD-like dynamo regime.

Figures (7)

• Figure 1: Magnetic field generation in the simulation with the baseline parameters. a) Time evolution of the box-integrated magnetic energy $E_B$ (solid black curve) and kinetic energy in the flows $E_U$ (dashed black), normalized to the initial value of $E_U$. With similar line styles, contributions from the $\{x, y, z\}$ components of $\mathbf{U}$ and $\mathbf{B}$ are shown in red, blue and green, respectively. The dotted line corresponds to an exponential growth of the magnetic field with a growth rate of $\gamma_B t_{\text{turn}} = 0.76$. b) Wave number spectra of the magnetic field energy. The wave number $k$ is normalized to $k_0$, and the spectrum is normalized to its value at $k=k_0$ for $t=0$. For reference, the dotted line indicates a power law $k^{-5.5}$.
• Figure 2: Time evolution during the Weibel instability phase. a) Dimensionless quantities: Pressure anisotropy of electrons (blue, $\Delta_e$) and ions (red, $\Delta_i$), normalized magnetic field energy (green, $\beta_e^{-1}$), and instantaneous magnetic field growth rate (purple, $\gamma_B/\omega_{p,e}$). b) Instantaneous magnetic growth rate spectra ($\gamma_Bt_{\text{turn}}$) for several time instances (color coded from blue to yellow for increasing time) across the time period of the fastest field growth, bound by the dotted vertical lines of panel a). The black curve corresponds to the time of fastest global magnetic field growth, indicated by the solid vertical line in panel a). The dotted horizontal and the dashed vertical line correspond to $\gamma_B=\Delta_e^{3/2}\omega_{pe}v_{\text{th},e}/c$ and $k=\Delta_e^{1/2}/\delta_e$, respectively.
• Figure 3: Magnitude of the magnetic field in 2-D cuts of the simulation domain, taken a) and d) at the time of the fastest magnetic growth during the Weibel phase, $t/t_{\text{turn}}=0.038$, b) and e) in the middle of the dynamo growth phase, $t/t_{\text{turn}}=2.0$, and c) and f) in the saturated phase, $t/t_{\text{turn}}=10.0$. a)-c) are cuts at $x=L/2$, while d)-f) are cuts at $y=L/2$ (the latter are morphologically similar to constant $z$ cuts, not shown). The normalizing, "equipartition" magnetic field $B_{\rm eq}$ is defined such that $B_{\rm eq}^2/(2\mu_0)$ equals the box-averaged kinetic energy density in the bulk flows at $t=0$.
• Figure 4: Magnetic field generation in simulations using $k_{0,e}/k_0=\{2,\,4,\,8,\,32\}$, shown in different rows. Left column: Time evolution of the box-integrated magnetic energy $E_B$ (solid black curve) and kinetic energy in the flows $E_U$ (dashed black), normalized to the initial value of $E_U$. With similar line styles, contributions from the $\{x, y, z\}$ components of $\mathbf{U}$ and $\mathbf{B}$ are shown in red, blue and green, respectively. Exponential magnetic growth is indicated by dotted lines with growth rates provided in the figure. Right column: Wave number spectra of the magnetic field energy. The wave number $k$ is normalized to $k_0$ and the spectra are normalized to its value at $k=k_0$ for $t=0$. Dotted lines indicate power laws for reference.
• Figure 5: Dependence of damping rates on closure parameters (circle markers, main figure) and wavenumber (diamond markers, inset figure). In both of these scans, star markers correspond to the baseline case. Dashed lines indicate fitted relevant power-law behavior. a) Mass flow damping rate as a function of $k_{0,i}/k_0$ and $k/k_0$. b) Magnetic field damping rate as a function of $k_{0,e}/k_0$ and $k/k_0$.