Dynamo in Weakly Collisional Nonmagnetized Plasmas Impeded by Landau Damping of Magnetic Fields

We perform fully kinetic simulations of flows known to produce dynamo in magnetohydrodynamics (MHD), considering scenarios with low Reynolds number and high magnetic Prandtl number, relevant for galaxy cluster scale fluctuation dynamos. We find that Landau damping on the electrons leads to a rapid decay of magnetic perturbations, impeding the dynamo. This collisionless damping process operates on spatial scales where electrons are nonmagnetized, reducing the range of scales where the magnetic field grows in high magnetic Prandtl number fluctuation dynamos. When electrons are not magnetized down to the resistive scale, the magnetic energy spectrum is expected to be limited by the scale corresponding to magnetic Landau damping or, if smaller, the electron gyroradius scale, instead of the resistive scale. In simulations we thus observe decaying magnetic fields where resistive MHD would predict a dynamo.

Figure 1

Volume integrated magnetic energy. Solid lines: kinetic simulation; dashed lines: resistive MHD induction equation. Red, blue, and green correspond to the contributions from the $x$, $y$, and $z$ field components to the total (black). For reference, $(3/2)n_i{T}_i{L}_0^3=5.1\times {10}^{-3}\mathrm{J}$.

Figure 2

Wave number spectra of magnetic energy, $E_B(k)$ (normalized to its value at $k_0$, $t=0$), for $t=\{0,1,2,\dots ,6\}\times {10}^{-11}\mathrm{s}$ (lines lightening). Solid lines: kinetic simulation; dashed lines: MHD induction equation; dotted line: MHD induction equation in the growing phase $t=2\times {10}^{-10}\mathrm{s}$.

Figure 3

Effective resistivity, $1/{\sigma }_{\mathrm{eff}}[\mathrm{\Omega }\mathrm{m}]$, as a function of collision scaling factor $C_{\nu }$, for four values of the wavelength of the current perturbation, increasing from $L_0/8$ to $L_0=9.73\mu \mathrm{m}$ (solid lines darkening). The Spitzer resistivity (dotted line), and the collisionless, unmagnetized theoretical limits (dashed lines) are also indicated.

Figure 4

Solid lines: The ratio of the relevant component of the electron viscous stress and the electric field force. In (a) the ratio is shown as a function of collision scaling factor $C_{\nu }$, for four values of the wavelength of the current perturbation, increasing from $L_0/8$ to $L_0=9.73\mu \mathrm{m}$ (lines darkening). In (b) the ratio is shown as a function of the electron magnetization $L_0/{\rho }_{e0}$, where ${\rho }_{e0}$ is the electron Larmor radius at a field strength of $B_0$. Here, the effective resistivity is also shown [dashed curve, normalized to its highest value, $1.65\times {10}^{-8}\mathrm{\Omega }\mathrm{m}$]; the wavelength is $L_0$, and $C_{\nu }=0.05$.

Figure 5

Volume integrated magnetic energy in a forced Roberts flow simulation, for $C_{\nu }=0$ (solid) and 0.3 (dashed). Red, blue, and green correspond to the contributions from the $x$, $y$, and $z$ field components to the total (black). For reference, $(3/2)n_i{T}_i{L}_0^3=9.94\times {10}^{-6}\mathrm{J}$.