Kineclinic magnetogenesis in relativistic collisionless plasmas

Abstract

The relativistic momentum equation of a collisionless plasma is reformulated to describe the time evolution of canonical vorticity. Compared to the non-relativistic counterpart, an additional source term for canonical vorticity is identified, which embodies the misalignment between the fluid momentum and fluid velocity gradients. This kineclinic term breaks the frozen-in condition of canonical vorticity, thereby enabling generation or dissipation of magnetic fields and vorticity. We verify the role of this effect through particle-in-cell simulations of a modified Beltrami flow. Kineclinicity should be finite for all relativistic plasma systems due to the general lack of a functional relationship between fluid momentum and fluid velocity.

Figures (2)

• Figure 1: Streak plots of various quantities (a) $B_z[m_e\omega_{pe}/e]$, (b) $(\Omega_{ez}-\Omega_{0ez})[m_e\omega_{pe}]$, (c) $(Q_{ez}-Q_{0ez})[m_e\omega_{pe}]$, (d) $\partial Q_{ez}/\partial t [m_e\omega_{pe}^2]$, (e) $\mathcal{C}_z~[m_e\omega_{pe}^2]$, (f) $\mathcal{B}_z~[m_e\omega_{pe}^2]$, (g) $\mathcal{R}_{ez} ~[m_e\omega_{pe}^2]$, and (h) ($\mathcal{C}_{ez}+\mathcal{B}_{ez}+\mathcal{R}_{ez})~[m_e\omega_{pe}^2]$ from the 2D PIC simulation. The three slices in each panel correspond to $t\omega_{pe}=25,35,$ and $45$.
• Figure 2: Scatter plot of normalized $\left<{p} \right>$ vs. $u$ for the simulation shown in Fig. \ref{['fig:2D_streak']}, displayed at times at $t\omega_{pe}\approx$ 0, 15, 30, and 45. Each scatter point corresponds to the value at a particular grid point. The black dashed line in panel (a) corresponds to the analytical relation ${\left<p\right>}= u/\sqrt{1-u^2}$. The inset plot in panel (a) corresponds to the same scatter plot for the non-relativistic $\gamma\approx 1$ case, which maintains a linear relationship at all $t\omega_{pe}$.