Critically balanced electron-magnetohydrodynamic cascade (source code)

= Critically balanced electron-magnetohydrodynamic cascade
{title2=$b_l\propto l_\perp^{2/3},\quad l_\parallel\propto l_\perp^{1/3}$}

<Critical balance> sets $\tau_{\mathrm{nl}}\sim\tau_w$, hence $l_\parallel\sim l_\perp/b_l$. A local strong cascade with constant <energy flux> has $\epsilon\sim v_A^3d_i b_l^3/l_\perp^2$, giving the displayed exponents and perpendicular <magnetic energy spectrum> $E_B(k_\perp)\propto k_\perp^{-7/3}$. The anisotropy becomes stronger towards small perpendicular scales.