= Weak electron-magnetohydrodynamic cascade
{title2=$b_l\sim[\epsilon l_\perp^3/(v_A^3d_i l_\parallel)]^{1/4}$}
For $b_ll_\parallel/l_\perp\ll1$, the <weak wave cascade> estimate gives $\tau_{\mathrm{cas}}\sim l_\perp^3/(v_Ad_i b_l^2l_\parallel)$. Constant <energy flux> $\epsilon\sim v_A^2b_l^2/\tau_{\mathrm{cas}}$ yields the displayed amplitude. An additionally isotropic local cascade has $b_l\propto l^{1/2}$ and shell-integrated <magnetic energy spectrum> $E_B(k)\propto k^{-2}$. These statements are phenomenological consequences of the chosen locality and decorrelation assumptions.
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