= Solution
The result is a <fluid Eulerian perturbation> generated by translating the entire equilibrium <phase-space distribution function> through $\xi_x$:
$$
f_\alpha(x,\mu,v_\parallel,t)=f_{0\alpha}(x-\xi_x,\mu,v_\parallel)+O(\xi_x^2),\qquad
\boxed{\Delta f_\alpha=\delta f_\alpha+\xi_x\partial_xf_{0\alpha}=0.}
$$
Here $\Delta$ follows the displaced <flux tube>. <Magnetic flux freezing> carries the tube and its particles across the equilibrium <pressure gradient>. To leading order the tube changes neither its field strength nor its length by enough to alter the particle <phase-space distribution function>: these changes are smaller by <plasma beta> or $L_p/R$. Parallel streaming remains within the same displaced tube, on which the original equilibrium <phase-space distribution function> was uniform. It therefore cannot erase the displacement-generated contrast between adjacent tubes. This is why the term $v_\parallel\delta b_x\partial_xf_{0\alpha}$ in <3/c> exactly cancels the apparent parallel relaxation of $-\xi_x\partial_xf_{0\alpha}$. No collisional restoration of a <Maxwell-Boltzmann distribution> is needed.
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