ERRATUM: "SUPERDIFFUSION OF COSMIC RAYS: IMPLICATIONS FOR COSMIC RAY ACCELERATION" (2014, ApJ, 784, 38)

This is a small correction to the published article in relation to the particular regime of CR diffusion, namely, the diffusion in the superAlfvenic turbulence. This correction makes the discussion in the paper self-consistent.

In the published article, Equations (12) and (13) are wrong. In fact, at scales larger than the Alfvenic scale l_A magnetic fields are entangled by turbulence and therefore the separation of magnetic field lines is a random walk process with the step l_A. Therefore, the mean squared separation between the magnetic field lines ${l}_{\perp }^{2}$ is increasing with the distance tracked along the magnetic field line s as

$$\begin{eqnarray}&&{l}_{\perp }^{2}\sim {{sl}}_{A}.\end{eqnarray} \tag{ 1 }$$

Therefore, for the scales $[{l}_{A},L]$, magnetic field lines undergo diffusion and the transport of cosmic rays that stream along magnetic field is diffusive on scales larger than l_A. As a result, Table 1 in the paper should be modified as we present below.

Table 1.  Regimes of MHD Turbulence and Magnetic Diffusion

Type of MHD turbulence	Injection velocity	Range of scales	Spectrum E(k)	Motion type	Ways of study	Magnetic diffusion	Squared separation of lines
Weak	${V}_{L}\lt {V}_{A}$	$[{l}_{{trans}},L]$	${k}_{\perp }^{-2}$	wave-like	analytical	diffusion	$\sim {{sLM}}_{A}^{2}$
Strong				anisotropic
subAlfvenic	${V}_{L}\lt {V}_{A}$	$[{l}_{{\min }},{l}_{{trans}}]$	${k}_{\perp }^{-5/3}$	eddy-like	numerical	Richardson	$\sim \tfrac{{s}^{3}}{L}{M}_{A}^{4}$
Strong				isotropic
superAlfvenic	${V}_{L}\gt {V}_{A}$	$[{l}_{A},L]$	${k}_{\perp }^{-5/3}$	eddy-like	numerical	diffusion	$\sim {{sl}}_{A}$
Strong				anisotropic
superAlfvenic	${V}_{L}\gt {V}_{A}$	$[{l}_{{\min }}],{l}_{A}$	${k}_{\perp }^{-5/3}$	eddy-like	numerical	Richardson	$\sim \tfrac{{s}^{3}}{L}{M}_{A}^{3}$

Note. L and l_min are the injection and perpendicular dissipation scales, respectively. ${M}_{A}\equiv \delta B/B$, ${l}_{{trans}}={{LM}}_{A}^{2}$ for ${M}_{A}\lt 1$ and ${l}_{A}={{LM}}_{A}^{-3}$. for ${M}_{A}\lt 1$. For weak Alfvenic turbulence, ${{\ell }}_{\parallel }$ does not change. s is measured along magnetic field lines.

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This mistake in the paper does not change any conclusions or results of the aforementioned work because cosmic ray propagation and acceleration in the limit of superAlfvenic turbulence considered in Section 7 used the correct diffusion coefficient given by Equation (39), which is consistent with our Equation (1) above. Equation (39) was obtained from physical considerations and not derived from Equations (12) and (13). In other words, the published article contained a contradiction and the present erratum removes this contradiction.