Errata for "Landau fluid models of collisionless magnetohydrodynamics",
P.B. Snyder, G.W. Hammett, and W. Dorland, Phys. Plasmas 4, 3974 (1997)
(PPPL-3260).

Last updated Aug. 27, 2009.

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In Eq. 5, the factor of $(p_\perp-p_\par)$ should be $(p_\par-p_\perp)$.

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Right after Eq. 33, in the expression for $r_{\par,\par,0s}$, the pressure
$p_{\par 0s}$ should be squared.  Likewise, on the next line, in the
expression for $r_{\perp,\perp 0 s}$, the factor of $p_{\perp 0s}$ should
also be squared.  (Found by Prateek Sharma.)

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On p.3980, 2 lines above Eq. 44, and on p.3981, 3 lines below the first
unnumbered displayed equation, a coefficient of 2 on the bb component of
the stress tensor should be replaced by a factor of 3, which is of course
required to insure that the stress tensor is traceless.

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2009.08.27:  On p. 3980, the first term on the 2cd line of Eq. 45, which
reads

-3 q_{\perp s} \grad \cdot \vec U

is wrong (it is dimensionally incorrect in this equation as it stands).  
The "U" should be replaced with "b" so that it reads:

-3 q_{\perp s} \grad \cdot \vec b

(Thanks to Alex Schekochihin for point this out.)

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A recent paper by J. Ramos (Phys. Plasmas 10, 3601 (2003)) derives a
similar set of fluid moment equations as derived in Snyder et al.  Ramos
does this by first taking moments of the full Vlasov-Boltzmann equation,
and then doing an MHD-like low-frequency (omega<<Omega_c) expansion.  Note
that this is the reverse order of what was done in the Snyder et al. paper,
where we first took the low-frequency limit of the Vlasov-Boltzmann
equation to get a drift-kinetic equation, and then took fluid moments of
that.  In principal one should get the same answer either way.  For some
reason, Ramos found one slight difference between Snyder's Eq. 19 for
$\partial q_{\perp s}/\partial t$, and his version of that equation.  I
have not tracked down the source of the difference.  (Other than simple
typos in one of our derivations, the only thing I can think of is that
sometimes there are some subtle differences in the order to which various
drifts have to be kept at different stages in the calculations, because
quasineutral restrictions extend to higher orders than usual.)