  Two-particle pseudorapidity correlations, measured using charged particles
with $p_{\mathrm{T}} >$ 0.5 GeV and $|\eta| <$ 2.4, from $\sqrt{s_{NN}}$ = 2.76
TeV Pb+Pb collisions collected in 2010 by the ATLAS experiment at the LHC are
presented. The correlation function $C_N(\eta_1,\eta_2)$ is measured for
different centrality intervals as a function of the pseudorapidity of the two
particles, $\eta_1$ and $\eta_2$. The correlation function shows an enhancement
along $\eta_- \equiv \eta_1 - \eta_2 \approx$ 0 and a suppression at large
$\eta_-$ values. The correlation function also shows a quadratic dependence
along the $\eta_+ \equiv \eta_1$ + $\eta_2$ direction. These structures are
consistent with a strong forward-backward asymmetry of the particle
multiplicity that fluctuates event to event. The correlation function is
expanded in an orthonormal basis of Legendre polynomials,
$T_n(\eta_1)T_m(\eta_2)$, and corresponding coefficients $a_{n,m}$ are
measured. These coefficients are related to mean-square values of the Legendre
coefficients, $a_n$, of the single particle longitudinal multiplicity
fluctuations: $a_{n,m} = \langle a_na_m \rangle$. Significant values are
observed for the diagonal terms $\langle a_n^2 \rangle$ and mixed terms
$\langle a_na_{n+2}\rangle$. Magnitude of $\langle a_{\mathrm{1}}^{\mathrm{2}}
\rangle$ is the largest and the higher order terms decrease quickly with
increase in $n$. The centrality dependence of the leading coefficient $\langle
a_{\mathrm{1}}^{\mathrm{2}} \rangle$ is compared to that of the mean-square
value of the asymmetry of the number of participating nucleons between the two
colliding nuclei, and also to the $\langle a_{\mathrm{1}}^{\mathrm{2}} \rangle$
calculated from HIJING.
