  This paper presents the effects of electron-positron pair production on the
linear growth of the resistive hose instability of a filamentary beam that
could lead to snake-like distortion. For both the rectangular radial density
profile and the diffuse profile reflecting the Bennett-type equilibrium for a
self-collimating flow, the modified eigenvalue equations are derived from a
Vlasov-Maxwell equation. While for the simple rectangular profile, current
perturbation is localized at the sharp radial edge, for the realistic Bennett
profile with an obscure edge, it is non-locally distributed over the entire
beam, removing catastrophic wave-particle resonance. The pair production
effects likely decrease the betatron frequency, and expand the beam radius to
increase the resistive decay time of the perturbed current; these also lead to
a reduction of the growth rate. It is shown that, for the Bennett profile case,
the characteristic growth distance for a preferential mode can exceed the
observational length-scale of astrophysical jets. This might provide the key to
the problem of the stabilized transport of the astrophysical jets including
extragalactic jets up to Mpc ($\sim 3\times 10^{24}$ cm) scales.
