  Any polynomial $f(x)\in\mathbb{Z}_q[x]$ defines a Witt vector $[f]\in
W(\mathbb{F}_q[x])$. Consider the Artin-Schreier-Witt tower $y^F-y=[f]$. This
is a tower of curves over $\mathbb{F}_q$, with total Galois group
$\mathbb{Z}_p$. We want to study the Newton slopes of zeta functions of this
tower. We reduce it to the Newton polygons of L-functions associated with
characters on the Galois groups. We prove that, when the conductors are large
enough, these Newton slopes are unions of arithmetic progressions which are
changing proportionally as the conductor increases. This is a generalization of
the result of \cite{Da}, where they get the same result in the case the
non-zero coefficients of $f(x)$ are roots of unity. To overcome the new
difficulty in our process, we apply some $(p^{\theta},T)$-topology.
