we fix a monic polynomial $\bar f(x) \in \mathbb{f}_q[x]$ over a finite field of characteristic $p$, and consider the $\mathbb{z}_{p^{\ell}}$-artin--schreier--witt tower defined by $\bar f(x)$; this is a tower of curves $\cdots \to c_m \to c_{m-1} \to \cdots \to c_0 =\mathbb{a}^1$, whose galois group is canonically isomorphic to $\mathbb{z}_{p^\ell}$, the degree $\ell$ unramified extension of $\mathbb{z}_p$, which is abstractly isomorphic to $(\mathbb{z}_p)^\ell$ as a topological group. we study the newton slopes of zeta functions of this tower of curves. this reduces to the study of the newton slopes of l-functions associated to characters of the galois group of this tower. we prove that, when the conductor of the character is large enough, the newton slopes of the l-function asymptotically form a finite union of arithmetic progressions. as a corollary, we prove the spectral halo property of the spectral variety associated to the $\mathbb{z}_{p^{\ell}}$-artin--schreier--witt tower. this extends the main result of davis--wan--xiao from rank one case $\ell=1$ to the higher rank case $\ell\geq 1$.