  We show that, in one spatial and arbitrary jump dimension, the averaged
solution of a Marcustype SPDE with pure jump L\'evy transport noise satisfies a
dissipative deterministic equation involving a fractional Laplace-type
operator. To this end, we identify the correct associated L\'evy measure for
the driving noise. We consider this a first step in the direction of a
non-local version of enhanced dissipation, a phenomenon recently proven to
occur for Brownian transport noise and the associated local parabolic PDE by
the first author. Moreover, we present numerical simulations, supporting the
fact that dissipation occurs for the averaged solution, with a behavior akin to
the diffusion due to a fractional Laplacian, but not in a pathwise sense.
