Recent numerical simulations have shown long-lived axisymmetric sub- and super-Keplerian flows in protoplanetary disks .
These zonal flows are found in local as well as global simulations of disks unstable to the magnetorotational instability .
This paper covers our study of the strength and lifetime of zonal flows and the resulting long-lived gas over- and underdensities as functions of the azimuthal and radial size of the local shearing box .
We further investigate dust particle concentrations without feedback on the gas and without self-gravity .
Strength and lifetime of zonal flows increases with the radial extent of the simulation box , but decreases with the azimuthal box size .
Our simulations support earlier results that zonal flows have a natural radial length scale of 5 to 7 gas pressure scale heights .
This is the first study that combines three-dimensional MHD simulations of zonal flows and dust particles feeling the gas pressure .
The pressure bumps trap particles with \textrm { St } = 1 very efficiently .
We show that \textrm { St } = 0.1 particles ( of some centimeters in size if at 5 \textrm { AU } in an MMSN ) reach a hundred-fold higher density than initially .
This opens the path for particles of \textrm { St } = 0.1 and dust-to-gas ratio of 0.01 or for particles of \textrm { St } \geq 0.5 and dust-to-gas ratio 10 ^ { -4 } to still reach densities that potentially trigger the streaming instability and thus gravoturbulent formation of planetesimals .