  Charged perfect fluid with vanishing Lorentz force and massless scalar field
is studied in the case of stationary cylindrically symmetric spacetime. The
scalar field can depend both on radial and longitudinal coordinates. Solutions
are found and classified according to scalar field gradient and magnetic field
relationship. Their physical and geometrical properties are examined and
discussion of particular cases, directly generalizing G\"{o}del-type
spacetimes, is presented.
