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tokens: variables, and powerful radio pulsars, such as the pulsar in the Crab nebula. In laboratory plasmas, jets, or directed flows, are observed in devices such as plasma focus (Beskin et al. 2017a ). The main puzzle of jets is their high degree of collimation. It is not clear how hot matter of jets, ionized gas in a strong magnetic field, confined in the cylindrical radius direction, which is the direction perpendicular to the axis of the jet. Neither hot gas nor external magnetic field is usually observed in the interstellar and intergalactic environment surrounding a jet. We will study the problem of radial equilibrium of the jet in the framework of ideal magnetohydrodynamics (MHD). This approximation is well suited for astrophysical jets. Dissipative effects are weak in hot plasma. In addition, large mean-free paths of particles, the presence of a strong magnetic field, in which cyclotron radii play the role of particle mean-free paths, and small cyclotron radii of ions in comparison with the characteristic scales of jets allow us to use ideal MHD for the description of astrophysical jets. It has been shown before that the problem of equilibrium of the jet in the radial direction within the framework of MHD is related to electric currents flowing inside the jet. If the jet carries uncompensated current, i.e. the total current of the jet is not zero, the current can be pinched to keep the hot jet in equilibrium (Blandford Payne 1982 ; Heyvaerts Norman 1989 ; Sulkanen Lovelace 1990 ; Li, Chiuch Begelman 1992 ; Pelletier Pudritz 1992 ; Sauty Tsinganos 1994 ). However, the question arises how to close the uncompensated current loop. If you let the return current flow outside the jet, it is not clear where it goes since track of the return current is usually not visible. It is more convenient to assume that return current flows inside the jet on its periphery. This raises the problem of the equilibrium of the jet in the region of return current. The return current repels from the direct one, and within the framework of a purely radial structure, there is no equilibrium, if there is no contribution of the surface current at the edge of the jet (Lery et al. 1998 ; Beskin Malyshkin 2000 ; Lyubarsky 2009 ; Beskin Nokhrina 2010 ). Here we will explore another possibility – the emergence of spiral structure in the region of return current flow. 2 CYLINDRICAL FLOW Let us consider stationary MHD equations in a coordinate system moving with the plasma flow along its axis with the velocity u . Here ρ is the plasma density of the jet, is velocity of the plasma, B is the magnetic field, and P (ρ) is the plasma pressure, which is a function of the density through the equation of state of the matter in the jet. Suppose first that all quantities depend only on the cylindrical radius coordinate r , that is, the jet is axisymmetric and homogeneous along axis z . In this case, the velocity and the magnetic field can be expressed as functions of r , Velocity v φ