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Detailed studies of relativistic jets in active galactic nuclei (AGN) requirehigh-fidelity imaging at the highest possible resolution. This can be achievedusing very long baseline interferometry (VLBI) at radio frequencies, combiningworldwide (global) VLBI arrays of radio telescopes with a space-borne antennaon board a satellite. We present multiwavelength images made of the radioemission in the powerful quasar S5 0836+710, obtained using a global VLBI arrayand the antenna Spektr-R of the RadioAstron mission of the Russian SpaceAgency, with the goal of studying the internal structure and physics of therelativistic jet in this object. The RadioAstron observations at wavelengths of18cm, 6cm, and 1.3cm are part of the Key Science Program for imaging radioemission in strong AGN. The internal structure of the jet is studied byanalyzing transverse intensity profiles and modeling the structural patternsdeveloping in the flow. The RadioAstron images reveal a wealth of structuraldetail in the jet of S5 0836+710 on angular scales ranging from 0.02mas to200mas. Brightness temperatures in excess of $10^{13}$\,K are measured in thejet, requiring Doppler factors of $\ge 100$ for reconciling them with theinverse Compton limit. Several oscillatory patterns are identified in the ridgeline of the jet and can be explained in terms of the Kelvin-Helmholtz (KH)instability. The oscillatory patterns are interpreted as the surface and bodywavelengths of the helical mode of the KH instability. The interpretationprovides estimates of the jet Mach number and of the ratio of the jet to theambient density, which are found to be $M_\mathrm{j}\approx 12$ and$\eta\approx 0.33$. The ratio of the jet to the ambient density should beconservatively considered an upper limit because its estimate relies onapproximations.

Multiband RadioAstron space VLBI imaging of the jet in quasar S5 0836+710