We have investigated the generation of magnetic ﬁelds associated with velocity shear between an unmagne-tized relativistic jet and an unmagnetized sheath plasma. We have examined the strong magnetic ﬁelds generated by ki-netic shear (Kelvin–Helmholtz) instabilities. Compared to the previous studies using counter-streaming performed by Alves et al. (2012), the structure of the kinetic Kelvin– Helmholtz instability (KKHI) of our jet-sheath conﬁgura-tion is slightly different, even for the global evolution of the strong transverse magnetic ﬁeld. In our simulations the major components of growing modes are the electric ﬁeld Ez, perpendicular to the ﬂow boundary, and the magnetic ﬁeld By, transverse to the ﬂow direction. After the By com-ponent is excited, an induced electric ﬁeld Ex, parallel to the ﬂow direction, becomes signiﬁcant. However, other ﬁeld components remain small. We ﬁnd that the structure and growth rate of KKHI with mass ratios mi/me = 1836 and mi/me = 20 are similar. In our simulations saturation in the nonlinear stage is not as clear as in counter-streaming cases.
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