Effect of Flow-aligned External Magnetic Fields on Mushroom Instability

Abstract Mushroom instability (MI) is a shear instability considered to be related to generating and amplifying magnetic fields in relativistic jets. While astrophysical jets are usually magnetized, how MI acts in magnetized jets remains poorly understood. In this paper, we investigate the effect of a flow-aligned external magnetic field on MI with both theoretical analyses and particle-in-cell (PIC) simulations. In the limit of a cold and collisionless plasma, we derive a generalized dispersion relation for linear growth rates of the magnetized MIs. Numerical solutions of the dispersion relation reveal that the external magnetic field always suppresses MI, though MIs are more robust against the field than electron-scale Kelvin–Helmholtz instabilities. Replacing protons in the shear flow with positrons enhances the instability growth in weakly magnetized regimes but suppresses it in strongly magnetized cases. Analyses are also extended to instabilities with an arbitrary wavevector in the shear interface plane, where a coupling effect is observed for subrelativistic scenarios. The 2D PIC simulations of single-mode MIs reach a good agreement with our analytical predictions, and we observe formation of a quasi-steady saturation structure of electrons in magnetized runs. In simulations with finite temperatures, we observe the competition and cooperation between MIs and a diffusion-induced direct current magnetic field.