  We study how external magnetic fields from 0 to 40 T influence positive
streamers in atmospheric pressure air, using 3D PIC-MCC (particle-in-cell,
Monte Carlo collision) simulations. When a magnetic field $\vec{B}$ is applied
perpendicular to the background electric field $\vec{E}$, the streamers deflect
towards the $+\vec{B}$ and $-\vec{B}$ directions which results in a branching
into two main channels. With a stronger magnetic field the angle between the
branches increases, and for the 40 T case the branches grow almost parallel to
the magnetic field. Due to the $\vec{E}\times\vec{B}$ drift of electrons we
also observe a streamer deviation in the opposite $-\vec{E}\times\vec{B}$
direction, where the minus sign appears because positive streamers propagate
opposite to the electron drift velocity. The deviation due to this
$\vec{E}\times\vec{B}$ effect is smaller than the deviation parallel to
$\vec{B}$. In both cases of $\vec{B}$ perpendicular and parallel to $\vec{E}$,
the streamer radius decreases with the magnetic field strength. We relate our
observations to the effects of electric and magnetic fields on electron
transport and reaction coefficients.
