  Context. The galactic winds of starburst galaxies (SBGs) give rise to
remarkable structures on kiloparsec scales. However, the evolution and shape of
these giant wind bubbles, as well as the properties of the shocks they develop,
are not yet fully understood. Aims. We aim to understand what shapes the
galactic winds of SBGs, with a particular focus on the role of large-scale
magnetic fields in the dynamical evolution of galactic wind-inflated bubbles.
In addition, we aim to explore where the conditions for efficient particle
acceleration are met in these systems. Methods. We performed
magnetohydrodynamic simulations with the AMRVAC code (Adaptive Mesh Refinement
Versatile Advection Code) with various configurations of the galactic medium
density profile and magnetization. Results. We observe that the large-scale
magnetic field, in which galactic winds expand, can impact the structure and
evolution of inflated bubbles. However, the typical structures observed in
starburst galaxies, such as M82, cannot be solely explained by the magnetic
field structures that have been considered. This highlights the importance of
other factors, such as the galactic disk, in shaping the galactic bubble.
Furthermore, in all the magnetized cases we investigated, the forward wave
resulting from the expanding bubbles only results in compression waves, whereas
the wind termination shock features high Mach numbers, making it a promising
site for diffusive shock acceleration up to $\sim 10^{2}$ PeV. The synthetic
X-ray images generated from our models reveal an envelope surrounding the
bubbles that extends up to 2 kpc, which could correspond to the polarized
emission observed from planar geometry in M82, as well as a large structure
inside the bubble corresponding to the shocked galactic wind.
