  Cosmic rays (CRs) leave their sources mainly along the local magnetic field;
in doing so they excite both resonant and nonresonant modes through streaming
instabilities. The excitation of these modes leads to enhanced scattering and
in turn to a large pressure gradient that causes the formation of bubbles of
gas, CRs, and self-generated magnetic fields expanding into the interstellar
medium. By means of hybrid Particle-In-Cell simulations, we show that, by
exciting the nonresonant instability, CRs excavate a cavity around their source
where the diffusivity is strongly suppressed. This finding invalidates the so
far largely adopted flux-tube assumption, under which particles move along
magnetic lines even in the nonlinear regime. This phenomenon is general and is
expected to occur around any sufficiently powerful CR source in the Galaxy. Our
results might provide a physical explanation of the numerous claims of
suppressed CR diffusion around Galactic sources such as supernova remnants,
pulsar wind nebulae, and stellar clusters.
