  The escape of cosmic rays from the Galaxy is expected to shape their spectrum
inside the Galaxy. Yet, this phenomenon is very poorly understood and, in the
absence of a physical description, it is usually modelled as free escape from a
given boundary, typically located at a few kpc distance from the Galactic disc.
We show that the assumption of free escape leads to the conclusion that the
cosmic ray current propagating in the circumgalactic medium is responsible for
a non resonant cosmic ray induced instability that in turn leads to the
generation of a magnetic field of strength $\sim 2\times 10^{-8}$ Gauss on a
scale $\sim 10$ kpc around our Galaxy. The self-generated diffusion produces
large gradients in the particle pressure that induce a displacement of the
intergalactic medium with velocity $\sim 10-100$ km/s. Cosmic rays are then
carried away by advection. If the overdensity of the intergalactic gas in a
region of size $\sim 10$ kpc around our Galaxy is $\gtrsim 100$ with respect to
the cosmological baryon density $\Omega_{b}\rho_{cr}$, then the flux of high
energy neutrinos as due to pion production becomes comparable with the flux of
astrophysical neutrinos recently measured by IceCube.
