The problem of the origin of Cosmic Rays (CRs) is a central one in high energy astrophysics. While it is firmly established that the bulk of CRs originates within the Galaxy, the way in which these particles are accelerated at their sources, as well as the way in which they are confined in the magnetized and turbulent interstellar medium (ISM) are still a matter of debate.
The last few years have seen improvements in our knowledge of CR energy spectra. In particular, the orthodox picture of a universal injection spectrum of Galactic sources and a power law scaling of the CR diffusion coefficient with energy has been undermined by more precise measurements of individual chemical spectra by a number of experiments: ATIC, AMS, BESS, CREAM, DAMPE and PAMELA.
The GRAPES goal was to face this wealth of data to achieve a better understanding of the physics of CR transport.
I developed a model where the turbulence responsible for the scattering of CRs is described by two components: the external turbulence with a Kolmogorov spectrum, and the waves generated by CR themselves through streaming instability.
A simple estimate shows that the nonlinear damping rate of turbulent waves equals the growth rate CR streaming instability at a rigidity of 300 GV tantalisingly close to the rigidity where a break is observed. CRs above the break diffuse on external turbulence, while self-generated turbulence dominates at lower energies.
By taking additionally into account the advection of turbulence from the Galactic disk where the sources of CRs and turbulence are assumed to be located, I obtained that the diffusive halo naturally arises, with a size of a few kiloparsecs, compatible with the value that typically best fits observations in parametric approaches to CR transport. Within this model local observables, as the proton spectrum, are consistently reproduced (figure).
Self-generated turbulence can also play a role around sources. For the first time, I showed that the steep cosmic-ray lepton density produced by the pulsar source excites turbulence, which significantly inhibits the propagation of these same CRs. This model fits some observational characteristics of the gamma-ray emission observed around these sources (known as TeV halos), as the increasing size of these TeV halos as a function of the pulsar age.
An effective approach aiming at describing primary and stable secondary CR nuclei was developed afterwards. This model is based on the weighted slab approach which allows one to solve the advection-diffusion equation including the whole chain of spallation reactions from heavier nuclei to lighter nuclei. By comparing the results of my calculations with observations I obtained solid estimates of the grammage transversed by CRs in the Galaxy and their characteristics confinement time (figure).
