The quest for the elusive dark matter (DM) that permeates the Universe (and in general the search for signatures of physics beyond the Standard Model at astronomical scales) provides a unique opportunity and a tough challenge to the high energy astrophysics community. In particular, the so-called DM indirect searches—mostly focused on a class of theoretically well-motivated DM candidates such as the weakly interacting massive particles—are affected by a complex astrophysical background of cosmic radiation. The understanding and modeling of such background require a deep comprehension of an intricate classical plasma physics problem, i.e., the interaction between high energy charged particles, accelerated in peculiar astrophysical environmen...