Astroparticle Physics

5.5 Pulsars 69Since this acceleration mechanism is quadratic in the cloudvelocity, this variant is often called Fermi mechanism of 2ndorder. The result of (5.16) remains correct even under relativistictreatment. Since the cloud velocity is rather low comparedto the particle velocities (u ≪ v ≈ c), the energy gainper collision (∼ u 2 ) is very small. Therefore, the accelerationof particles by the Fermi mechanism requires a verylong time. In this acceleration type one assumes that magneticclouds act as collision partners – and not normal gasclouds – because the gas density and thereby the interactionprobability is larger in magnetic clouds.Another important aspect is that cosmic-ray particleswill lose some of their gained energy by interactions withthe interstellar or intergalactic gas between two collisions.This is why this mechanism requires a minimum injectionenergy above which particles can only be effectively accelerated.These injection energies could be provided by theFermi mechanism of 1st order, that is, by shock acceleration.slow energy increaseinjection energy5.5 Pulsars“Rhythmically pulsating radio source,Can you not tell us what terrible forceRenders your density all so immenseTo account for your signal so sharp andintense?”Dietrick E. ThomsenJonathan EberhartSpinning magnetized neutron stars (pulsars) are remnantsof supernova explosions. While stars typically have radiiof 10 6 km, they shrink under a gravitational collapse to asize of just about 20 km. This process leads to densities of6 × 10 13 g/cm 3 comparable to nuclear densities. In this processelectrons and protons are so closely packed that in processesof weak interactions neutrons are formed:p + e − → n + ν e . (5.17)Since the Fermi energy of electrons in such a neutron staramounts to several hundred MeV, the formed neutrons cannotdecay because of the Pauli principle, since the maximumenergy of electrons in neutron beta decay is only 0.78 MeVand all energy levels in the Fermi gas of electrons up to thisenergy and even beyond are occupied.neutron star