How do pulsars and magnetars emit lots of radiation?

Firstly I thought that Pulsars are rapidly rotating, highly magnetic compact stars. The rotating magnetic field of a pulsar acts as a generator, accelerating energetic charged particles that then stream along the field lines”. At a glance the answer looks quite decent but second look does not convinces me. First important thing how are these magnetic fields are formed? For a electrically charged particles moving in a ring generates a magnetic field but the particles in neutron stars are neutrons which are electrically neutral. Then a second one was the equations which are involved in it, when protons collide with electrons during the formation of neutron star they form neutrons and give out neutrino, to what I have learnt, the equation does not feels good as when a neutron gets converted into a proton by beta decay an electron and an anti-neutrino is emitted so if we reverse this in time a proton, electron and anti-neutrino forms a neutron which is different from the previous equation, why are there two sets of equations for this?

$$\mathrm{I}.$$ A pulsar is a neutron star that is mostly made up of neutrons. On the surface, gravitational pressure does not hinder the $$\beta^{-}$$ decay of neutrons, and so charged particles such as electrons and protons can form a magnetic field due to the whirling rotation of these objects. The small size and the high angular momentum create enormous magnetic fields capable of "tapering" the atoms.
$$\mathrm{II.}$$ It is not correct to say that electrons collide on protons, during the gravitational collapse. More precisely, due to the gravitational pressure, a $$\beta$$-inverse decay is triggered, which can be written as: $$\bar{\nu}_{e} + p \rightarrow n + e^+$$ i.e. electronic anti-neutrino, $$\bar{\nu}_e$$, and a proton, p, exchange a $$W^+$$ virtual boson, and produce a neutron plus a positron. This positrons then collide with the free elctrons in the star during the collapsing and emits photons: $$e^-+e^+\rightarrow 2\gamma$$
• Should be $e^+ + e^- \rightarrow \gamma + \gamma$ – Triatticus Jan 13 at 18:29