We discuss properties of the ultra-luminous $X$-ray source in the galaxy M82, NuSTAR J095551+6940.8, containing an accreting neutron star. The neutron star has surface magnetic field $ B_{NS} approx 1.4 times 10^{13 } , {rm G}$ and experiences accret
ion rate of $9 times 10^{-7} M_odot {rm , yr}^{-1} $. The magnetospheric radius, close to the corotation radius, is $sim 2 times 10^8$ cm. The accretion torque on the neutron star is reduce well below what is expected in a simple magnetospheric accretion due to effective penetration of the stellar magnetic field into the disk beyond the corotation radius. As a result, the radiative force of the surface emission does not lead to strong coronal wind, but pushes plasma along magnetic field lines towards the equatorial disk. The neutron star is nearly an orthogonal rotator, with the angle between the rotation axis and the magnetic moment $geq 80$ degrees. Accretion occurs through optically thick -- geometrically thin and flat accretion curtain, which cuts across the polar cap. High radiation pressure from the neutron star surface is nevertheless smaller than that the ram pressure of the accreting material flowing through the curtain, and thus fails to stop the accretion. At distances below few stellar radii the magnetic suppression of the scattering cross-section becomes important. The $X$-ray luminosity (pulsed and persistent components) comes both from the neutron star surface as a hard $X$-ray component and as a soft component from reprocessing by the accretion disk.
We advance a Solar flare model of magnetar activity, whereas a slow evolution of the magnetic field in the upper crust, driven by electron MHD (EMHD) flows, twists the external magnetic flux tubes, producing persistent emission, bursts and flares. At
the same time the neutron star crust plastically relieves the imposed magnetic field stress, limiting the strain $ epsilon_t $ to values well below the critical strain $ epsilon_{crit}$ of a brittle fracture, $ epsilon_t sim 10^{-2}epsilon_{crit} $. Magnetar-like behavior, occurring near the magnetic equator, takes place in all neutron stars, but to a different extent. The persistent luminosity is proportional to cubic power of the magnetic field (at a given age), and hence is hardly observable in most rotationally powered neutron stars. Giant flares can occur only if the magnetic field exceeds some threshold value, while smaller bursts and flares may take place in relatively small magnetic fields. Bursts and flares are magnetospheric reconnection events that launch Alfven shocks which convert into high frequency whistlers upon hitting the neutron star surface. The resulting whistler pulse induces a strain that increases with depth both due to the increasing electron density (and the resulting slowing of the waves), and due to the increasing coherence of a whistler pulse with depth. The whistler pulse is dissipated on a time scale of approximately a day at shallow depths corresponding to $rho sim 10^{10} {rm g cm}^{-3}$; this energy is detected as enhanced post-flare surface emission.
We discuss three topics: (i) the dynamics of afterglow jet breaks; (ii) the origin of Fermi-LAT photons; (iii) the electromagnetic model of short GRBs
Relativistic outflows carrying large scale magnetic fields have large inductive potential and may accelerate protons to ultra high energies. We discuss a novel scheme of Ultra-High Energy Cosmic Ray (UHECR) acceleration due to drifts in magnetized, c
ylindrically collimated, sheared jets of powerful active galaxies (with jet luminosity $geq 10^{46}$ erg s$^{-1}$). A positively charged particle carried by such a plasma is in an unstable equilibrium if ${bf B} cdot abla times {bf v}< 0$, so that kinetic drift along the velocity shear would lead to fast, regular energy gain. The highest rigidity particles are accelerated most efficiently implying the dominance of light nuclei for energies above the ankle in our model: from a mixed population of pre-accelerated particle the drift mechanism picks up and boosts protons preferably.
