Plasma magnetization by a nonuniform electromagnetic beam

I. Introduction Understanding the origin of magnetic fields in cosmic and laser produced plasmas has been of great theoretical as well as experimental interest [1–3]. The generation of seed magnetic fields in the early universe is a long-standing mystery in astrophysics. A very weak magnetic field (typically of the order of one to thirty microgauss) in the early universe has been of much interest to the scientific community. Our galaxy and many other spiral galaxies are endowed with coherent magnetic fields ordered on scales = 10 kpc with typical strength [4,5]. Furthermore, the cosmic magnetic field is strongly correlated with the large-scale structures (e.g. currents filaments and sheets) of the Universe [6, 7]. The origin of cosmological, galactic and large-scale extra-galactic magnetic fields is one of the main unresolved problems of astrophysics and cosmology. The existence of these magnetic field are relevant to the processes which took place in the early universe. Because of the Universe's high conductivity, two important quantities are almost conserved during the evolution of the Universe: the magnetic flux and the magnetic helicity. The magnetic field in ionized media is generated on account of electrical currents or of rotational electric fields. The self-excitation of large scale magnetic fields in astrophysical bodies, such as the Sun, stars, galaxies, etc [8, 9], is a challenging issue. The main problem of most particle physics mechanisms of the origin of seed magnetic fields is how to produce them coherently on cosmological (large) scales [10]. During the last few decades, the generation of magnetic fields has been studied in different areas of physics, such as in cosmic environments (e.g. supernova remnants, gamma-ray bursts), and in laser produced plasmas. Thus, magnetic fields are found to be important in every scale hierarchy of various plasma systems. The usual question posed is: How can an initially magnetic-field free plasma give rise to a non-zero " seed magnetic field " ? The answer to this question rests on identifying suitable mechanisms that are responsible for creating the electron current and the electric field that are required for generating the seed magnetic field. Neglecting the displacement current in Maxwell's equations, we have