Self-generated Magnetic Fields And Nonlinear Effect In The Nonextensive Distributed Plasmas

There are many cosmic magnetic fields observed in galaxies, stars, or planets, and the self-generated magnetic fields measured in laser-produced plasma, so this problem is an increasing focus on physics of plasmas and a variety of theories has been proposed to explain it. The basic idea of our theory is that the interactions of wave-wave and wave-particle can generate the nonlinear currents, then the currents can produce the low-frequency fields and the fields can induce the low-frequency magnetic fields. This theorical research about the self-generated magnetic fields is conducive to studying the problem about the physical progress of the interaction between plasma and materials in laser inertial confusion, and the problem about the fine structure of celestial bodies depending on intermittent magnetic flux.Because it is better choice to analyze the long-range interactions physical system taking the extensive statistical theory than the extensive statistical theory, it is reasonable that we presume the nonextensive q-distributed plasmas with the long-range electrostatic force and that are supported with the observation of celestial bodies. It is significative and necessary that the investigation of the self-generated magnetic fields is expanded from the Maxwellian-distributed plasmas to the q-distributed plasmas. As well, the self-generated magnetic fields, with q-distributed plasmas instead of Maxwellian distributed plasmas, is worthy of studying in laser-produced plasma because of the strong and fast interaction. The theorical results are more abundant in q-distributed plasmas than Maxwellian-distributed plasmas due to parameter q.Firstly, the governing equations for self-generated magnetic fields are derived form Vlasov equation in kinetic theory, assuming the nonextensive distribution plasma and taking the wave-wave and wave-particle nonlinear interactions into account. The equations consist of the ion-acoustic equation driven by the pondermotive force because of the spatially inhomogeneous transverse plasmons, the perturbed density equation caused by the pondermotive force of plasmons, and the envelope field describing the evolution of the slowly varying magnetic field excited from the intrinsic rotation of the high frequency wave field.Secondly, the governing equations for self-generated magnetic fields with the nonextensive q-distributed plasmas are linearly analysed by the perturbation method. The analytical solutions for the maximum growth rate and the corresponding characteristic scale, the collape speed of modulation instability are obtained in the approximative case. We get the plasmons-conservation equation through the order of magnitude approximation analysis and show a asymptotical self-similar collapse solution. It is indicated that the perturbation of magnetic fields is modulation instability and the instability lead to the local struture of fields for homogeneous transverse plasmons. The result of modulation instability is modified by variable parameter q, include of Maxwellian-distributed case.Consequently, we study that anomalous magnetic viscosity caused by collape magnetic flux in accretion disks with q-distributed plasmas. The phenomena of anomalous viscosity is investigated by applying the theories about self-generated magnetic fields with the nonextensive q-distributed plasmas because the accretion disks should be the turbulent state. The theorical results are more close to the observation data in order and the magnitude is fitting by choosing the appropriate variable parameter q.Finally, we give the numerical results (evolution figure) of the governing equations and apply it to the self-generated magnetic fields in solar corona, the auroral zones with kilometer radiation (AKR) and laser-produced plasma. The self-generated magnetic field in the nonextensive q-distributed plasmas is calculated in the quasistatic limit and the evolution figure is plotted with different parameter q, by scalarizing the governing equations in two dimensions with three field components and taking a difference method. We calculate the maximum magnetic fields and the corresponding scale based on the distributed plots and the corresponding contour plots of magnetic fields in the space. Then we constrast it to the observation data of magnetic fields and the characteristic scale. The evolution figure denotes that the collape is a main characteristic of the self-generated magnetic fields. When q is smaller, the speed of collapse is faster, the maximum magnetic field is stronger and the local spatial scale is smaller.