Nonlinear oscillations and waves in multi-species cold plasmas

The spatio-temporal evolution of nonlinear oscillations in multi-species plasma is revisited to provide more insight into the physics of phase mixing by constructing two sets of nonlinear solutions up to the second order. The first solution exhibits perfect oscillations in the linear regime and phase mixing appears only nonlinearly in the second order as a response to the ponderomotive forces. This response can be both direct and indirect. The indirect contribution of the ponderomotive forces appears through self-consistently generated low frequency fields. Furthermore, the direct and indirect contributions of the ponderomotive forces on the phase mixing process is explored and it is found that the indirect contribution is negligible in an electron-ion plasma and it disappears in the case of electron-positron plasma, yet represents an equal contribution in the electron-positron-ion plasma. However, the second solution does not exhibit any phase mixing due to the absence of ponderomotive forces but results in an undistorted nonlinear traveling wave. These investigations have relevance for laboratory/astrophysical multi-species plasma.Comment: Accepted in Physics of Plsama

Nonlinear electrostatic oscillations in a cold magnetized electron-positron plasma

We study the spatio-temporal evolution of the nonlinear electrostatic oscillations in a cold magnetized electron-positron (e-p) plasma using both analytics and simulations. Using a perturbative method we demonstrate that the nonlinear solutions change significantly when a pure electrostatic mode is excited at the linear level instead of a mixed upper-hybrid and zero-frequency mode that is considered in a recent study. The pure electrostatic oscillations undergo phase mixing nonlinearly. However, the presence of the magnetic field significantly delays the phase-mixing compared to that observed in the corresponding unmagnetized plasma. Using 1D PIC simulations we then analyze the damping of the primary modes of the pure oscillations in detail and infer the dependence of the phase-mixing time on the magnetic field and the amplitude of the oscillations. The results are remarkably different from those found for the mixed upper-hybrid mode mentioned above. Exploiting the symmetry of the e-p plasma we then explain a generalized symmetry of our non-linear solutions. The symmetry allows us to construct a unique nonlinear solution up to the second order which does not show any signature of phase mixing but results in a nonlinear wave traveling at upper-hybrid frequency. Our investigations have relevance for laboratory/astrophysical e-p plasmas

Lower-hybrid oscillations in a cold magnetized electron-positron-ion plasma

International audienc

Generation of low frequency plasma waves after the wave-breaking

International audienc

Special municipal bodies

Tato diplomová práce je zaměřena na zvláštní orgány obcí. Zabývá se nejen těmito druhy orgánů obcí, ale vymezuje i orgány obce, které jsou zřizovány ve všech obcích na území České republiky. Podává ucelené obecné informace o zvláštních orgánech obcí a některých typech, např. povodňová komise. Detailně se pak věnuje obecní policii a přestupkové komisi.Katedra správního právaNeobhájenoThis diplom thesis aims at the Special municipal bodies. It not only pursues the Special municipal bodies but defines also those municipal bodies established in all municipal districts within the Czech Republic. Moreover, the thesis provides general information about this type of bodies and information about some specific kinds, for example the Flood committee. It attends in great detail to local Municipal police and the Public Commision infringement.