SUMMARYThis paper considers the transmission problem for the system of piezoelectricity having piecewise constant coe cients. Under suitable geometric conditions imposed on the domain and the interfaces where the coe cients have a jump discontinuity, results on boundary observation and exact controllability are established.
SUMMARYThis paper considers transmission problem for the system of electromagneto-elasticity having piecewise constant coe cients in a bounded domain. The result on exact boundary controllability is obtained provided the interfaces, where the coe cients have a jump discontinuity, are all star-shaped with respect to one and the same point and the coe cients satisfy a certain monotonicity conditions.
Abstract. In this paper, we derive the dispersion equations for field-aligned cyclotron waves in two-dimensional (2-D) magnetospheric plasmas with anisotropic temperature. Two magnetic field configurations are considered with dipole and circular magnetic field lines. The main contribution of the trapped particles to the transverse dielectric permittivity is estimated by solving the linearized Vlasov equation for their perturbed distribution functions, accounting for the cyclotron and bounce resonances, neglecting the drift effects, and assuming the weak connection of the left-hand and right-hand polarized waves. Both the bi-Maxwellian and bi-Lorentzian distribution functions are considered to model the ring current ions and electrons in the dipole magnetosphere. A numerical code has been developed to analyze the dispersion characteristics of electromagnetic ion-cyclotron waves in an electron-proton magnetospheric plasma with circular magnetic field lines, assuming that the steady-state distribution function of the energetic protons is bi-Maxwellian. As in the uniform magnetic field case, the growth rate of the proton-cyclotron instability (PCI) in the 2-D magnetospheric plasmas is defined by the contribution of the energetic ions/protons to the imaginary part of the transverse permittivity elements. We demonstrate that the PCI growth rate in the 2-D axisymmetric plasmasphere can be significantly smaller than that for the straight magnetic field case with the same macroscopic bulk parameters.
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