Modulation instability of dispersive electromagnetic waves in a Josephson junction in a finite-thickness plate

Modulation instability of finite-amplitude dispersive electromagnetic waves is studied in the framework of nonlocal electrodynamics of a Josephson junction in a finite-thickness plate. The dispersion equation is derived for the increment of small amplitude perturbations. For this type of waves, the regions of development of modulation instability and stability of waves are determined. It is shown that modulation instability of waves develops in a finite range of wavevectors Q _B1(k, D, L) < Q < Q _B2(k, A, D, L), while waves are stable in the important long-wave region 0 ≤ Q ≤ Q _B1(k, D, L) and for Q ≥ Q _B2(k, A, D, L). The unique possibility of controlling the modulation instability region by dispersion parameter k, viz., the wave vector (or frequency ω(k)) of the modes in the linear approximation.     

Modulation instability of electromagnetic excitations in the nonlocal Josephson electrodynamics of thin magnetic superconducting films

The modulation instability of plane finite-amplitude nonlinear waves with the Josephson frequency is studied for a Josephson contact in thin nonmagnetic and magnetic (two-dimensional) superconducting films. Dispersion relations for the increments of small-amplitude perturbations are derived. Modulation instability is shown to develop in the finite range 0<Q<Q _b of the wavevectors of amplitude perturbations for the nonmagnetic films and for any perturbation wavevector 0<Q<∞ for the magnetic films.     

Modulation instability of electromagnetic excitations in nonlocal Josephson electrodynamics of thin films of nonmagnetic and magnetic (two-and three-dimensional) superconductors

Modulation instability of nonlinear electromagnetic excitations (oscillating with the Josephson frequency) of finite amplitude is investigated in a Josephson junction in a film of a nonmagnetic, as well as of a magnetic (two-or three-dimensional), superconductor. The instability is accompanied by a nonlinear shift in frequency. Dispersion relations are derived for the time increment of small perturbations of the amplitude. It is shown that, for this type of excitations in a Josephson junction in a thin film of nonmagnetic superconductor, modulation instability develops only in a certain finite range of wave vectors, whereas in a thin film of a two-or three-dimensional magnetic superconductor it develops for any wave vector.     

Magnetohydrodynamic Kelvin-Helmholtz instability for finite-thickness fluid layers

We have derived the analytical formulas for the Kelvin-Helmholtz instability (KHI) of two superposed finite-thickness fluid layers with the magnetic field effect into consideration. The linear growth rate of KHI will be reduced when the thickness of the fluid with large density is decreased or the thickness of fluid with small density is increased. When the thickness and the magnetic field act together on the KHI, the effect of thickness is more obvious when the magnetic field intensity is weak. The magnetic field transition layer destabilizes (enforces) the KHI, especially in the case of small thickness of the magnetic field transition layer. When considering the effect of magnetic field, the linear growth rate of KHI always decreases after reaching the maximum with the increase of total thickness. The stronger the magnetic field intensity is, the more obvious the growth rate decreases with the total thickness. Thus, it should be included in applications where the effect of fluid thickness on the KHI cannot be ignored, such as in double-cone ignition scheme for inertial confinement fusion.     

Nonlocal Josephson electrodynamics of electromagnetic excitations in a superconducting magnetic (three-dimensional) thin film

The integro-differential equation for the dynamics of the phase difference with temporal and spatial nonlocality for a Josephson junction in a superconducting three-dimensional magnetic thin film is derived. The equation is valid for any type of magnetic ordering. The magnetic subsystem is shown to significantly renormalize the spectrum of small-amplitude electromagnetic excitations, which, as a result, are damped.     

Parametric instability of a cantilever beam subjected to two electromagnetic excitations: Experiments and analytical validation

An electromagnetic device, acting like a spring with alternating stiffness, has been designed to parametrically excite the cantilever beam. However, only one parametric excitation (induced by one electromagnetic device) was considered in current research, and the effects of the design parameters of the device upon the instability were studied inadequately. Actually, multiple parametric excitations with various phases and amplitudes would bring significant impacts to the system instability. The electromagnetic device with various design parameters could cause the unstable regions to change evidently. Thus, the parametric instability of a cantilever beam subjected to two electromagnetic excitations is studied experimentally and analytically in the paper. The governing equations for the beam system are established utilizing the assumed mode method, and then verified through a DC current test. Based upon these, the instability experiments for the cantilever beam with one or two electromagnetic excitations are conducted in detail. Two design parameters of the device (magnet spacing and device location) are investigated, respectively, for their effects upon the instability regions. When two electromagnetic devices operate together to bring two parametric stiffness excitations with various phases and amplitudes to the cantilever beam, the variations of both simple and combination instability regions with coil current are observed and discussed. The above experimental results are all found to agree well with the analytical ones.     

Coulomb excitations of a nuclear slab in relativistic mean-field theory

Time-dependent relativistic mean-field theory is used to describe the dynamic behaviour of a nuclear slab excited at time zero by a rapid Coulomb push. At small incident energies of the projectile, we observe oscillations of small amplitude with isovector character. With increasing excitation energy, the motion becomes increasingly anharmonic, and parts of the nuclear material are ejected. At the highest energies, we find a rapid dissociation between the proton and neutron part of the slab. It turns out that the character of the oscillations is strongly influenced by the strength of the ρ-meson coupling. For vanishing coupling, we observe two modes corresponding in nature to the Goldhaber-Teller mode and the Steinwedel-Jensen mode of the giant dipole resonance in realistic nuclei. At larger ρ-meson coupling, the Goldhaber-Teller mode is more and more suppressed, and one is left with one strongly damped mode of the Steinwedel-Jensen type.     

Fractional Josephson current through a Luttinger liquid with topological excitations

Recently, the Majorana fermion has received great attentions due to its promising application in the fault-tolerant quantum computation. This application requires more accessible methods to detect the motion and braiding of the Majorana fermions. We use a Luttinger liquid ring to achieve this goal, where the ring geometry is nontrivial in the sense that it leads to fermion-parity-dependent topological excitations. First, we briefly review the essential physics of the Luttinger liquid and the Majorana fermion, in order to give an introduction of the general framework used in the following main work. Then, we theoretically investigated the DC Josephson effect between two topological superconductors via a Luttinger liquid ring. A low-energy effective Hamiltonian is derived to show the existence of the fractional Josephson current. Also, we find that the amplitude of the Josephson current, which is determined by the correlation function of Luttinger liquid, exhibits different behaviors in terms of the parity of Luttinger liquid due to the topological excitations. Our results suggest a possible method to detect the Majorana fermions and their tunneling process.     

Modulation instability for a relaxational Kerr medium

We investigated on the influence of a temporally dispersive Kerr effect on the modulation instability and the propagation of solitary wave pulse. The modulation instability gain is derived and compared with numerical calculations. The role of nonlinear response time on reshaping the solitary pulse is examined.     

Spatial modulation instability in a Kerr slab waveguide

We report the observation of noise-initiated modulational instability in AlGaAs slab waveguides at 1.55 microm . Experiments were performed with the local, ultrafast Kerr nonlinearity at half the bandgap. The agreement between experiment and theory for the periodicity versus intensity was good.     

Control of the perturbation-wave-vector range of modulation instability of dispersive electromagnetic waves in the nonlocal Josephson electrodynamics of a thin superconducting film

Modulation instability of dispersive electromagnetic waves propagating through a Josephson junction in a thin superconducting film is investigated in the framework of the nonlocal Josephson electrodynamics. A dispersion relation is found for the time increment of small perturbations of the amplitude. For dispersive waves, it is first established that spatial nonlocality suppresses the modulation instability in the range of perturbation wave vectors 0≤Q≤Q_B1(k), i.e., in the long-wavelength range of experimental interest. The modulation instability range Q_B1(k)<Q<Q_B2(k, A, L) can be controlled (which is a unique possibility) by varying a dispersion parameter, namely, the wave vector k [or the frequency ω(k)] of linear-approximation waves. In the wave-vector ranges 0≤Q≤Q_B1(k) and Q≤Q_B2(k, A, L), waves are shown to be stable.     

Criterion for long-wavelength electromagnetic instability of a homogeneous relativistic plasma

Electromagnetic instability of an unmagnetized homogeneous relativistic plasma with an anisotropic velocity distribution having a center of symmetry is analyzed. A stability criterion is derived for slowly varying long-wavelength perturbations. The criterion is formulated as a set of equalities that are not valid for ellipsoidal velocity distributions, but can be satisfied for other anisotropic distributions. The relativistic case is special only in that the rest mass is replaced with the relativistic one.     

Modulation instability in a medium with a nonlocal nonlinearity

The general conditions of appearance of the modulation instability of spatially homogeneous regimes in media with a nonlocal response of nonlinearity are determined. By using, as an example, the nonlocality in the form of the truncated Lennard-Jones potential, which is characteristic of interatomic interaction in Bose-Einstein condensates, the region of stability is found and the character of structures arising upon the loss of stability is discussed.     

Structure for localizing electromagnetic waves with a left-handed-medium slab and a conducting plane

A new structure is proposed for localizing electromagnetic waves and energies with a left-handed-medium (LHM) slab and a perfectly electrically conducting (PEC) plane. When a current source is placed in front of a perfectly matched LHM slab with negative permittivity -epsilon0 and negative permeability -mu0 and a PEC plane is placed at the image point, we show rigorously that all the electromagnetic waves are confined in a region between the source and the PEC plane, and the fields outside the region are completely zero. Such an energy-localization system would be useful in medical treatments that use concentrated optical and microwave energies. However, a perfectly matched LHM is unphysical and does not exist in nature. Hence we further study the loss and retardation effects of LHM on the energy localization. Numerical results are presented for the lossy LHM structure to demonstrate the energy localization.