The negative-mass instability (NMI), previously found in ion traps, appears as a distinct regime of the sideband instability in nonlinear plasma waves with trapped particles. As the bounce frequency of these particles decreases with the bounce action, bunching can occur if the action distribution is inverted in trapping islands. In contrast to existing theories that also infer instabilities from the anharmonicity of bounce oscillations, spatial periodicity of the islands turns out to be unimportant, and the particle distribution can be unstable even if it is flat at the resonance. An analytical model is proposed which describes both single traps and periodic nonlinear waves and concisely generalizes the conventional description of the sideband instability in plasma waves. The theoretical results are supported by particle-in-cell simulations carried out for a regime accentuating the NMI effect. Introduction. -It is well known that bounce oscillations of particles autoresonantly trapped in a wave can couple to wave sidebands, rendering them unstable [1][2][3]. The sideband instability (SI) was extensively studied in the past [4][5][6][7][8], more recently in application to free electron lasers [9] and storage rings [10], and now is attracting renewed attention [11,12] in the context of intense laserplasma interactions (LPI) and the associated trappedparticle modulational instability (TPMI) [13], which is the SI's geometrical-optics limit [14]. Yet little effort was paid to unifying SI theories that appeared after the original Kruer-Dawson-Sudan work [1], further termed KDS. As a consequence, their results are often neglected today, and that, in turn, leads to misapplications [15]. Thus, even though quantitative predictions may be better left to simulations in any case, a transparent theory is needed (particularly as a practical tool for interpreting LPI-related numerical data) that would both comprehensively capture and elucidate the SI paradigmatic physics.
Through particle-in-cell simulations, we show that plasma waves carrying trapped electrons can be amplified manyfold via compressing plasma perpendicularly to the wave vector. These simulations are the first ab initio demonstration of the conservation of nonlinear action for such waves, which contains a term independent of the field amplitude. In agreement with the theory, the maximum of amplification gain is determined by the total initial energy of the trapped-particle average motion but otherwise is insensitive to the particle distribution. Further compression destroys the wave; electrons are then untrapped at suprathermal energies and form a residual beam. As compression continues, the bump-on-tail instability is triggered each time one of the discrete modes comes in resonance with this beam. Hence, periodic bursts of the electrostatic energy are produced until a wide quasilinear plateau is formed.
M-type barium hexaferrite films have been grown by liquid phase epitaxy and examined by x-ray diffraction, scanning electron microscopy, atomic force microscopy, and conventional and Lorentz-mode transmission electron microscopy (TEM). These films exhibit a diamond chevron shaped "brick wall" microstructure with c-axis oriented hexaferrite platelets. The films are oriented with their c axes in-plane, and parallel to the M-plane sapphire substrate, and exhibit a 30 rotation about the c axis with respect to the substrate. Rocking curves showed (20À20) and (22À40) FWHM values of 1.09 and 1.56 , respectively, for the thinner of two samples, and 0.31 and 0.50 for the thicker sample. The magnetic domain structures have been characterized by Lorentz-mode TEM and the domain walls were found to be pinned to small angle tilt boundaries. Using the measured rocking curve values, the effect of the overall crystalline misorientation on the dispersion of the magnetocrystalline anisotropy of the samples is estimated to be less than half a percent. Since M-type barium hexaferrite was originally examined in the late 1930s by Adelskold, 1 and further studied by Gorter and Braun at Philips in the 1950s, 2,3 the unique properties associated with its anisotropic magnetic and crystalline structures have made the system of great interest to both scientists and engineers. [4][5][6] These properties include high permeability, electrical resisitivity, and high ferromagnetic resonance (FMR) frequencies, with relatively narrow FMR linewidths. Additionally, the ability to grow hexaferrite films with the crystallographic c axis aligned either in plane or perpendicular to the plane provide these materials with magnetic anisotropy that make them suitable for various applications. Phase shifters, delay lines, filters, and antenna applications can be fabricated from films with in-plane anisotropy, and isolator and circulator applications can be fabricated from films possessing perpendicular magnetic anisotropy. 7 While these properties are important in determining hexaferrites' utility as microwave materials, they also have excellent radiation resistance and high power handling capacities that make them ideal for next-generation microwave devices, especially for use in extreme environments. 8,9 The structure of the hexaferrites is unique in that all the observed structures, including M type, Y type, Z type and so on, are made up of common subunits that are present in different numbers and repeat sequences. 4,10 All subunits are built upon a close packed lattice of oxygen with different metal ion arrangements. For example, in the case of M-type barium hexaferrite, the stacking sequence is RSR*S* in which R represents a rhombohedral subunit and S represents a spinel subunit. The asterisk (*) represents a 180 rotation of the subunit about the c axis.In growing epitaxial films, the lattice mismatch between the substrate and the film causes crystalline domains to form. 11 This generally has deleterious effects on the properties of the film for use at ...
We describe a Monte Carlo renormalization group approach to the calculation of critical behavior for percolation models. This approach can be utilized to determine the renormalized bond probabilities and the values of the critical exponents. We illustrate the method for two-dimensional bond percolation, but the method is also applicable to other percolation models and other dimensions.
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