Abstract:
We evaluated the parametric instabilities of LCGT (Japanese interferometric gravitational wave detector project) arm cavity. The number of unstable modes of LCGT is 10-times smaller than that of Advanced LIGO (U.S.A.). Since the strength of the instabilities of LCGT depends on the mirror curvature more weakly than that of Advanced LIGO, the requirement of the mirror curvature accuracy is easier to be achieved. The difference in the parametric instabilities between LCGT and Advanced LIGO is because of the thermal noise reduction methods (LCGT, cooling sapphire mirrors; Advanced LIGO, fused silica mirrors with larger laser beams), which are the main strategies of the projects. Elastic Q reduction by the barrel surface (0.2 mm thickness Ta$_2$O$_5$) coating is effective to suppress instabilities in the LCGT arm cavity. Therefore, the cryogenic interferometer is a smart solution for the parametric instabilities in addition to thermal noise and thermal lensing.

Abstract:
We address the existence and properties of one-dimensional solitons maintained by localized parameter gain in focusing and defocusing lossy nonlinear media. Localized parametric gain supports both fundamental and multipole solitons. We found that the family of fundamental solitons is partly stable in focusing nonlinear medium, and completely stable in defocusing medium, while all higher-order solitons are unstable. In addition to numerical results, the existence threshold for the solitons, and a particular stable exact solution are obtained in an exact analytical form.

Abstract:
Inter-site interactions play a crucial role in polar gases in optical lattices even in the absence of hopping. We show that due to these long-range interactions a destabilized stack of quasi-one dimensional Bose-Einstein condensates develops a correlated modulational instability in the non-overlapping sites. Interestingly, this density pattern may evolve spontaneously into soliton filaments or a crystal of solitons that can be so created for the first time in ultra-cold gases. These self-assembled structures may be observed under realistic conditions within current experimental feasibilities.

Abstract:
We present a simple feedback description of parametric instabilities which can be applied to a variety of optical systems. Parametric instabilities are of particular interest to the field of gravitational-wave interferometry where high mechanical quality factors and a large amount of stored optical power have the potential for instability. In our use of Advanced LIGO as an example application, we find that parametric instabilities, if left unaddressed, present a potential threat to the stability of high-power operation.

Abstract:
We reveal that even weak inherent discreteness of a nonlinear model can lead to instabilities of the localized modes it supports. We present the first example of an oscillatory instability of dark solitons, and analyse how it may occur for dark solitons of the discrete nonlinear Schrodinger and generalized Ablowitz-Ladik equations.

Abstract:
A detailed simulation of Advanced LIGO test mass optical cavities shows that parametric instabilities will excite acoustic modes in the test masses in the frequency range 28-35 kHz and 64-72 kHz. Using nominal Advanced LIGO optical cavity parameters with fused silica test masses, parametric instability excites 7 acoustic modes in each test mass, with parametric gain R up to 7. For the alternative sapphire test masses only 1 acoustic mode is excited in each test mass with R ~ 2. Fine tuning of the test mass radii of curvature cause the instabilities to sweep through various modes with R as high as ~2000. Sapphire test mass cavities can be tuned to completely eliminate instabilities using thermal g-factor tuning with negligible degradation of the noise performance. In the case of fused silica test mass, instabilities can be minimized but not eliminated.

Abstract:
The nature of transverse instabilities to dark solitons and dispersive shock waves for the (2+1)-dimensional defocusing nonlinear Schrodinger equation / Gross-Pitaevskii (NLS / GP) equation is considered. Special attention is given to the small (shallow) amplitude regime, which limits to the Kadomtsev-Petviashvili (KP) equation. We study analytically and numerically the eigenvalues of the linearized NLS / GP equation. The dispersion relation for shallow solitons is obtained asymptotically beyond the KP limit. This yields 1) the maximum growth rate and associated wavenumber of unstable perturbations; and 2) the separatrix between convective and absolute instabilities. The latter result is used to study the transition between convective and absolute instabilities of oblique dispersive shock waves (DSWs). Stationary and nonstationary oblique DSWs are constructed analytically and investigated numerically by direct simulations of the NLS / GP equation. The instability properties of oblique DSWs are found to be directly related to those of the dark soliton. It is found that stationary and nonstationary oblique DSWs have the same jump conditions in the shallow and hypersonic regimes. These results have application to controlling nonlinear waves in dispersive media.

Abstract:
Advanced gravitational wave interferometric detectors will operate at their design sensitivity with nearly 1MW of laser power stored in the arm cavities. Such large power may lead to the uncontrolled growth of acoustic modes in the test masses due to the transfer of optical energy to the mechanical modes of the arm cavity mirrors. These parametric instabilities have the potential of significantly compromising the detector performance and control. Here we present the design of "acoustic mode dampers" that use the piezoelectric effect to reduce the coupling of optical to mechanical energy. Experimental measurements carried on an Advanced LIGO-like test mass shown a 10-fold reduction in the amplitude of several mechanical modes, thus suggesting that this technique can greatly mitigate the impact of parametric instabilities in advanced detectors.

Abstract:
Almost all sources of high energy particles and photons are associated with jet phenomena. Prominent sources of such highly relativistic outflows are pulsar winds and Active Galactic Nuclei. The current understanding of these jets assumes diluted plasmas which are best described as kinetic phenomena. In this kinetic description particle acceleration to ultra-relativistic speeds can occur in completely unmagnetized and neutral plasmas through insetting effects of instabilities. Even though the morphology and nature of particle spectra are understood to a certain extent, the composition of the jets is not known yet. While Poynting-flux dominated jets are certainly composed of electron-positron plasmas, the understanding of the governing physics in AGN jets is mostly unclear. In this article we investigate how the constituting elements of an electron-positron-proton plasma behave differently under the variation of the fundamental mass-ratio m_p/m_e. We studied initially unmagnetized counterstreaming plasmas using fully relativistic three-dimensional particle-in-cell simulations to investigate the influence of the mass-ratio on particle acceleration and magnetic field generation in electron-positron-proton plasmas. We covered a range of mass-ratios m_p/m_e between 1 and 100 with a particle number composition of n_{p^+}/n_{e^+} of 1 in one stream, only protons are injected in the other, whereas electrons are present in both to guarantee charge neutrality in the simulation box. We find that with increasing proton mass the instability takes longer to develop and for mass-ratios > 20 the particles seem to be accelerated in two phases which can be accounted to the individual instabilities of the different species. This means that for high mass ratios the coupling between electrons/positrons and the heavier protons, which occurs in low mass-ratios, disappears.

Abstract:
Parametric instabilities driven by partially coherent radiation in plasmas are described by a generalized statistical Wigner-Moyal set of equations, formally equivalent to the full wave equation, coupled to the plasma fluid equations. A generalized dispersion relation for Stimulated Raman Scattering driven by a partially coherent pump field is derived, revealing a growth rate dependence, with the coherence width $\sigma$ of the radiation field, scaling with $1/\sigma$ for backscattering (three-wave process), and with $1/\sigma^{1/2}$ for direct forward scattering (four-wave process). Our results demonstrate the possibility to control the growth rates of these instabilities by properly using broadband pump radiation fields.