Nonlinear evolution of two fast-particle-driven modes near the linear stability threshold

A system of two coupled integro-differential equations is derived and solved for the non-linear evolution of two waves excited by the resonant interaction with fast ions just above the linear instability threshold. The effects of a resonant particle source and classical relaxation processes represented by the Krook, diffusion, and dynamical friction collision operators are included in the model, which exhibits different nonlinear evolution regimes, mainly depending on the type of relaxation process that restores the unstable distribution function of fast ions. When the Krook collisions or diffusion dominate, the wave amplitude evolution is characterized by modulation and saturation. However, when the dynamical friction dominates, the wave amplitude is in the explosive regime. In addition, it is found that the finite separation in the phase velocities of the two modes weakens the interaction strength between the modes

Gaussian Beam Diffraction and Self-Focusing in Weakly Anisotropic and Dissipative Nonlinear Plasma

The paper presents a simple and effective method to calculate polarization and diffraction of the Gaussian beam in nonlinear and weakly dissipative plasma. The presented approach is a combination of quasi-isotropic approximation of geometric optics with complex geometrical optics. Quasi-isotropic approximation describes the evolution of polarization vector reducing the Maxwell equations to coupled ordinary differential equations of the first order for the transverse components of the electromagnetic field. Complex geometrical optics describes the Gaussian beam diffraction and self-focusing and deals with ordinary differential equations for Gaussian beam width, wave front curvature, and amplitude evolution. As a result, the quasi-isotropic approximation + complex geometrical optics combination reduces the problem of diffraction and polarization evolution of an electromagnetic beam to the solution of the ordinary differential equations, which enable to prepare fast and effective numerical algorithms. Using combined complex geometrical optics/quasi-isotropic approximation for weakly anisotropic plasma, we assume that nonlinearity of anisotropy tensor is small and we restrict ourselves to considering only isotropic nonlinearity. The quasi-isotropic approximation effectively describes the evolution of microwave and IR electromagnetic beams in polarimetric and interferometric measurements in thermonuclear reactors and the complex geometrical optics method can be applied for modeling of electron cyclotron absorption and current drive in tokamaks

Gaussian Beam Diffraction and Self-Focusing in Weakly Anisotropic and Dissipative Nonlinear Plasma

The paper presents a simple and effective method to calculate polarization and diffraction of the Gaussian beam in nonlinear and weakly dissipative plasma. The presented approach is a combination of quasi-isotropic approximation of geometric optics with complex geometrical optics. Quasi-isotropic approximation describes the evolution of polarization vector reducing the Maxwell equations to coupled ordinary differential equations of the first order for the transverse components of the electromagnetic field. Complex geometrical optics describes the Gaussian beam diffraction and self-focusing and deals with ordinary differential equations for Gaussian beam width, wave front curvature, and amplitude evolution. As a result, the quasi-isotropic approximation + complex geometrical optics combination reduces the problem of diffraction and polarization evolution of an electromagnetic beam to the solution of the ordinary differential equations, which enable to prepare fast and effective numerical algorithms. Using combined complex geometrical optics/quasi-isotropic approximation for weakly anisotropic plasma, we assume that nonlinearity of anisotropy tensor is small and we restrict ourselves to considering only isotropic nonlinearity. The quasi-isotropic approximation effectively describes the evolution of microwave and IR electromagnetic beams in polarimetric and interferometric measurements in thermonuclear reactors and the complex geometrical optics method can be applied for modeling of electron cyclotron absorption and current drive in tokamaks

On the wave amplitude blow-up in the Berk–Breizman model for nonlinear evolution of a plasma wave driven resonantly by fast ions

In this paper the Berk–Breizman (BB) model of plasma wave instability arising on the stability threshold is considered. An interesting although physically unacceptable feature of the model is the explosive behaviour occurring in the regime of small values of the collision frequency parameter. We present an analytical description of the explosive solution, based on a fitting to the numerical solution of the BB equation with the collision parameter equal to zero. We find that the chaotic behaviour taking place for small but non-zero values of the collision parameter is absent in this case; therefore, chaotic behaviour seems to be an independent phenomenon not directly related to the blow-up regime. The time and the velocity dependence of the distribution function are found numerically and plotted to better understand what actually happens in the model. It allows us to obtain a good qualitative understanding of the time evolution of the mode amplitude including the linear growth of the amplitude, reaching its maximum and then decreasing towards the zero value. Nevertheless, we have no satisfactory physical explanation of the amplitude evolution when the amplitude vanishes at some time and then revives but with an opposite phase

Simplified models for the nonlinear evolution of two fast-particle-driven modes near the linear stability threshold

An analytical model that is based on purely differential equations of the nonlinear dynamics of two plasma modes driven resonantly by high-energy ions near the instability threshold is presented here. The well-known integro-differential model of Berk and Breizman (BB) extended to the case of two plasma modes is simplified here to a system of two coupled nonlinear differential equations of fifth order. The effects of the Krook, diffusion and dynamical friction (drag) relaxation processes are considered, whereas shifts in frequency and wavenumber between the modes are neglected. In spite of these simplifications the main features of the dynamics of the two plasma modes are retained. The numerical solutions to the model equations show competition between the two modes for survival, oscillations, chaotic regimes and \u27blow-up\u27 behavior, similar to the BB model

Mechanical analogy of the nonlinear dynamics of a driven unstable mode near marginal stability

The universal integrodifferential model equation derived by Berk [Phys. Rev. Lett. 76, 1256 (1996)] for studying the nonlinear evolution of unstable modes driven by kinetic wave particle resonances near the instability threshold is reduced to a differential equation and next as a further simplification to a nonlinear oscillator equation. This mechanical analogy properly reproduces most of the essential physics of the system and allows an understanding of the qualitative features of the theory of Berk

Efficacy of fungicides and essential oils against bacterial diseases of fruit trees

In the framework of the performed studies, the antibacterial activity of the following fungicides was evaluated: Miedzian 50 WG (active substance - a.s. 50% copper oxychloride), Ridomil MZ Gold 68 WG (a.s. 3.8% metalaxyl-M and 64%, mancozeb), Euparen Multi 50 WG (a.s. 50% tolylfluanid), Captan 80 WG [a.s. 80% N-(captan)], Dithane Neotec 75 WG (a.s. 75% mancozeb). The evaluation also concerned the essential oils: lavender, sage, lemon balm, clove, and a preparation based on thyme oil (BioZell). Each preparation and compound was tested against the following bacterial pathogens: Erwinia amylovora, Xanthomonas arboricola pv. corylina, X. arboricola pv. juglandis, Pseudomonas syringae pv. syringae, Agrobacterium tumefaciens (presently Rhizobium radiobacter). Each preparation and compound was tested at a concentration of 1,000 ppm of active substance. Copper oxychloride was also tested at a concentration of 1,500 ppm. Among the tested fungicides, metalaxyl-M with mancozeb, mancozeb alone, and copper oxychloride inhibited all of the tested strains of pathogenic bacteria. Tolylfluanid did not inhibit any of the bacteria used. Out of the investigated essential oils, the strongest inhibitors of bacteria were: sage, cloves, and BioZell. The protective activity of the above mentioned fungicides was also evaluated in vivo. They were assessed against fire blight on apple blossoms and pear fruitlets, against bacterial canker on sweet cherry fruitlets, and against crown gall on sunflower seedlings (the test plant). All fungicides were applied at the same concentrations as those in the in vitro tests. Only copper oxychloride was found to show protective activity against the studied diseases. This result indicates that the antibacterial properties of the other fungicides did not correspond with their activity on the plant organs used in the in vivo experiment

Ferromagnetic and spin wave resonances in thin layer of expanded austenite phase

Four samples of austenite coatings deposited by reactive magnetron sputtering on silicon substrate at four different temperatures and pressures were investigated by ferromagnetic resonance (FMR) method at room temperature. The expanded austenite phase S (γ N ) layers with thickness in the 160-273 nm range and concentration of magnetic atoms: 72 % Fe, 18 % Cr and 10 % Ni, were obtained. The coatings with nanometric size grains were strongly textured and grown mostly in [100] direction, perpendicular to the sample surface. Intense FMR spectra were recorded at various angles between the static magnetic field direction and the sample surface. A strong magnetic anisotropy of the main uniform FMR mode was observed and the effective magnetization 4πM eff determined. Spin wave resonance (SWR) modes were observed in all investigated samples in out-of-plane geometry of the magnetic field. The resonance fields of SWR modes in our samples varied linearly with the spin wave mode number. The value of the effective magnon stiffness constant was determined assuming a parabolic shape of the magnetization variation across the sample thickness. © 2014 Versita Warsaw and Springer-Verlag Wien