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Analytical Theory
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G G Plunk – One of the best experts on this subject based on the ideXlab platform.

collisionless microinstabilities in stellarators i Analytical Theory of trapped particle modes
Physics of Plasmas, 2013CoAuthors: P Helander, J H E Proll, G G PlunkAbstract:This is the first in a series of papers about collisionless, electrostatic microinstabilities in stellarators, with an emphasis on trappedparticle modes. It is found that, in socalled maximumJ configurations, trappedparticle instabilities are absent in large regions of parameter space. Quasiisodynamic stellarators have this property (approximately), and the Theory predicts that trapped electrons are stabilizing to all eigenmodes with frequencies below the electron bounce frequency. The physical reason is that the bounceaveraged curvature is favorable for all orbits, and that trapped electrons precess in the direction opposite to that in which drift waves propagate, thus precluding waveparticle resonance. These considerations only depend on the electrostatic energy balance and are independent of all geometric properties of the magnetic field other than the maximumJ condition. However, if the aspect ratio is large and the instability phase velocity differs greatly from the electron and ion thermal speeds, it is possible to derive a variational form for the frequency showing that stability prevails in a yet larger part of parameter space than what follows from the energy argument. Collisionless trappedelectron modes should therefore be more stable in quasiisodynamic stellarators than in tokamaks.

collisionless microinstabilities in stellarators i Analytical Theory of trapped particle modes
arXiv: Plasma Physics, 2013CoAuthors: P Helander, J H E Proll, G G PlunkAbstract:This is the first of two papers about collisionless, electrostatic microinstabilities in stellarators, with an emphasis on trappedparticle modes. It is found that, in socalled maximum$J$ configurations, trappedparticle instabilities are absent in large regions of parameter space. Quasiisodynamic stellarators have this property (approximately), and the Theory predicts that trapped electrons are stabilizing to all eigenmodes with frequencies below the electron bounce frequency. The physical reason is that the bounceaveraged curvature is favorable for all orbits, and that trapped electrons precess in the direction opposite to that in which drift waves propagate, thus precluding waveparticle resonance. These considerations only depend on the electrostatic energy balance, and are independent of all geometric properties of the magnetic field other than the maximum$J$ condition. However, if the aspect ratio is large and the instability phase velocity differs greatly from the electron and ion thermal speeds, it is possible to derive a variational form for the frequency showing that stability prevails in a yet larger part of parameter space than what follows from the energy argument. Collisionless trappedelectron modes should therefore be more stable in quasiisodynamic stellarators than in tokamaks.
P Helander – One of the best experts on this subject based on the ideXlab platform.

collisionless microinstabilities in stellarators i Analytical Theory of trapped particle modes
Physics of Plasmas, 2013CoAuthors: P Helander, J H E Proll, G G PlunkAbstract:This is the first in a series of papers about collisionless, electrostatic microinstabilities in stellarators, with an emphasis on trappedparticle modes. It is found that, in socalled maximumJ configurations, trappedparticle instabilities are absent in large regions of parameter space. Quasiisodynamic stellarators have this property (approximately), and the Theory predicts that trapped electrons are stabilizing to all eigenmodes with frequencies below the electron bounce frequency. The physical reason is that the bounceaveraged curvature is favorable for all orbits, and that trapped electrons precess in the direction opposite to that in which drift waves propagate, thus precluding waveparticle resonance. These considerations only depend on the electrostatic energy balance and are independent of all geometric properties of the magnetic field other than the maximumJ condition. However, if the aspect ratio is large and the instability phase velocity differs greatly from the electron and ion thermal speeds, it is possible to derive a variational form for the frequency showing that stability prevails in a yet larger part of parameter space than what follows from the energy argument. Collisionless trappedelectron modes should therefore be more stable in quasiisodynamic stellarators than in tokamaks.

collisionless microinstabilities in stellarators i Analytical Theory of trapped particle modes
arXiv: Plasma Physics, 2013CoAuthors: P Helander, J H E Proll, G G PlunkAbstract:This is the first of two papers about collisionless, electrostatic microinstabilities in stellarators, with an emphasis on trappedparticle modes. It is found that, in socalled maximum$J$ configurations, trappedparticle instabilities are absent in large regions of parameter space. Quasiisodynamic stellarators have this property (approximately), and the Theory predicts that trapped electrons are stabilizing to all eigenmodes with frequencies below the electron bounce frequency. The physical reason is that the bounceaveraged curvature is favorable for all orbits, and that trapped electrons precess in the direction opposite to that in which drift waves propagate, thus precluding waveparticle resonance. These considerations only depend on the electrostatic energy balance, and are independent of all geometric properties of the magnetic field other than the maximum$J$ condition. However, if the aspect ratio is large and the instability phase velocity differs greatly from the electron and ion thermal speeds, it is possible to derive a variational form for the frequency showing that stability prevails in a yet larger part of parameter space than what follows from the energy argument. Collisionless trappedelectron modes should therefore be more stable in quasiisodynamic stellarators than in tokamaks.
Zhanshan Wang – One of the best experts on this subject based on the ideXlab platform.

analytic Theory of alternate multilayer gratings operating in single order regime
Optics Express, 2017CoAuthors: Xiaowei Yang, Qiushi Huang, Igor V Kozhevnikov, Hongchang Wang, Matthew Hand, Kawal Sawhney, Zhanshan WangAbstract:Using the coupled wave approach (CWA), we introduce the Analytical Theory for alternate multilayer grating (AMG) operating in the singleorder regime, in which only one diffraction order is excited. Differing from previous study analogizing AMG to crystals, we conclude that symmetrical structure, or equal thickness of the two multilayer materials, is not the optimal design for AMG and may result in significant reduction in diffraction efficiency. The peculiarities of AMG compared with other multilayer gratings are analyzed. An influence of multilayer structure materials on diffraction efficiency is considered. The validity conditions of Analytical Theory are also discussed.

unified Analytical Theory of single order soft x ray multilayer gratings
Journal of The Optical Society of America Boptical Physics, 2015CoAuthors: Xiaowei Yang, I V Kozhevnikov, Qiushi Huang, Zhanshan WangAbstract:A universal Analytical Theory of soft xray multilayer gratings operating in the singleorder regime is developed here. The singleorder regime, in which an incident wave excites only the diffracted wave, is characterized by the maximum possible diffraction efficiency tending to the reflectivity of a conventional multilayer mirror. The Theory is applied to analysis of different multilayer gratings, including lamella multilayer gratings, sliced multilayer gratings, blazed multilayer gratings, and blazed lamella multilayer gratings. A simple Analytical formula that describes the diffraction efficiency of an arbitrary multilayer grating as a function of the wavelength and the incidence angle is deduced. Expressions for the peak value of the diffraction efficiency and the generalized Bragg condition corresponding to the maximum efficiency are obtained. The high accuracy of the deduced Analytical expressions is justified by comparison with rigorous numerical calculations. Comparative analysis of different types of gratings is performed. The advantages and disadvantages of different gratings in practical applications are discussed.