Threshold Condition

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Ali Mostafazadeh - One of the best experts on this subject based on the ideXlab platform.

  • Lasing-Threshold Condition for oblique TE and TM modes, spectral singularities, and coherent perfect absorption
    Physical Review A, 2015
    Co-Authors: Ali Mostafazadeh, Mustafa Sarisaman
    Abstract:

    We study spectral singularities and their application in determining the Threshold gain coefficient $g^{(E/M)}$ for oblique transverse electric/magnetic (TE/TM) modes of an infinite planar slab of homogenous optically active material. We show that $g^{(E)}$ is a monotonically decreasing function of the incidence angle $\theta$ (measured with respect to the normal direction to the slab), while $g^{(M)}$ has a single maximum, $\theta_c$, where it takes an extremely large value. We identify $\theta_c$ with the Brewster's angle and show that $g^{(E)}$ and $g^{(M)}$ coincide for $\theta=0$ (normal incidence), tend to zero as $\theta\to 90^\circ$, and satisfy $g^{(E)} \theta_c$ is smaller inside the gain region than outside it. The converse is true for the TM waves with $\theta

  • lasing Threshold Condition for oblique te and tm modes spectral singularities and coherent perfect absorption
    Physical Review A, 2015
    Co-Authors: Ali Mostafazadeh, Mustafa Sarisaman
    Abstract:

    We study spectral singularities and their application in determining the Threshold gain coefficient $g^{(E/M)}$ for oblique transverse electric/magnetic (TE/TM) modes of an infinite planar slab of homogenous optically active material. We show that $g^{(E)}$ is a monotonically decreasing function of the incidence angle $\theta$ (measured with respect to the normal direction to the slab), while $g^{(M)}$ has a single maximum, $\theta_c$, where it takes an extremely large value. We identify $\theta_c$ with the Brewster's angle and show that $g^{(E)}$ and $g^{(M)}$ coincide for $\theta=0$ (normal incidence), tend to zero as $\theta\to 90^\circ$, and satisfy $g^{(E)} \theta_c$ is smaller inside the gain region than outside it. The converse is true for the TM waves with $\theta<\theta_c$ and all TE waves.

  • nonlinear spectral singularities of a complex barrier potential and the lasing Threshold Condition
    Physical Review A, 2013
    Co-Authors: Ali Mostafazadeh
    Abstract:

    A spectral singularity is a mathematical notion with an intriguing physical realization in terms of certain zero-width resonances. In optics it manifests as lasing at the Threshold gain. We explore the application of their recently-developed nonlinear generalization in the study of the effect of a nonlinearity on the lasing Threshold Condition for an infinite planar slab of gain medium. In particular, for a Kerr nonlinearity, we derive an explicit expression for the intensity of the emitted waves from the slab and discuss the implications of our results for the time-reversed system that acts as a coherent perfect absorber.

Mustafa Sarisaman - One of the best experts on this subject based on the ideXlab platform.

  • lasing Threshold Condition for oblique te and tm modes spectral singularities and coherent perfect absorption
    Physical Review A, 2015
    Co-Authors: Ali Mostafazadeh, Mustafa Sarisaman
    Abstract:

    We study spectral singularities and their application in determining the Threshold gain coefficient $g^{(E/M)}$ for oblique transverse electric/magnetic (TE/TM) modes of an infinite planar slab of homogenous optically active material. We show that $g^{(E)}$ is a monotonically decreasing function of the incidence angle $\theta$ (measured with respect to the normal direction to the slab), while $g^{(M)}$ has a single maximum, $\theta_c$, where it takes an extremely large value. We identify $\theta_c$ with the Brewster's angle and show that $g^{(E)}$ and $g^{(M)}$ coincide for $\theta=0$ (normal incidence), tend to zero as $\theta\to 90^\circ$, and satisfy $g^{(E)} \theta_c$ is smaller inside the gain region than outside it. The converse is true for the TM waves with $\theta<\theta_c$ and all TE waves.

  • Lasing-Threshold Condition for oblique TE and TM modes, spectral singularities, and coherent perfect absorption
    Physical Review A, 2015
    Co-Authors: Ali Mostafazadeh, Mustafa Sarisaman
    Abstract:

    We study spectral singularities and their application in determining the Threshold gain coefficient $g^{(E/M)}$ for oblique transverse electric/magnetic (TE/TM) modes of an infinite planar slab of homogenous optically active material. We show that $g^{(E)}$ is a monotonically decreasing function of the incidence angle $\theta$ (measured with respect to the normal direction to the slab), while $g^{(M)}$ has a single maximum, $\theta_c$, where it takes an extremely large value. We identify $\theta_c$ with the Brewster's angle and show that $g^{(E)}$ and $g^{(M)}$ coincide for $\theta=0$ (normal incidence), tend to zero as $\theta\to 90^\circ$, and satisfy $g^{(E)} \theta_c$ is smaller inside the gain region than outside it. The converse is true for the TM waves with $\theta

J.d. Callen - One of the best experts on this subject based on the ideXlab platform.

  • Threshold Condition for non linear tearing modes in tokamaks
    Nuclear Fusion, 1997
    Co-Authors: M.f. Zabiego, J.d. Callen
    Abstract:

    The non-linear evolution of low mode number tearing modes is analysed, emphasizing the need for a Threshold Condition, to account for observations in tokamaks. The discussion is illustrated by two models recently introduced in the literature. The models can be compared with the available data and/or serve as a basis for planning experiments in order either to test theory (by means of beta -limit scaling laws, as proposed in this paper) or to attempt to control undesirable tearing modes. Introducing a Threshold Condition in the tearing mode stability analysis is found to reveal some bifurcation points and thus domains of intrinsic stability in the island dynamics operational space

  • Threshold Condition for nonlinear tearing modes in tokamaks
    1996
    Co-Authors: M.f. Zabiego, J.d. Callen
    Abstract:

    Low-mode-number tearing, mode nonlinear evolution is analyzed emphasizing the need for a Threshold Condition, to account for observations in tokamaks. The discussion is illustrated by two models recently introduced in the literature. The models can be compared with the available data and/or serve as a basis for planning some experiments in order to either test theory (by means of beta-limit scaling laws, as proposed in this paper) or attempt to control undesirable tearing modes. Introducing a Threshold Condition in the tearing mode stability analysis is found to reveal some bifurcation points and thus domains of intrinsic stability in the island dynamics operational space.

M.f. Zabiego - One of the best experts on this subject based on the ideXlab platform.

  • Threshold Condition for non linear tearing modes in tokamaks
    Nuclear Fusion, 1997
    Co-Authors: M.f. Zabiego, J.d. Callen
    Abstract:

    The non-linear evolution of low mode number tearing modes is analysed, emphasizing the need for a Threshold Condition, to account for observations in tokamaks. The discussion is illustrated by two models recently introduced in the literature. The models can be compared with the available data and/or serve as a basis for planning experiments in order either to test theory (by means of beta -limit scaling laws, as proposed in this paper) or to attempt to control undesirable tearing modes. Introducing a Threshold Condition in the tearing mode stability analysis is found to reveal some bifurcation points and thus domains of intrinsic stability in the island dynamics operational space

  • Threshold Condition for nonlinear tearing modes in tokamaks
    1996
    Co-Authors: M.f. Zabiego, J.d. Callen
    Abstract:

    Low-mode-number tearing, mode nonlinear evolution is analyzed emphasizing the need for a Threshold Condition, to account for observations in tokamaks. The discussion is illustrated by two models recently introduced in the literature. The models can be compared with the available data and/or serve as a basis for planning some experiments in order to either test theory (by means of beta-limit scaling laws, as proposed in this paper) or attempt to control undesirable tearing modes. Introducing a Threshold Condition in the tearing mode stability analysis is found to reveal some bifurcation points and thus domains of intrinsic stability in the island dynamics operational space.

Shui Wang - One of the best experts on this subject based on the ideXlab platform.

  • electromagnetic ion cyclotron waves instability Threshold Condition of suprathermal protons by kappa distribution
    Journal of Geophysical Research, 2007
    Co-Authors: Fuliang Xiao, Qinghua Zhou, Huiyong He, Huinan Zheng, Shui Wang
    Abstract:

    [1] The well-known generalized Lorentzian (kappa) distribution generally provides a good representation for the high-energy tail population of natural cosmic suprathermal plasmas. In this study we examine the electromagnetic ion cyclotron waves (EMIC) instability driven by the temperature anisotropy Condition (T⊥/T∥ > 1) of suprathermal protons modeled with a typical kappa distribution in a cold multispecies plasma (electron, H+, He+, and O+). Since the EMIC wave instability is found to be significant typically above the O+ band, we apply a linear theory to study the instability Threshold Condition for the He+ and H+ bands particularly around the geostationary orbit. The instability Threshold Condition, as in the case for a regular bi-Maxwellian, is found to follow a typical form T⊥/T∥ − 1 = S/β∥α, with higher values in the He+ band than those in the H+ band in the case of the strong wave instability owing to a lower maximum wave growth in the He+ band. As the spectral index κ increases, the instability Threshold Condition generally decreases and tends to the lowest limiting values of the bi-Maxwellian, since the evaluation by the bi-Maxwellian generally overestimates the maximum wave growth. The densities of the cold components (particularly protons) have impacts on the Threshold Condition primarily in the H+ band, with a higher density of cold protons leading to a lower value of the Threshold Condition. The results above may further reveal the nature of this instability Threshold Condition for the EMIC waves in any other space plasmas where an anisotropic suprathermal ion component and cold multicomponents are present together.

  • whistler instability Threshold Condition of energetic electrons by kappa distribution in space plasmas
    Journal of Geophysical Research, 2006
    Co-Authors: Fuliang Xiao, Qinghua Zhou, Huinan Zheng, Shui Wang
    Abstract:

    [1] Observational studies clearly reveal that natural space plasmas generally possess a pronounced non-Maxwellian high-energy tail distribution that can be well modeled by a generalized Lorentzian (kappa) distribution. In this study we consider the whistler mode wave instability driven by the anisotropy Condition (T⊥/T∥ > 1) of energetic electrons modeled with a typical kappa distribution in the presence of a cold plasma population. We use a linear theory to study the instability Threshold Condition for two typical plasma regions of interest: the higher-density (or a weakly magnetized) region and the lower-density (or a strongly magnetized) region. We find that (1) as in the case for a regular bi-Maxwellian, the energetic electron anisotropy T⊥/T∥ is subject to the Threshold Condition of this whistler instability, and the instability Threshold Condition obeys a general form T⊥/T∥ − 1 = S/β∥α, with a narrow range of the fitting parameter 0.25 ≤ α ≤ 0.52 over 0.01 ≤ β∥ ≤ 2.0; (2) the instability Threshold Condition in the higher-density (or a weakly magnetized) region is generally lower than that in the lower-density (or a strongly magnetized) region, specifically, with the fitting parameter range 0.3 ≤ S ≤ 5.0 in the higher-density (or a weakly magnetized) region, while 0.32 ≤ S ≤ 6.94 in the lower-density (or a strongly magnetized) region; and (3) the instability Threshold Condition for the kappa distribution generally decreases as the spectral index κ increases and tends to the lowest limiting values of the bi-Maxwellian as κ → ∞. The results above may present a further insight into the nature of this instability Threshold Condition for the whistler mode waves in the outer radiation belts of the Earth, the inner Jovian magnetosphere, or other space plasmas where an anisotropic hot electron component and a cold plasma component are both present.