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  • 1
    ISSN: 1420-9136
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Physics
    Notes: Summary Energetic electrons are continually removed from the radiation belts by resonant pitch-angle scattering with ELF turbulence. A realistic simulation of the concomitant precipitation loss of such electrons to the atmosphere shows it to be a significant source for the nocturnal ionospheric D-region. During geomagnetically quiet (non-storm) periods, precipitating electrons are expected to provide the dominant nocturnal ionization source at medium invariant latitudes corresponding to field lines just inside the plasmapause. When the level of scattering turbulence is high the quiet time precipitation can dominate for an extended range of latitudes (Λ∼ 55° to 65°). Observed fluctuations in the level of scattering turbulence should produce modulations in the concentration of nocturnal middle latitude D-region electrons which may be detected using radio probing techniques.
    Type of Medium: Electronic Resource
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  • 2
    ISSN: 1476-4687
    Source: Nature Archives 1869 - 2009
    Topics: Biology , Chemistry and Pharmacology , Medicine , Natural Sciences in General , Physics
    Notes: [Auszug] The Van Allen radiation belts are two regions encircling the Earth in which energetic charged particles are trapped inside the Earth's magnetic field. Their properties vary according to solar activity and they represent a hazard to satellites and humans in space. An important challenge has ...
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  • 3
    Electronic Resource
    Electronic Resource
    New York, NY : American Institute of Physics (AIP)
    Physics of Fluids 3 (1991), S. 1835-1847 
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: In the linear theory of waves in a hot plasma if the zeroth-order velocity distribution function is taken to be Maxwellian, then there arises a special, complex-valued function of a complex variable ξ=x+iy, namely Z(ξ), known as the plasma dispersion function. In space physics many particle distributions possess a high-energy tail that can be well modeled by a generalized Lorentzian (or kappa) distribution function containing the spectral index κ. In this paper, as a natural analog to the definition of Z(ξ), a new special function Z@B|κ(ξ) is defined based on the kappa distribution function. Here, Z*κ(ξ) is called the modified plasma dispersion function. For any positive integral value of κ, Z@B|κ(ξ) is calculated in closed form as a finite series. General properties, including small-argument and large-argument expansions, of Z*κ(ξ) are given, and simple explicit forms are given for Z@B|1(ξ), Z*2(ξ), ..., Z@B|6(ξ). A comprehensive set of graphs of the real and imaginary parts of Z*κ(ξ) is presented. It is demonstrated how the modified plasma dispersion function approaches the plasma dispersion function in the limit as κ→∞, a result to be expected since the (appropriately defined) kappa distribution function formally approaches the Maxwellian as κ→∞. The function Z@B|κ(ξ) is expected to be instrumental in studying microinstabilities in plasmas when the particle distribution function is not only the standard generalized Lorentzian, but also of the Lorentzian type,including inter alia, the loss-cone, bi-Lorentzian, and product bi-Lorentzian distributions.
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  • 4
    Electronic Resource
    Electronic Resource
    [S.l.] : American Institute of Physics (AIP)
    Physics of Fluids 29 (1986), S. 4091-4102 
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: Analytical solutions are presented for the linear growth or damping rate caused by resonant particle interactions with plasma waves propagating in any arbitrary direction relative to the ambient magnetic field. For the case of three realistic and widely adopted representations for the particle distribution function, namely for a bi-Maxwellian, a bi-Lorenzian, and a loss-cone distribution, the angular dependence of the net growth rate can be expressed in terms of simple, smoothly varying functions involving modified Bessel functions of the first and second kind. Furthermore, in the limits of both quasilongitudinal and quasitransverse wave propagation, the analytical results reduce to simple algebraic expressions that may readily be used to compare the contributions from any specific harmonic resonance. These analytical solutions eliminate the need for costly and time-consuming numerical integration that hitherto was the standard procedure for obtaining growth rates for oblique waves.
    Type of Medium: Electronic Resource
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  • 5
    Electronic Resource
    Electronic Resource
    [S.l.] : American Institute of Physics (AIP)
    Physics of Fluids 30 (1987), S. 3761-3766 
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: The theory of kinetic instabilities in a plasma when the instabilities are driven by wave-particle resonance is addressed. Recent progress on the linear theory of resonant oblique wave growth in plasmas is extended to plasmas modeled by three standard forms of distribution, a bi-Maxwellian, a bi-Lorenzian, and a loss cone, each incorporating a field-aligned beam. The wave growth rates are shown to be functions of dimensionless integrals that can be expressed in terms of Bessel functions of argument equal to a normalized wave-normal variable. A marginal stability criterion is obtained, and accordingly we identify a threshold beam velocity for unstable growth of the waves. The simple analytical results derived can be readily applied to a wide variety of problems on oblique wave growth in space plasmas that hitherto were amenable only to extensive computer calculations.
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  • 6
    Electronic Resource
    Electronic Resource
    [S.l.] : American Institute of Physics (AIP)
    Physics of Plasmas 3 (1996), S. 2496-2501 
    ISSN: 1089-7674
    Source: AIP Digital Archive
    Topics: Physics
    Notes: Space and astrophysical plasmas typically possess particle distribution functions with a power-law tail (in energy) that are well modeled by generalized Lorentzian distributions with an associated spectral index κ. Dispersion equations for linear waves of any mode in a plasma described by a Lorentzian-type particle distribution involve the modified plasma dispersion function Zκ*, a special function analogous to the plasma dispersion function Z that arises when the particle distribution is Maxwellian. The function Zκ*, originally defined by Summers and Thorne [Phys. Fluids B 3, 1835 (1991)] for integral values of κ, was recently generalized to real values of κ by Mace and Hellberg [Phys. Plasmas 2, 2098 (1995)]. In the present paper, a general formula is derived for the modified plasma dispersion function Zκ* corresponding to half-integral values of κ, and simple, explicit closed-form expressions are given for the functions Z3/2*, Z5/2*, Z7/2*, Z9/2*, and Z11/2*. These results complement the simple, closed-form expressions for the functions Zκ*, for κ=1, 2, 3,..., that already exist in the literature. © 1996 American Institute of Physics.
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  • 7
    Electronic Resource
    Electronic Resource
    New York, NY : American Institute of Physics (AIP)
    Physics of Fluids 3 (1991), S. 2117-2123 
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: Space plasmas typically possess a particle distribution function with an enhanced high-energy tail that is well modeled by a generalized Lorentzian (or kappa) distribution with spectral index κ. The modified plasma dispersion function Z@B|κ(ξ) [Summers and Thorne, Phys. Fluids B 3, (large-closed-square)(large-closed-square)(large-closed-square)(large-closed-square) (1991)] is employed to analyze the Landau damping of (electrostatic) Langmuir waves and ion-acoustic waves in a hot, isotropic, unmagnetized, generalized Lorentzian plasma, and the solutions are compared with the classical results for a Maxwellian plasma. Numerical solutions for the real and imaginary parts of the wave frequency ω0−iγ are obtained as a function of the normalized wave number kλD, where λD is the electron Debye length. For both particle distributions the electrostatic modes are strongly damped, γ/ω0(very-much-greater-than)1, at short wavelengths, kλD(very-much-greater-than)1. This collisionless damping becomes less severe at long wavelengths, kλD(very-much-less-than)1, but the attenuation of Langmuir waves is much stronger for a generalized Lorentzian plasma than for a Maxwellian plasma. This will further localize Langmuir waves to frequencies just above the electron plasma frequency in plasmas with a substantial high-energy tail. Landau damping of ion-acoustic waves is only slightly affected by the presence of a high-energy tail, but is strongly dependent on the ion temperature. Owing to the simple analytical form of the modified plasma dispersion function when κ=2 (corresponding to a pronounced high-energy tail), exact analytical results for the real and imaginary parts of the wave frequency can be found in this case; similar solutions are not available for a Maxwellian plasma.
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  • 8
    Electronic Resource
    Electronic Resource
    [S.l.] : American Institute of Physics (AIP)
    Physics of Plasmas 1 (1994), S. 2012-2025 
    ISSN: 1089-7674
    Source: AIP Digital Archive
    Topics: Physics
    Notes: Expressions are derived for the elements of the dielectric tensor for linear waves propagating at an arbitrary angle to a uniform magnetic field in a fully hot plasma whose constituent particle species σ are modeled by generalized Lorentzian distribution functions. The expressions involve readily computable single integrals whose integrands involve only elementary functions, Bessel functions, and modified plasma dispersion functions, the latter being available in the form of finite algebraic series. Analytical forms for the integrals are derived in the limits λ→0 and λ→∞, where λ=(k⊥ρLσ)2/2, with k⊥ the component of wave vector perpendicular to the ambient magnetic field, and ρLσ the Larmor radius for the particle species σ. Consideration is given to the important limits of wave propagation parallel and perpendicular to the ambient magnetic field, and also to the cold plasma limit. Since most space plasmas are well modeled by generalized Lorentzian particle distribution functions, the results obtained in this paper provide a powerful tool for analyzing kinetic (micro-) instabilities in space plasmas in a very general context, limited only by the assumptions of linear plasma theory.
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