Nonlinear interactions of two compressional hydromagnetic waves
TL;DR: In this paper, nonlinear interactions of two azimuthally symmetric compressional hydromagnetic waves propagating in a cylindrical waveguide filled with cold magnetized plasma are investigated.
Abstract: Nonlinear interactions of two azimuthally symmetric compressional hydromagnetic waves propagating in a cylindrical waveguide filled with cold magnetized plasma are investigated. Two cases are considered: the nonlinear interaction of two identical oppositely propagating compressional waves and the nonlinear interaction of two compressional waves propagating with equal group velocities. In the first case the second-order perturbation fields generated through self- and mutual interactions of the waves are calculated and their effect on the otherwise-formed simple linear standing-wave pattern is studied. The possibility of observing a resonant nonlinear interaction is shown. In the second case, in order to describe the nonlinear evolution of the wave amplitudes, two coupled nonlinear Schrodinger (NLS) equations are presented. When excited individually, both the waves are seen to be modulationally stable; but when excited simultaneously, a strong nonlinear wave-wave coupling comes into play, which makes the waves modulationally unstable. The corresponding growth rate of the instability is also calculated.
Citations
More filters
01 Jan 1974
TL;DR: In this paper, the use of the compressional hydromagnetic mode (also called the magnetosonic or simply, the fast wave) is examined in some detail with respect to the heating of a tritium plasma containing a few percent deuterium.
Abstract: The use of the compressional hydromagnetic mode (also called the magnetosonic or, simply, the fast wave) is examined in some detail with respect to the heating of a tritium plasma containing a few percent deuterium. Efficient absorption of wave energy by the deuteron component is found when ω = ωC (deuterons), with Qwave 100. Reasonable efficiencies are found also for electron heating, but coherence effects between transit-time and Landau damping for electrons reduce the total absorption for both processes to one-half of the transit-time power, calculated separately.The fusion output of a two-component neutral-injected plasma can be enhanced by selective heating of the injected deuterons. Also, selective deuteron absorption may be used for ion-tail creation by radiofrequency excitation alone, as an alternative to neutral injection. The dominant behaviour of the high-energy deuteron distribution function is found to be f(v) ~ exp[(3/2)∫vdv / ], where is the Chandrasekhar-Spitzer drag coefficient, and is the Kennel-Engelmann quasi-linear diffusion coefficient for wave-particle interaction at the deuteron cyclotron frequency. An analytic solution to the one-dimensional Fokker-Planck equation, with r.f.-induced diffusion, is developed, and using this solution together with Duane's fit to the D-T fusion cross-section, it is found that the nuclear-fusion power output from an r.f.-produced two-component plasma can significantly exceed the incremental (radiofrequency) power input.
557 citations
TL;DR: In this paper, the transverse modulational instability of two collinear waves is investigated, using a coupled nonlinear Schrodinger-equation model, and it is shown that the presence of the second laser field increases the growth rate of the instability and decreases the scale length of the most unstable filaments.
Abstract: The transverse modulational instability, or filamentation, of two collinear waves is investigated, using a coupled nonlinear Schrodinger-equation model. For infinite media it is shown that the presence of the second laser field increases the growth rate of the instability and decreases the scale length of the most unstable filaments. Systems of two copropagating waves are shown to be convectively unstable and systems of two counterpropagating waves are shown to be absolutely unstable, even when the ratio of backward- to forward-wave intensity is small. For two counterpropagating waves in finite media, the threshold intensities for the absolute instability depend only weakly on the ratio of wave intensities. The general theory is applied to the pondermotive filamentation of two light waves in homogeneous plasma.
45 citations
TL;DR: The modulational instability of two equal-amplitude copropagating and counter-propagating waves has been studied in this paper, where the authors show that the wave instability is either absolute or convective in nature.
Abstract: A brief review is given of the modulational instability of a single wave. Some aspects of the modulational instability of two colinear waves are then studied. In general, the waves are modulationally unstable with a maximal growth rate which is larger than the modulational growth rate of either wave alone. Moreover, waves which are modulationally stable by themselves are often unstable in the other's presence. This is true for both copropagating and counterpropagating waves. An important property of an instability is whether it is absolute or convective in nature. The modulational instability of two equal-amplitude copropagating waves is usually, but not always, convective. The modulational instability of two equal-amplitude counterpropagating waves is always absolute. Some applications of current interest are discussed.
31 citations
TL;DR: In this article, coupled mode equations have been derived to describe the nonlinear interactions of a magneto-hydrodynamic wave with its second harmonic propagating in a planar waveguide filled with cold magnetized plasma.
Abstract: To describe the nonlinear interactions of a magneto-hydrodynamic wave with its second harmonic propagating in a planar waveguide filled with cold magnetized plasma, coupled mode equations have been derived. Solution of these equations shows the possibility of energy transfer between the fundamental and the second harmonic.
9 citations
01 Jan 1992
TL;DR: In this paper, the authors assume the existence of a hydrogen-bonded chain and discuss its consequences on the dynamics of the charge carriers, and they put a special emphasis on the role of the coupling between the protons and heavy ions motions.
Abstract: The transport of protons in hydrogen-bonded systems is a long standing problem which has not yet obtained a satisfactorily theoretical description. Although this problem was examined first for ice, it is relevant in many systems and in particular in biology for the transport along proteins or for proton conductance across membranes, an essential process in cell life. This broad relevance makes the study of proton conduction very appealing. Since the original work of Bernal and Fowler on ice1, the idea that the transport occurs through chains of hydrogen bonds has been well accepted. Such “proton wires” were invoked by Nagle and Morowitz2 for proton transport across membranes proteins and more recently across lipid bilayers3. In this report, we assume the existence of such an hydrogen-bonded chain and discuss its consequences on the dynamics of the charge carriers. We show that this assumption leads naturally to the idea of soliton transport and we put a special emphasis on the role of the coupling between the protons and heavy ions motions. The model is presented in section II. In section III we show how the coupling affects strongly the dynamics of the charge carriers and in section IV we discuss the role it plays in the thermal generation of carriers. The work presented in section III has been performed in 1986 and 87 with St Pnevmatikos and N. Flytzanis4 and was then completed in collaboration with D. Hochstrasser and H. Bilttner5. Therefore the results presented in this part are not new but we think that they are appropriate in the context of this multidisciplinary workshop because they provide a rather complete (and tractable) example of the solition picture for proton conduction.
1 citations
References
More filters
Book•
01 Jan 1944
TL;DR: The tabulation of Bessel functions can be found in this paper, where the authors present a comprehensive survey of the Bessel coefficients before and after 1826, as well as their extensions.
Abstract: 1. Bessel functions before 1826 2. The Bessel coefficients 3. Bessel functions 4. Differential equations 5. Miscellaneous properties of Bessel functions 6. Integral representations of Bessel functions 7. Asymptotic expansions of Bessel functions 8. Bessel functions of large order 9. Polynomials associated with Bessel functions 10. Functions associated with Bessel functions 11. Addition theorems 12. Definite integrals 13. Infinitive integrals 14. Multiple integrals 15. The zeros of Bessel functions 16. Neumann series and Lommel's functions of two variables 17. Kapteyn series 18. Series of Fourier-Bessel and Dini 19. Schlomlich series 20. The tabulation of Bessel functions Tables of Bessel functions Bibliography Indices.
9,584 citations
TL;DR: In this article, the authors used the method of multiple scales to derive the two coupled nonlinear partial differential equations which describe the evolution of a three-dimensional wavepacket of wavenumber k on water of finite depth.
Abstract: In this note we use the method of multiple scales to derive the two coupled nonlinear partial differential equations which describe the evolution of a three-dimensional wave-packet of wavenumber k on water of finite depth. The equations are used to study the stability of the uniform Stokes wavetrain to small disturbances whose length scale is large compared with 2π/ k . The stability criterion obtained is identical with that derived by Hayes under the more restrictive requirement that the disturbances are oblique plane waves in which the amplitude variation is much smaller than the phase variation.
1,021 citations
TL;DR: In this paper, the use of the compressional hydromagnetic mode (also called the magnetosonic or simply, the fast wave) is examined in some detail with respect to the heating of a tritium plasma containing a few percent deuterium.
Abstract: The use of the compressional hydromagnetic mode (also called the magnetosonic or, simply, the fast wave) is examined in some detail with respect to the heating of a tritium plasma containing a few percent deuterium. Efficient absorption of wave energy by the deuteron component is found when ω = ωC (deuterons), with Qwave 100. Reasonable efficiencies are found also for electron heating, but coherence effects between transit-time and Landau damping for electrons reduce the total absorption for both processes to one-half of the transit-time power, calculated separately.The fusion output of a two-component neutral-injected plasma can be enhanced by selective heating of the injected deuterons. Also, selective deuteron absorption may be used for ion-tail creation by radiofrequency excitation alone, as an alternative to neutral injection. The dominant behaviour of the high-energy deuteron distribution function is found to be f(v) ~ exp[(3/2)∫vdv / ], where is the Chandrasekhar-Spitzer drag coefficient, and is the Kennel-Engelmann quasi-linear diffusion coefficient for wave-particle interaction at the deuteron cyclotron frequency. An analytic solution to the one-dimensional Fokker-Planck equation, with r.f.-induced diffusion, is developed, and using this solution together with Duane's fit to the D-T fusion cross-section, it is found that the nuclear-fusion power output from an r.f.-produced two-component plasma can significantly exceed the incremental (radiofrequency) power input.
592 citations