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At least 721 records · Page 40
All sourcesNASA NTRSDOE OSTI
DOE OSTI2019

A Hermitian symmetric space Fokas–Lenells equation: Solitons, breathers, rogue waves

Highlights: • We study a Hermitian symmetric space Fokas–Lenells equation. • We obtain multi-soliton, kink–breather and rogue wave solutions for this equation. • We analyse the dynamical behaviour of these exact solutions. - Abstract: Based on the zero-curvature representation, we propose a Hermitian symmetric space Fokas–Lenells equation associated with a 4 × 4 matrix spectral problem. Resorting to the gauge transformation between spectral problems, we find a restrictive condition of the spectral functions that can ensure the symmetry of the new potential matrix, from which n-fold classical Darboux transformations and N-fold generalized Darboux transformations of this equation are constructed with the help of the limit technique and an iterative procedure. Utilizing the Darboux transformations and Mathematica software, we obtain various solutions for the Hermitian symmetric space Fokas–Lenells equation, including the multi-soliton solution, kink–breather solution, eye-shaped rogue wave solution, one-peaky shaped rogue wave solution, and dark two-peaky shaped rogue wave solution. By varying the values of the free parameters, we obtain different types of spatial–temporal distribution structures for the solutions, including the fundamental, line and triangular patterns. Furthermore, the dynamical behaviour of these solutions, including the fusion and fission processes of rogue waves, is analysed in detail.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRS1987

A quartic dispersion equation for internal gravity waves in the thermosphere

A new quartic dispersion equation in the square of the complex vertical wave number is derived by employing the 'shallow atmosphere' approximation and an ion drag approximation. These approximations allow the coefficients of the quartic equation to be given in terms of the corresponding cubic equation (which neglects the Coriolis force and the zonal ion drag component), but modified to take into account these neglected effects. Coupling between the extraordinary viscosity wave mode and the other three wave modes is highlighted and numerical solutions are compared for this quartic equation, an exact eighth order equation and the cubic equation. For the first time the validity of using the 'shallow atmosphere' approximation to describe internal gravity wave motions is demonstrated.

Hickey, M. P.↗
NASA NTRS1993

Wave and pseudo-diffusion equations from squeezed states

We show that the probability distributions P(sub n)(q,p;y) := the absolute value squared of (n(p,q;y), which are obtained from squeezed states, obey an interesting partial differential equation, to which we give two intuitive interpretations: as a wave equation in one space dimension; and as a pseudo-diffusion equation. We also study the corresponding Wehrl entropies S(sub n)(y), and we show that they have minima at zero squeezing, y = 0.

Daboul, Jamil↗
NASA NTRS2007

Chaotic Motion of Relativistic Electrons Driven by Whistler Waves

Canonical equations governing an electron motion in electromagnetic field of the whistler mode waves propagating along the direction of an ambient magnetic field are derived. The physical processes on which the equations of motion are based .are identified. It is shown that relativistic electrons interacting with these fields demonstrate chaotic motion, which is accompanied by the particle stochastic heating and significant pitch angle diffusion. Evolution of distribution functions is described by the Fokker-Planck-Kolmogorov equations. It is shown that the whistler mode waves could provide a viable mechanism for stochastic energization of electrons with energies up to 50 MeV in the Jovian magnetosphere.

Khazanov, G. V.↗
DOE OSTI2025

Solution of the linear wave-particle kinetic equation for global modes of arbitrary frequency in a tokamak

The linear response of a plasma to perturbations of arbitrary frequency and wavelength is derived for any axisymmetric magnetized toroidal plasma. An explicit transformation to action-angle coordinates is achieved using orthogonal magnetic coordinates and the Littlejohn Lagrangian, establishing the validity of this result to arbitrary order in normalized Larmor radius. The global resonance condition for compressional modes is clarified in more detail than in previous works, confirming that the poloidal orbit-average of the cyclotron frequency gives the desired result at lowest order in Larmor radius. The global plasma response to the perturbation at each resonance is captured by a poloidal and gyroaverage of the perturbing potential. A “global gyroaveraging” of the potential is a natural by-product of this analysis which takes into account the changing of the magnetic field over an orbit. The resonance condition depends on two arbitrary integers which completely separately capture the effects poloidal non-uniformity and finite Larmor radius in generating sidebands. We learn that poloidal sidebands generated for compressional modes are dominated by the change in gyrofrequency over the orbit, which is very different to shear modes where the gyrofrequency only contributes via a finite Larmor radius effect. This increases the number of bounce harmonics required to compute the linear drive, giving a more complicated resonance map. An example calculation is given comparing resonance of shear and compressional modes in a published DIII-D case.

Compressional↗
DOE OSTI2015

Kinetic theory of turbulence for parallel propagation revisited: Formal results

In a recent paper, Gaelzer et al. [Phys. Plasmas 22, 032310 (2015)] revisited the second-order nonlinear kinetic theory for turbulence propagating in directions parallel/anti-parallel to the ambient magnetic field. The original work was according to Yoon and Fang [Phys. Plasmas 15, 122312 (2008)], but Gaelzer et al. noted that the terms pertaining to discrete-particle effects in Yoon and Fang's theory did not enjoy proper dimensionality. The purpose of Gaelzer et al. was to restore the dimensional consistency associated with such terms. However, Gaelzer et al. was concerned only with linear wave-particle interaction terms. The present paper completes the analysis by considering the dimensional correction to nonlinear wave-particle interaction terms in the wave kinetic equation.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
NASA NTRS1995

Study of nonlinear MHD equations governing the wave propagation in twisted coronal loops

The solar corona, modelled by a low beta, resistive plasma slab, sustains MHD wave propagations due to shearing footpoint motions in the photosphere. By using a numerical algorithm the excitation and nonlinear development of MHD waves in twisted coronal loops are studied. The plasma responds to the footpoint motion by sausage waves if there is no twist. The twist in the magnetic field of the loop destroys initially developed sausage-like wave modes and they become kinks. The transition from sausage to kink modes is analyzed. The twist brings about mode degradation producing high harmonics and this generates more complex fine structures. This can be attributed to several local extrema in the perturbed velocity profiles. The Alfven wave produces remnants of the ideal 1/x singularity both for zero and non-zero twist and this pseudo-singularity becomes less pronounced for larger twist. The effect of nonlinearity is clearly observed by changing the amplitude of the driver by one order of magnitude. The magnetosonic waves also exhibit smoothed remnants of ideal logarithmic singularities when the frequency of the driver is correctly chosen. This pseudo-singularity for fast waves is absent when the coronal loop does not undergo any twist but becomes pronounced when twist is included. On the contrary, it is observed for slow waves even if there is no twist. Increasing the twist leads to a higher heating rate of the loop. The larger twist shifts somewhat uniformly distributed heating to layers inside the slab corresponding to peaks in the magnetic field strength.

Parhi, S.↗
NASA NTRS2012

The Effects of Wave Escape on Fast Magnetosonic Wave Turbulence in Solar Flares

One of the leading models for electron acceleration in solar flares is stochastic acceleration by weakly turbulent fast magnetosonic waves ("fast waves"). In this model, large-scale flows triggered by magnetic reconnection excite large-wavelength fast waves, and fast-wave energy then cascades from large wavelengths to small wavelengths. Electron acceleration by large-wavelength fast-waves is weak, and so the model relies on the small-wavelength waves produced by the turbulent cascade. In order for the model to work, the energy cascade time for large-wavelength fast waves must be shorter than the time required for the waves to propagate out of the solar-flare acceleration region. To investigate the effects of wave escape, we solve the wave kinetic equation for fast waves in weak turbulence theory, supplemented with a homogeneous wave-loss term.We find that the amplitude of large-wavelength fast waves must exceed a minimum threshold in order for a significant fraction of the wave energy to cascade to small wavelengths before the waves leave the acceleration region.We evaluate this threshold as a function of the dominant wavelength of the fast waves that are initially excited by reconnection outflows.

Pongkitiwanichakul, Peera↗
DOE OSTI2012

Electromagnetic weak turbulence theory revisited

The statistical mechanical reformulation of weak turbulence theory for unmagnetized plasmas including fully electromagnetic effects was carried out by Yoon [Phys. Plasmas 13, 022302 (2006)]. However, the wave kinetic equation for the transverse wave ignores the nonlinear three-wave interaction that involves two transverse waves and a Langmuir wave, the incoherent analogue of the so-called Raman scattering process, which may account for the third and higher-harmonic plasma emissions. The present paper extends the previous formalism by including such a term.

42 ENGINEERING↗
DOE OSTI2017

Raman amplification of laser pulses near the threshold for plasma wave breaking

Equations are derived for the amplitudes of counter-propagating laser pulses near the threshold for plasma wave breaking, which allow one to describe laser pulses with durations on the order of the plasma oscillation period. In the quasi-monochromatic approximation, they take the form of conventional threewave equations with an additional nonlinearity for the plasma wave. The amplitudes of the amplified laser pulses estimated using these equations agree with results obtained by solving the complete equations. It is shown that Raman amplification of a weak quasi-monochromatic signal (plasma noise) in rarified plasma is significantly suppressed. At the same time, according to numerical simulations, the amplification of laser pulses with durations on the order of the plasma oscillation period is suppressed insignificantly. This result opens new prospects in the application of Raman compression of laser pulses without additional frequency modulation.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2015

Soliton solutions and chaotic motions of the Zakharov equations for the Langmuir wave in the plasma

For the interaction between the high-frequency Langmuir waves and low-frequency ion-acoustic waves in the plasma, the Zakharov equations are studied in this paper. Via the Hirota method, we obtain the soliton solutions, based on which the soliton propagation is presented. It is found that with λ increasing, the amplitude of u decreases, whereas that of v remains unchanged, where λ is the ion-acoustic speed, u is the slowly-varying envelope of the Langmuir wave, and v is the fluctuation of the equilibrium ion density. Both the head-on and bound-state interactions between the two solitons are displayed. We observe that with λ decreasing, the interaction period of u decreases, while that of v keeps unchanged. It is found that the Zakharov equations cannot admit any chaotic motions. With the external perturbations taken into consideration, the perturbed Zakharov equations are studied for us to see the associated chaotic motions. Both the weak and developed chaotic motions are investigated, and the difference between them roots in the relative magnitude of the nonlinearities and perturbations. The chaotic motions are weakened with λ increasing, or else, strengthened. Periodic motion appears when the nonlinear terms and external perturbations are balanced. With such a balance kept, one period increases with λ increasing.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
NASA NTRS1966

Gravity waves in a realistic atmosphere.

Internal atmospheric gravity waves in isothermal medium, solving hydrodynamic equations, determining wave propagation in realistic atmosphere for range of wave parameters, wind amplitude, reflected energy, etc

WIND CIRCULATION↗