Beyond the modulational approximation in the wave triplet interaction

Iorra, P.; Marini, Samuel; Peter, E.; Pakter, Renato; Rizzato, Felipe Barbedo

doi:10.1016/j.physa.2015.05.094

Cited by 4 publications

(10 citation statements)

References 27 publications

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“…In order to avoid chaos, we took parameters such as the frequency of the envelope is much smaller than the plasma frequency. 2 On the other hand, if we ignore the direct interaction between the waves, the longitudinal mode J grows exponentially after a rearrangement time. 14 The growth ceases just after the onset of a mixing process in the phase space (the distribution function becomes a non-single valued function), J reaches the saturation, and then it oscillates around a mean value with a frequency comparable to the plasma frequency.…”

Section: Discussionmentioning

confidence: 99%

“…9 Thus, the waves exchange energy, varying their amplitudes slowly, in a way that the total energy of the system is conserved, as seen in Ref. 2.…”

Section: Introductionmentioning

confidence: 96%

“…In the analysis of a single triplet of waves, the interaction between the waves takes place when resonant conditions are established, i.e., the waves must satisfy frequency and wavelength matching conditions. This implies a relation like [1][2][3][4][5][6][7][8] If the interaction parameter which is proportional to the plasma frequency is small enough, then the evolution of the envelope of the waves is well described by the modulational approximation-the dynamics of the envelope is regular and periodic. 9 Thus, the waves exchange energy, varying their amplitudes slowly, in a way that the total energy of the system is conserved, as seen in Ref.…”

Section: Introductionmentioning

confidence: 99%

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Triplet and beam interaction in a plasma

et al. 2017

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The interaction of three waves requires wavelength and frequency matching conditions. Without the presence of a particle beam, if the conditions are satisfied and if the frequency of the envelope is lower than the lowest frequency of the waves, they exchange energy and the evolution of the envelope of each wave is given by a constant plus a sinusoidal function. On the other hand, if a particle beam propagates within electrostatic and electromagnetic fields with no wavelength and frequency match, the energy exchange between the modes is done due to the particles. One of the modes could be amplified in this scheme. In the present work, we propose a model where a nonrelativistic particle beam propagates in a plasma within two electromagnetic modes and one electrostatic mode with wavelength and frequency matching conditions. Then, the waves are allowed to exchange energy between themselves and with the particle beam as well. We present new features in comparison to the isolated triplet interaction and to the beam-wave interaction. These features are relevant for a more realistic triplet interaction model.

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Section: Discussionmentioning

confidence: 99%

“…9 Thus, the waves exchange energy, varying their amplitudes slowly, in a way that the total energy of the system is conserved, as seen in Ref. 2.…”

Section: Introductionmentioning

confidence: 96%

Section: Introductionmentioning

confidence: 99%

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Triplet and beam interaction in a plasma

et al. 2017

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“…That is, there would be no temporal variation in the perturbative coefficient corresponding to the same wave vector of the single-mode reference state. For this reason, it is necessary to modify the standard prescription for beatification, in order to obtain our beatified four-wave model with similar characteristics to the system (30). 5 A penalty paid for the reference state not being an equilibrium is that the beatification needs to be carried out to one higher order to retain consistent nonlinearity.…”

Section: Beatificationmentioning

confidence: 99%

“…Returning to the case at hand, the matrix of ( 27), we have demonstrated by inserting this J μ into the left-hand-side of (37b) its failure to vanish. Therefore, (26) is not a Poisson bracket, and the equations of motion (30) are not a Hamiltonian system with (28) as Hamiltonian. This failure of the Jacobi identity is not surprising, since it has been known for some time that direct Fourier truncation destroys the Jacobi identity.…”

Section: The Jacobi Identitymentioning

confidence: 99%

A method for Hamiltonian truncation: a four-wave example

Viscondi¹,

Caldas²,

Morrison³

2016

J. Phys. A: Math. Theor.

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A method for extracting finite-dimensional Hamiltonian systems from a class of 2+1 Hamiltonian mean field theories is presented. These theories possess noncanonical Poisson brackets, which normally resist Hamiltonian truncation, but a process of beatification by coordinate transformation near a reference state is described in order to perturbatively overcome this difficulty. Two examples of four-wave truncation of Euler's equation for scalar vortex dynamics are given and compared: one a direct non-Hamiltonian truncation of the equations of motion, the other obtained by beatifying the Poisson bracket and then truncating. arXiv:1509.09247v2 [physics.flu-dyn]

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