Intuitive and rigorous derivation of spontaneous emission and Landau damping of Langmuir waves through classical mechanics

Escande, Dominique; Zekri, S.; Elskens, Yves

doi:10.1063/1.871943

Cited by 33 publications

(86 citation statements)

References 20 publications

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“…While there were direct observations of trapping, i.e., resonant, effects during wave-particle interaction [2], in this Letter we report the first experimental evidence of the nonresonant, nonlinear electron velocity modulation by a single wave. This effect is important because, as recalled below, it is at the root of Landau damping in plasma physics [3][4][5].…”

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confidence: 98%

“…(1). The self-consistent Hamiltonian enables us to recover the Landau effect for the wave and to prove that it corresponds to a synchronization of the particles with the wave [3][4][5]; the time average force corresponding to this synchroniza-tion is maximum for particles with a relative velocity jvj jj= 3 p k 0r in the wave frame. In conclusion, a basic wave-particle interaction experiment has been performed in a TWT with a test electron beam.…”

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confidence: 99%

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Experimental Observation of Nonlinear Synchronization due to a Single Wave

2005

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A test electron beam is propagated in a specially designed traveling wave tube. It interacts with a nonresonant wave, and its energy distribution is recorded at the tube output. We report the direct experimental observation of the spatially periodic electron velocity bunching, and of a nonlinear effect on the electron velocity modulation: the synchronization of the particles with the wave responsible for Landau damping in plasma physics. The results are explained by second order perturbation theory in the wave amplitude.

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confidence: 98%

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confidence: 99%

Experimental Observation of Nonlinear Synchronization due to a Single Wave

2005

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“…The Landau effect can also be recovered by a statistical approach ( [63] and section 4 of reference [48]). There the wave phase and amplitude evolutions are computed by perturbation theory in the coupling parameter ε of the self-consistent Hamiltonian.…”

Section: A Recovering Vlasovian Linear Theory With a Mechanical Undementioning

confidence: 99%

How to Face the Complexity of Plasmas?

Escande

2013

Nonlinear Systems and Complexity

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This paper has two main parts. The first part is subjective and aims at favoring a brainstorming in the plasma community. It discusses the present theoretical description of plasmas, with a focus on hot weakly collisional plasmas. It comprises two sub-parts. The first one deals with the present status of this description. In particular, most models used in plasma physics are shown to have feet of clay, there is no strict hierarchy between them, and a principle of simplicity dominates the modeling activity. At any moment the description of plasma complexity is provisional and results from a collective and somewhat unconscious process. The second sub-part considers possible methodological improvements, some of them specific to plasma physics, some others of possible interest for other fields of science. The proposals for improving the present situation go along the following lines: improving the way papers are structured and the way scientific quality is assessed in the referral process, developing new data bases, stimulating the scientific discussion of published results, diversifying the way results are made available, assessing more quality than quantity, making available an incompressible time for creative thinking and non purpose-oriented research. Some possible improvements for teaching are also indicated. The suggested improvement of the structure of papers would be for each paper to have a "claim section" summarizing the main results and their most relevant connection to previous literature. One of the ideas put forward is that modern nonlinear dynamics and chaos might help revisiting and unifying the overall presentation of plasma physics.The second part of this chapter is devoted to one instance where this idea has been developed for three decades: the description of Langmuir wave-electron interaction in one-dimensional plasmas by a finite dimensional Hamiltonian. This part is more specialized, and is written like a classical scientific paper. This Hamiltonian approach enables recovering Vlasovian linear theory with a mechanical understanding. The quasilinear description of the weak warm beam is discussed, and it is shown that self-consistency vanishes when the plateau forms in the tail distribution function. This leads to consider the various diffusive regimes of the dynamics of particles in a frozen spectrum of waves with random phases. A recent numerical simulation showed that diffusion is quasilinear when the plateau sets in, and that the variation of the phase of a given wave with time is almost non fluctuating for random realizations of the initial wave phases. This led to new analytical calculations of the average behavior of the self-consistent dynamics when the initial wave phases are random. Using Picard iteration technique, they confirm numerical results, and exhibit a spontaneous emission of spatial inhomogeneities.Non quia difficilia sunt, non audemus, sed quia non audemus, difficilia sunt. It is not because things are difficult that we do not dare, it is because we do not dare that things a...

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“…The essential features of the fully nonlinear dynamics of the system are retained in this model, even if a single wavelength is taken into account [1,7]. The Hamiltonian (1) has the following constant of motion:…”

Section: Phase Space Analysismentioning

confidence: 99%

Large-amplitude oscillations and chaos in a Hamiltonian plasma system with many degrees of freedom

Farina¹,

Pozzoli

2004

Phys. Rev. E

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Taking the beam-plasma system as a reference Hamiltonian system with many degrees of freedom, the connection between the development of large amplitude oscillations and stochasticity of the system (measured through the time-dependent maximum Lyapunov exponent) is investigated. It is found that the development of self-consistent large amplitude oscillations occurs in correspondence with the onset of chaos, and is related to a well defined change of topology of the phase space of the system. It is also shown that in a (Hamiltonian) linearly stable regime the development of large amplitude oscillations can occur when weakly dissipative processes are introduced.

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Intuitive and rigorous derivation of spontaneous emission and Landau damping of Langmuir waves through classical mechanics

Cited by 33 publications

References 20 publications

Experimental Observation of Nonlinear Synchronization due to a Single Wave

Experimental Observation of Nonlinear Synchronization due to a Single Wave

How to Face the Complexity of Plasmas?

Large-amplitude oscillations and chaos in a Hamiltonian plasma system with many degrees of freedom

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