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Nonlinear Langmuir Wave Processes

Langmuir waves are electrostatic waves that exist in a weakly magnetized plasma with dispersion relation
ω2 ≈ ωpe2 + 3k2Ve2, where ω is the wave angular frequency, ωpe is the electron plasma frequency, k is the wave number and Ve is the electron thermal speed. These Langmuir waves may interact with other waves such as ion acoustic waves, other Langmuir waves and radio waves (wave-wave processes), or with the electrons and protons in the plasma (wave-particle interactions). Such interactions are responsible for many physical processes that take place within a plasma such as the flattening of electron beams and in radio emission.

Often, the rates and efficiencies of these processes are not proportional to the energy density (∝ E2) but instead on higher powers of E. They are then nonlinear phenomena. Examples include nonlinear wave particle scattering processes, such as scattering off thermal ions (STI), nonlinear wave-wave processes, solitons (solitary waves) and other localized structures.

STI involves waves scattering off the polarization cloud of electrons about each thermal ion in the plasma of the waves involved, and such processes therefore are nonlinear phenomena. Examples of wave-wave interactions include three wave interactions including electrostatic decay, L → L' + S where L and L' are Langmuir waves and S is an ion sound wave, stimulated emission of fundamental radiation L → S' + T where T is a radio wave at the plasma frequency, and coalescence of Langmuir waves giving harmonic emission via L + L'→ T' where T' is a radio wave at twice the plasma frequency.


V.Yu. Belashov and S.V. Vladimirov, Solitary Waves in Dispersive Complex Media, Springer, Berlin, 2005.

I.H. Cairns, Role of collective effects in dominance of scattering off thermal ions over Langmuir wave decay: Analysis, simulations and space applications, Phys. Plasmas, 7, 4901, 2000.

B. Li, A.J. Willes, P.A. Robinson and I.H. Cairns, Dynamics of beam-driven Langmuir and ion-acoustic waves including electrostatic decay, Phys. Plasmas, 10, 2748, 2003.

B. Li, A.J. Willes, P.A. Robinson and I.H. Cairns, Second harmonic electromagnetic emission via beam-driven Langmuir waves, Phys. Plasmas, 12, 012103, 2005.

J.J. Mitchell, I.H. Cairns and P.A. Robinson, New constraints and energy conversion efficiencies for plasma emission, Phys. Plasmas, 10, 3315, 2003.

S.V. Vladimirov, V.N. Tsytovich, S.I. Popel and F.Kh. Khakimov, Modulational Interactions in Plasmas, Kluwer Academic Publishers, Dortrecht, 1995.



Figure 1. Wave levels for (a) harmonic transverse waves and (b) Langmuir waves from a quasilinear code that includes electron-Langmuir interactions and nonlinear Langmuir processes L → L' + S, L → S' + T and L + L' → T'. [Li et al., 2005]

Figure 2. An example of a soliton.


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