Similarity solutions for nonlinear Landau damping of Alfvén waves

1982 ◽  
Vol 28 (2) ◽  
pp. 317-323 ◽  
Author(s):  
J. F. McKenzie
Keyword(s):  
Power Spectrum ◽  
Basic Feature ◽  
Similarity Solutions ◽  
Alfven Waves ◽  
Landau Damping ◽  
Alfvén Waves ◽  
Wave Spectra ◽  
Initial Strength ◽  
Long Wavelength ◽  
Nonlinear Landau Damping

In this paper we develop similarity solutions for the problem of nonlinear Landau damping of Alfvén waves. These solutions which are applicable to power-law wave spectra illustrate not only the basic feature of the damping process, namely that short-wavelength waves decay more rapidly than long-wavelength waves, but also how the damping depends on the initial strength of the power spectrum and its distribution in wavenumber.

scholarly journals The role of nonlinear Landau damping and the bounced motion of protons in the formation of dissipative structures in the solar wind plasma

1999 ◽  
Vol 6 (3/4) ◽  
pp. 161-167 ◽  
Author(s):  
M. Prakash ◽  
P. H. Diamond
Keyword(s):  
Solar Wind ◽  
Geomagnetic Field ◽  
Large Amplitude ◽  
Solar Wind Plasma ◽  
Acoustic Mode ◽  
Alfven Waves ◽  
Landau Damping ◽  
Alfvén Waves ◽  
Ion Acoustic ◽  
Nonlinear Landau Damping

Abstract. The present work examines the effects arising from the nonlinear Landau damping and the bounced motion of protons (trapped in the mirror geometry of the geomagnetic field) in the formation of nonlinear Alfvénic structures. These structures are observed at distances 1-5AU in the solar wind plasma (with ß ~ 1). The dynamics of formation of these structures can be understood using kinetic nonlinear Schrodinger (KNLS) model. The structures emerge due to balance of nonlinear steepening (of large amplitude Alfvén waves) by the linear Landau damping of ion-acoustic modes in a finite ß solar wind plasma. The ion-acoustic mode is driven nonlinearly by the large amplitude Alfvén waves. At the large amplitudes of Alfvén wave, the effects due to nonlinear Landau damping become important. These nonlinear effects are incorporated into the KNLS model by modifying the heat flux dissipation coefficient parallel to the ambient magnetic field. The effects arising from the bounced motion (of mirroring protons) are studied using a one-dimensional Vlasov equation. The bounced motion of the protons can lead to growth of the ion-acoustic mode, propagating in the mirror geometry of the geomagnetic field. The significance of these studies in the formation of dissipative quasistationary structures observed in solar wind plasma is discussed.

Linear kinetic Alfvén waves in inhomogeneous plasma: Effects of Landau damping

2016 ◽  
Vol 113 (2) ◽  
pp. 25001 ◽  
Author(s):  
R. P. Sharma ◽  
R. Goyal ◽  
Nidhi Gaur ◽  
Earl E. Scime
Keyword(s):  
Inhomogeneous Plasma ◽  
Alfven Waves ◽  
Landau Damping ◽  
Alfvén Waves ◽  
Plasma Effects ◽  
Linear Kinetic ◽  
Kinetic Alfvén Waves

Nonlinear Landau Damping of Alfvén Waves in a High β Plasma

1982 ◽  
Vol 37 (8) ◽  
pp. 809-815 ◽  
Author(s):  
Heinrich J. Völk ◽  
Catherine J. Cesarsky
Keyword(s):  
Wave Length ◽  
Wave Spectrum ◽  
Nonlinear Damping ◽  
Alfven Waves ◽  
Alfvén Waves ◽  
Propagating Waves ◽  
Damping Rate ◽  
Nonlinear Landau Damping ◽  
The Waves ◽  
The Magnetic Field

A study is made of the nonlinear damping of parallel propagating Alfvén waves in a high β plasma. Two circularly polarized parallel propagating waves give rise to a beat wave, which in general contains both a longitudinal electric field component and a longitudinal gradient in the magnetic field strength. The wave damping is due to the interactions of thermal particles with these fields. If the amplitudes of the waves are low, a given wave (ω1, k1) is damped by the presence of all longer wavelength waves; thus, if the amplitudes of the waves in the wave spectrum increase with wave length, the effect of the longest waves is dominant.However, when the amplitude of the waves is sufficiently high, the particles are trapped in the wave packets, and the damping rate may be considerably reduced. We calculate the induced electrostatic field, and examine the trapping of thermal particles in a pair of waves. Finally, we give examples of modified damping rates of a wave in the presence of a spectrum of waves, and show that, when the trapping is effective, the waves are mostly damped by their interactions with waves of comparable wavelengths

Landau damped kinetic Alfvén waves and coronal heating

2009 ◽  
Vol 76 (2) ◽  
pp. 239-246 ◽  
Author(s):  
R. P. SHARMA ◽  
SACHIN KUMAR
Keyword(s):  
Solar Corona ◽  
Initial Conditions ◽  
Planck Equation ◽  
Alfven Waves ◽  
Coronal Heating ◽  
Landau Damping ◽  
Alfvén Waves ◽  
Energetic Electrons ◽  
Turbulent Spectra ◽  
Kinetic Alfvén Waves

AbstractSome recent observations of solar corona suggest that the kinetic Alfvén waves (KAWs) turbulence may be responsible for electron acceleration in solar corona and coronal heating. In the present research, we investigate the turbulent spectra of KAW due to filamentation process in the presence of Landau damping and particle energization. We present here the numerical simulation of model equation governing the nonlinear dynamics of the KAW in the presence of Landau damping. When the ponderomotive and Joule heating nonlinearities are incorporated in the KAW dynamics, the power spectra of the turbulent field is evaluated and used for particle heating. Our results reveal the formation of damped coherent magnetic filamentary structures and the turbulent spectra. The effect of Landau damping is to make the turbulent spectra steeper. Two types of scalings k−3.6 and k−4 have been obtained. We have studied the turbulence with different initial conditions. Using the Fokker–Planck equation with the new velocity space diffusion coefficient, we find the distribution function of energetic electrons in these turbulent structures. Landau damped KAWs may be responsible for the acceleration of the energetic electrons in solar corona and coronal heating.

scholarly journals Nonlinear long-wavelength torsional Alfvén waves

2010 ◽  
Vol 526 ◽  
pp. A80 ◽  
Author(s):  
S. Vasheghani Farahani ◽  
V. M. Nakariakov ◽  
T. Van Doorsselaere ◽  
E. Verwichte
Keyword(s):  
Alfven Waves ◽  
Alfvén Waves ◽  
Long Wavelength

Alfvén waves in relativistic plasmas

1968 ◽  
Vol 2 (4) ◽  
pp. 509-516 ◽  
Author(s):  
F. C. Hoh
Keyword(s):  
Relativistic Effects ◽  
Alfven Waves ◽  
Landau Damping ◽  
Alfvén Waves ◽  
Relativistic Plasmas ◽  
Vlasov Plasma

Expressions for Alfvén waves, their Landau damping, and magnetosonic waves are derived in a homogeneous relativistic Vlasov plasma. Relativistic effects reduce the speed of both waves.

scholarly journals Contribution of observed multi frequency spectrum of Alfvén waves to coronal heating

2019 ◽  
Vol 623 ◽  
pp. A37 ◽  
Author(s):  
P. Pagano ◽  
I. De Moortel
Keyword(s):  
Active Region ◽  
Power Spectrum ◽  
Solar Corona ◽  
Coronal Loop ◽  
Alfven Waves ◽  
Mhd Waves ◽  
Alfvén Waves ◽  
Coronal Loops ◽  
Phase Mixing ◽  
Transverse Oscillations

Context. Whilst there are observational indications that transverse magnetohydrodynamic (MHD) waves carry enough energy to maintain the thermal structure of the solar corona, it is not clear whether such energy can be efficiently and effectively converted into heating. Phase-mixing of Alfvén waves is considered a candidate mechanism, as it can develop transverse gradient where magnetic energy can be converted into thermal energy. However, phase-mixing is a process that crucially depends on the amplitude and period of the transverse oscillations, and only recently have we obtained a complete measurement of the power spectrum for transverse oscillations in the corona. Aims. We aim to investigate the heating generated by phase-mixing of transverse oscillations triggered by buffeting of a coronal loop that follows from the observed coronal power spectrum as well as the impact of these persistent oscillations on the structure of coronal loops. Methods. We considered a 3D MHD model of an active region coronal loop and we perturbed its footpoints with a 2D horizontal driver that represents a random buffeting motion of the loop footpoints. Our driver was composed of 1000 pulses superimposed to generate the observed power spectrum. Results. We find that the heating supply from the observed power spectrum in the solar corona through phase-mixing is not sufficient to maintain the million-degree active region solar corona. We also find that the development of Kelvin–Helmholtz instabilities could be a common phenomenon in coronal loops that could affect their apparent life time. Conclusions. This study concludes that is unlikely that phase-mixing of Alfvén waves resulting from an observed power spectrum of transverse coronal loop oscillations can heat the active region solar corona. However, transverse waves could play an important role in the development of small scale structures.

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