Nonlinear Landau damping of purely perpendicular Bernstein modes

1986 ◽  
Vol 36 (1) ◽  
pp. 111-125 ◽  
Author(s):  
Spilios Riyopoulos
Keyword(s):  
Cyclotron Frequency ◽  
Nonlinear Damping ◽  
Landau Damping ◽  
Linear Dispersion ◽  
Linear Dispersion Relation ◽  
Small Wave ◽  
Damping Rate ◽  
Vlasov’S Equation ◽  
Nonlinear Landau Damping ◽  
The Magnetic Field

The linear dispersion relation for Bernstein modes, obtained by the integration of Vlasov's equation along the unperturbed cyclotron orbits, predicts that the modes propagating perpendicularly to the magnetic field are undamped. However, when the frequency is close to a multiple of the cyclotron frequency, most of the particles become trapped for small wave amplitude and the unperturbed orbit approximation breaks down. The trapped particle trajectories are calculated analytically here using a resonant Hamiltonian approximation. Integration, consistent with the wave, along the orbits yields the nonlinear damping rate in a manner similar to that used by O'Neil for the damping of unmagnetized electrostatic modes. The results can be extended for the general case of almost perpendicular, short-wavelength electrostatic modes near cyclotron harmonics.

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

scholarly journals NON-ABELIAN MEDIUM EFFECTS IN QUARK–GLUON PLASMA

2002 ◽  
Vol 17 (10) ◽  
pp. 1435-1447 ◽  
Author(s):  
JI-SHENG CHEN ◽  
JIA-RONG LI ◽  
PENG-FEI ZHUANG
Keyword(s):  
Quark Gluon Plasma ◽  
Kinetic Equations ◽  
Wave Interaction ◽  
Gluon Plasma ◽  
Landau Damping ◽  
Medium Effects ◽  
Third Order ◽  
Damping Rate ◽  
Nonlinear Landau Damping ◽  
Color Field

Based on the kinetic theory, the non-Abelian medium property of hot Quark–Gluon Plasma is investigated. The nonlinearity of the plasma comes from two aspects: The nonlinear wave–wave interaction and self-interaction of color field. The non-Abelian color permittivity is obtained by expanding the kinetic equations to third order. As an application, the nonlinear Landau damping rate and the nonlinear eigen frequency shift are calculated in the longwave length limit.

scholarly journals Nonlinear Landau Damping Rate of a Driven Plasma Wave

2009 ◽  
Vol 103 (15) ◽  
Author(s):  
Didier Bénisti ◽  
David J. Strozzi ◽  
Laurent Gremillet ◽  
Olivier Morice
Keyword(s):  
Plasma Wave ◽  
Landau Damping ◽  
Damping Rate ◽  
Nonlinear Landau Damping

Non-linear scattering of electromagnetic waves near the ion cyclotron frequency in an inhomogeneous plasma

1968 ◽  
Vol 2 (3) ◽  
pp. 353-363 ◽  
Author(s):  
J. Teichmann
Keyword(s):  
Magnetic Field ◽  
Electromagnetic Waves ◽  
Cyclotron Frequency ◽  
Inhomogeneous Plasma ◽  
Landau Damping ◽  
Left Hand ◽  
Right Hand ◽  
Non Linear ◽  
Ion Cyclotron ◽  
The Magnetic Field

The non-linear induced scattering by plasma particles of right-hand and left- hand polarized electromagnetic waves propagating along the magnetic field, is studied. The non-linear Landau damping for frequencies near the ion cyclotron frequency in a weak turbulent inhomogeneous plasma is determined.

scholarly journals Excitation of chorus with small wave normal angles due to BPA mechanism into density ducts

2019 ◽  
Author(s):  
Peter A. Bespalov ◽  
Olga N. Savina
Keyword(s):  
Magnetic Field ◽  
Cyclotron Frequency ◽  
Angular Spectrum ◽  
Electron Cyclotron ◽  
Electron Cyclotron Frequency ◽  
Proposed Model ◽  
Small Wave ◽  
Pulse Amplifier ◽  
Wave Normal ◽  
The Magnetic Field

Abstract. We examine specific features of the realization of the beam pulse amplifier mechanism (BPA) of chorus excitation in the density ducts having a width of the order of 100–300 km with refractive reflection. The dispersion characteristics of whistler emissions in a planar duct under conditions for the fulfillment of the WKB approximation and refractive reflection from the walls of the duct are analyzed. It is shown that in the enhanced duct, discrete spectral elements of chorus with a narrow angular spectrum along the external magnetic field can be excited at frequencies somewhat lower than half the electron cyclotron frequency. In the depleted duct at frequencies somewhat higher than half the electron cyclotron frequency chorus with a narrow angular spectrum along the magnetic field can be excited. The proposed model explains the possibility of excitation of chorus with small angles of the wave normal when the BPA mechanism is implemented. It is noted that the properties of chorus, such as the intensity and a typical angle of the wave normal, can be different for the lower and upper band chorus.

Effect of the plasma inhomogeneity on the nonlinear damping of monochromatic waves

1972 ◽  
Vol 8 (3) ◽  
pp. 341-355 ◽  
Author(s):  
E. Asseo ◽  
G. Laval ◽  
R. Pellat ◽  
R. Welti ◽  
A. Roux
Keyword(s):  
Inhomogeneous Plasma ◽  
Inertial Force ◽  
Resonant Interaction ◽  
Nonlinear Damping ◽  
Damping Coefficient ◽  
Landau Damping ◽  
Plasma Inhomogeneity ◽  
Asymptotic Expressions ◽  
Trapping Force ◽  
Damping Rate

We study the resonant interaction of particles with a monochromatic wave in an inhomogeneous plasma. The effects of the inhomogeneity are represented by a variable phase velocity of the wave. This introduces, in the wave frame, an inertial force due to the non-Galilean transformation of co-ordinates. Asymptotic expressions are obtained for the spatial damping coefficient of the wave in two physically different cases.(i) When the inertial force is greater than the force due to the trapping (strong inhomogeneity case) instead of the null asymptotic behaviour that one obtains in the homogeneous case, the spatial nonlinear damping coefficient behaves asymptotically like the linear Landau damping coefficient.(ii) When the inertial force is lower than the trapping force (weakinhomogeneity case), the spatial nonlinear damping coefficient for short distances is proportional to the ratio of the inertial force to the trapping force. For long distances, this coefficient is proportional to the square of the preceding ratio multiplied by the number of trapping lengths. In both cases, the proportionality coefficient is the linear spatial Landau damping rate.

scholarly journals Excitation of chorus with small wave normal angles due to beam pulse amplifier (BPA) mechanism in density ducts

2019 ◽  
Vol 37 (5) ◽  
pp. 819-824
Author(s):  
Peter A. Bespalov ◽  
Olga N. Savina
Keyword(s):  
Magnetic Field ◽  
Cyclotron Frequency ◽  
Angular Spectrum ◽  
Electron Cyclotron ◽  
Electron Cyclotron Frequency ◽  
Proposed Model ◽  
Small Wave ◽  
Pulse Amplifier ◽  
Wave Normal ◽  
The Magnetic Field

Abstract. We examine specific features of the realisation of the beam pulse amplifier (BPA) mechanism of chorus excitation in the density ducts that have a width of the order of 100–300 km with refractive reflection. The dispersion characteristics of whistler emissions in a planar duct under conditions for the fulfilment of the Wentzel–Kramers–Brillouin (WKB) approximation and refractive reflection from the “walls” of the duct are analysed. It is shown that in the enhanced duct, discrete spectral elements of chorus with a narrow angular spectrum along the external magnetic field can be excited at frequencies somewhat lower than half of the electron cyclotron frequency. In the depleted duct at frequencies somewhat higher than half of the electron cyclotron frequency, chorus with a narrow angular spectrum along the magnetic field can be excited. The proposed model explains the possibility of excitation of chorus with small angles of the wave normal when the BPA mechanism is implemented. It is noted that the properties of chorus, such as the intensity and a typical angle of the wave normal, can be different for the lower- and upper-band chorus.

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