Revisiting the validity of quasilinear theory

AbstractThe random walk of magnetic field lines in the presence of magnetic turbulence in plasmas is investigated from first principles. An isotropic model is employed for the magnetic turbulence spectrum. An analytical investigation of the asymptotic behavior of the field-line mean-square displacement 〈(Δx)2〉 is carried out, in terms of the position variable z. It is shown that 〈(Δx)2〉 varies as ~z ln z for large distance z. This result corresponds to a superdiffusive behavior of field line wandering. This investigation complements previous work, which relied on a two-component model for the turbulence spectrum. Contrary to that model, quasilinear theory appears to provide an adequate description of the field-line random walk for isotropic turbulence.

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A more general model equation of nonlinear Rayleigh waves and their quasilinear solutions

Modern Physics Letters B ◽

10.1142/s0217984916500962 ◽

2016 ◽

Vol 30 (08) ◽

pp. 1650096 ◽

Cited By ~ 4

Author(s):

Shuzeng Zhang ◽

Xiongbing Li ◽

Hyunjo Jeong

Keyword(s):

Rayleigh Waves ◽

General Equation ◽

Wave Motion ◽

Numerical Solutions ◽

Second Harmonic ◽

Approximate Equation ◽

Finite Amplitude ◽

Sound Beam ◽

Quasilinear Theory ◽

Sound Beams

A more general two-dimensional wave motion equation with consideration of attenuation and nonlinearity is proposed to describe propagating nonlinear Rayleigh waves of finite amplitude. Based on the quasilinear theory, the numerical solutions for the sound beams of fundamental and second harmonic waves are constructed with Green’s function method. Compared with solutions from the parabolic approximate equation, results from the general equation have more accuracy in both the near distance of the propagation direction and the far distance of the transverse direction, as quasiplane waves are used and non-paraxial Green’s functions are obtained. It is more effective to obtain the nonlinear Rayleigh sound beam distributions accurately with the proposed general equation and solutions. Brief consideration is given to the measurement of nonlinear parameter using nonlinear Rayleigh waves.

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1202. Quasilinear theory of electron beam relaxation in a magnetic- active plasma

Vacuum ◽

10.1016/0042-207x(68)90896-8 ◽

1968 ◽

Vol 18 (9) ◽

pp. 530

Keyword(s):

Electron Beam ◽

Active Plasma ◽

Quasilinear Theory

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Quasi-linear theory of the loss-cone instability

Journal of Plasma Physics ◽

10.1017/s0022377800003123 ◽

1967 ◽

Vol 1 (1) ◽

pp. 105-112 ◽

Cited By ~ 13

Author(s):

A. A. Galeev

Keyword(s):

Linear Equation ◽

Free Path ◽

Linear Theory ◽

Particle Distribution ◽

Mean Free Path ◽

Ion Distribution ◽

Quasilinear Theory ◽

Loss Cone ◽

Small Loss ◽

The Mean

The loss-cone instability of plasma confined in a mirror-type trap is considered. Relaxation of the particle distribution in the trap with a length larger than the mean free path between ‘turbulent’ collisions is described by conventional quasilinear theory. A quasi-linear equation for the ion distribution is solved analytically for the case of a small loss-cone volume of particles in velocity space (it takes place, for instance, in the case of a trap with a larger mirror ratio).

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