A nonlinear theory of cosmic-ray pitch-angle diffusion in homogeneous magnetostatic turbulence

Goldstein, M. L.

doi:10.1086/154239

Cited by 109 publications

(72 citation statements)

References 9 publications

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“…In the years after QLT had been developed, it was noticed that the theory is not able to describe pitch-angle scattering at 90 • (corresponding to μ = 0) correctly. This problem, which is known as the 90 • −scattering problem, was then investigated in numerous papers (see, e.g., Jones et al 1973;Völk 1973;Owens 1974;Völk 1975;Goldstein 1976;Jones et al 1978). In these articles, QLT has been improved by replacing unperturbed orbits by more appropriate models.…”

Section: Introductionmentioning

confidence: 99%

Analytical description of nonlinear cosmic ray scattering: isotropic and quasilinear regimes of pitch-angle diffusion

Shalchi¹,

Skoda²,

Tautz³

et al. 2009

A&A

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Aims. We investigate pitch-angle scattering, which is a fundamental process in the physics of cosmic rays. Methods. By employing the second-order quasilinear theory, the pitch-angle Fokker-Planck coefficient is calculated analytically for the first time.Results. We demonstrate that for sufficiently strong turbulence the pitch-angle Fokker-Planck coefficient is isotropic. The derived results can be used to compute the parallel mean free path for all forms of the turbulence spectrum. We also consider applications, namely the transport of solar energetic particles and the propagation of cosmic rays in the Galaxy. Conclusions. The previously used assumption of isotropic pitch-angle diffusion is indeed correct for sufficiently strong turbulence. An analytical description of nonlinear particle scattering is possible.

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Section: Introductionmentioning

confidence: 99%

Analytical description of nonlinear cosmic ray scattering: isotropic and quasilinear regimes of pitch-angle diffusion

Shalchi¹,

Skoda²,

Tautz³

et al. 2009

A&A

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“…Most models of this propagation up to the quasilinear approximation assume that to zeroth order such particles follow a helical orbit along the mean spiral field while undergoing some spatial diffusion due to the effects of field fluctuations (Jokipii, 1971;Vlk, 1975a,b)° Recent nonlinear approaches (V61k, 1975b;Goldstein, 1976;Jones et al, 1977) and the local approximation quasilinear approach of Klimas et al (1976a,b; seek to remedy the inability of previous theories to accurately describe the more complex motions of cosmic ray particles with large (near 900) pitch angles and/or moderate to strong magnetic turbulence. There have been several attempts to determine the radial distance dependence of the cosmic ray diffusion tensor (Jokipii, 1973;V6Ik et al, 1974), but these have relied heavily on theoretical models for the spatial dependence of the magnetic spectrum which.may not correspond to the real situation (V5lk, 1975b).…”

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confidence: 99%

Heliocentric distance dependence of the interplanetary magnetic field

Behannon

1978

Reviews of Geophysics

130

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“…Although quasi-linear theory has proven successful in explaining the physics of the propagation of cosmic rays, the question of scattering through a pitch angle of 90 o has not yet been successfully resolved. The 90 o problem has been analyzed by several authors in the course of the years, in particular Völk (1973), Klimas and Sandri (1973) and Goldstein (1976Goldstein ( , 1980. In this paper we wish to present a self-consistent, yet simple theory, that resolves the problem by including mirror interaction with waves self generated by quasi-linear interaction itself.…”

Section: Introductionmentioning

confidence: 99%

Cosmic Ray Pitch Angle Scattering Through 90{degree}

Kulsrud¹,

Felice²

2000

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We study the problem of cosmic ray diffusion in the galactic disk with particular attention to the problem of particle scattering through the θ = cos −1 (v /v) = 90 o pitch angle in momentum space by wave-particle mirror interaction (here v is the cosmic ray velocity parallel to the average galactic magnetic field). We consider the case in which cosmic rays are the only source of magnetic turbulence, which originates as the relativistic particles try to stream through the interstellar plasma faster than the local Alfven speed. The wave growth rate is proportional to the cosmic ray anisotropy and the amplitude of hydro-magnetic waves generated by this streaming instability is limited by the presence of various damping mechanisms. We study the propagation of cosmic rays in the different phases of the I.S.M., in particular the coronal regions (where the main form of wave dissipation is non-linear Landau damping) and the warm regions (where charge exchange between the ions and the neutral atoms gives rise to the dominant form of wave dissipation). We also account for ion-cyclotron damping of small wavelength waves. The effect of a spectrum of waves is to limit the anisotropy of the cosmic ray distribution function, and hence to limit their drift velocity. We show that quasi-linear resonant scattering cannot account for particle diffusion everywhere in momentum space, and that particles with θ ∼ 90 o must change their pitch angle by mirror interaction with long wavelength waves generated by the θ ∼ 0 particles. We match the quasi-linear scattering with the adiabatic mirroring in a small boundary layer in momentum space close to the θ ∼ 90 o point and then we calculate the diffusion coefficient together with the cosmic ray drift velocity. We show that scattering through the 90 o point is very efficient and we calculate the correction to the particle diffusion coefficient due to the presence of mirroring.-3 -

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A nonlinear theory of cosmic-ray pitch-angle diffusion in homogeneous magnetostatic turbulence

Cited by 109 publications

References 9 publications

Analytical description of nonlinear cosmic ray scattering: isotropic and quasilinear regimes of pitch-angle diffusion

Analytical description of nonlinear cosmic ray scattering: isotropic and quasilinear regimes of pitch-angle diffusion

Heliocentric distance dependence of the interplanetary magnetic field

Cosmic Ray Pitch Angle Scattering Through 90{degree}

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