Interplanetary Plasma Scattering Diagnostics from Anisotropy-time Profiles of Solar Energetic Particles

Schlickeiser, R.; Artmann, S.; Dröge, W.

doi:10.2174/1876534300902010001

Cited by 6 publications

(8 citation statements)

References 17 publications

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“…The use of turbulence that is asymmetric, which more closely mirrors reality than an assumed perfectly symmetric situation, brings to light new effects of field line drift that have to be accounted for in discussions of field line diffusion and that then alter the perception of the underlying physical behavior in these turbulent systems. Because measurements indicate that magnetic turbulence in the solar wind has indeed a nonaxisymmetric component (e.g., de Koning & Bieber 2003), these results may be important for the interpretation of energetic particle events (e.g., Schlickeiser et al 2009). Future work should, therefore, investigate the quantitative difference of the effect in relativistic solar wind turbulence (Matthaeus et al 1990).…”

Section: Discussionmentioning

confidence: 98%

The role of magnetic helicity for field line diffusion and drift

Tautz

Lerche

2011

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Aims. This paper discusses the systematic drift of magnetic field lines under the influence of asymmetric turbulence where the asymmetry is caused by Alfvén wave helicity. Methods. The basic method of investigation is numerically tracing random magnetic field lines to discuss the average displacement of field lines owing to the asymmetric turbulence. Results. The main result is that as long as one has any non-zero degree of asymmetric turbulence, there is a systematic drift of field lines on average; an effect not seen when the turbulence is taken to be symmetric. This result implies that diffusion of field lines takes place relative to the mean drift and so alters the consequences for discussions of field line diffusion.

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Section: Discussionmentioning

confidence: 98%

The role of magnetic helicity for field line diffusion and drift

Tautz

Lerche

2011

A&A

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“…Schlickeiser & Shalchi (2008) gave a systematic derivation of the diffusion approximation in a weak focusing limit, when the adiabatic focusing length is much greater than the turbulent scattering length of cosmic-ray particles. The diffusion approximation is the standard approximation for studying the cosmic-ray transport (e.g., Schlickeiser et al 2009;Artmann et al 2011;Tautz et al 2012, and references therein). Hence it is useful to know its limitations that are related to the fact that the signal propagation speed is infinite in the diffusion limit.…”

Section: Discussionmentioning

confidence: 99%

“…The formula gives a reasonably accurate fit to the observed SEP anisotropy profiles (Schlickeiser et al 2009;Artmann et al 2011). However, since |A| ≤ 3 by definition, an unsatisfactory feature, related to the infinite signal propagation speed of the diffusion equation, is that A → ∞ as t → 0.…”

Section: An Application To the Transport Of Solar Energetic Particlesmentioning

confidence: 99%

The telegraph equation for cosmic-ray transport with weak adiabatic focusing

Litvinenko

Schlickeiser

2013

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Time-dependent solutions of a spatial diffusion equation are often used to describe the transport of solar energetic particles, accelerated in large solar flares. Approximate analytical solutions of the diffusion approximation can complement and guide detailed numerical solutions of the Fokker-Planck equation for the particle distribution function. The accuracy of the diffusion approximation is limited, however, because the signal propagation speed is infinite in the diffusion limit. An improved description of cosmic-ray transport is provided by the telegraph equation, characterised by a finite signal propagation speed. We derive the telegraph equation for the particle density, taking into account adiabatic focusing in a large-scale interplanetary magnetic field in a weak focusing limit. As an illustration, we calculate a propagating pulse solution of the telegraph equation, determine the rise time when the maximum particle intensity is reached at a given distance from the Sun, and compare the results with those obtained in the diffusion approximation. In comparison with the diffusion equation, the telegraph equation predicts an asymmetrical shape of the pulse and a shorter rise time. These potentially significant differences suggest that the more accurate telegraph equation should be used in analysis of the solar energetic particle data, at least to quantify the accuracy of the focused diffusion model.

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“…As shown in Schlickeiser et al (2009), the ComptonGetting anisotropy (Eq. (26)) is small compared to the streaming anisotropy (Eq.…”

Section: Anisotropy-time Profilesmentioning

confidence: 97%

A diffusive description of the focused transport of solar energetic particles

Artmann

Schlickeiser

Agueda

et al. 2011

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The transport of solar energetic charged particles along the interplanetary magnetic field in the ecliptic plane of the sun can be described roughly by a one-dimensional diffusion equation. Large-scale spatial variations of the guide magnetic field can be taken into account by adding an additional term to the diffusion equation that includes the effect of adiabatic focusing. We solve this equation analytically by assuming a point-like particle injection in time and space and a spatial power-law dependence for the focusing length and the spatial diffusion coefficient. We infer the intensity-and anisotropy-time profiles of solar energetic particles from this solution. Through these the influence of different assumptions for the diffusion parameters can be seen in a mathematically closed form. The comparison of calculated and measured intensity-and anisotropy-time profiles, which are a powerful diagnostic tool for interplanetary particle transport, gives information about the large-scale spatial dependence of the focusing length and the diffusion coefficient. For an exceptionally large solar energetic particle event, which did occur on 2001 April 15, we fit the 27−512 keV electron intensities and anisotropies observed by the Wind spacecraft using the theoretically derived profiles. We find a linear spatial dependence of the mean free path along the guiding magnetic field. We also find the mean free path to be energy independent, which supports the theory of "velocity-dependent diffusion". This means that the intensity profiles for the discussed energies exhibit the same shape if they are plotted against the traveled distance and not against the time. In this case the profiles differ only in their maximum values and we can determine the energy spectra of the solar flare electrons out of the scaling factor we need to fit the data. The derived spectra exhibits a power-law dependence ∝E −3 kin in an energy range from ∼50 keV to ∼500 keV.

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Interplanetary Plasma Scattering Diagnostics from Anisotropy-time Profiles of Solar Energetic Particles

Cited by 6 publications

References 17 publications

The role of magnetic helicity for field line diffusion and drift

The role of magnetic helicity for field line diffusion and drift

The telegraph equation for cosmic-ray transport with weak adiabatic focusing

A diffusive description of the focused transport of solar energetic particles

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