Compound perpendicular transport of charged particles with drift, advection, wave propagation effects, and an arbitrary turbulence spectrum

Shalchi, A.; Webb, G. M.; Roux, J. A. le; Zank, G. P.

doi:10.1007/s10509-009-0021-y

Cited by 7 publications

(9 citation statements)

References 23 publications

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“…The D D  ratio may depend on the particle velocity and the turbulence energy level (Zank et al 2004;Li et al 2012, and references therein). Shalchi et al (2009) have considered a compound diffusion of charged particles in the solar wind at the high turbulence level, taking into account particle drift, advection and wave propagation effects. Their results indicate that perpendicular mean free path may increase as the proton energy decreases below ∼300 MeV (their Figure 1).…”

Section: Discussionmentioning

confidence: 99%

Solar Interacting Protons Versus Interplanetary Protons in the Core Plus Halo Model of Diffusive Shock Acceleration and Stochastic Re-Acceleration

Kocharov

Laitinen

Vainio

et al. 2015

ApJ

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With the first observations of solar γ-rays from the decay of pions, the relationship of protons producing ground level enhancements (GLEs) on the Earth to those of similar energies producing the γ-rays on the Sun has been debated. These two populations may be either independent and simply coincident in large flares, or they may be, in fact, the same population stemming from a single accelerating agent and jointly distributed at the Sun and also in space. Assuming the latter, we model a scenario in which particles are accelerated near the Sun in a shock wave with a fraction transported back to the solar surface to radiate, while the remainder is detected at Earth in the form of a GLE. Interplanetary ions versus ions interacting at the Sun are studied for a spherical shock wave propagating in a radial magnetic field through a highly turbulent radial ray (the acceleration core) and surrounding weakly turbulent sector in which the accelerated particles can propagate toward or away from the Sun. The model presented here accounts for both the first-order Fermi acceleration at the shock front and the second-order, stochastic re-acceleration by the turbulence enhanced behind the shock. We find that the re-acceleration is important in generating the γ-radiation and we also find that up to 10% of the particle population can find its way to the Sun as compared to particles escaping to the interplanetary space.

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Section: Discussionmentioning

confidence: 99%

Solar Interacting Protons Versus Interplanetary Protons in the Core Plus Halo Model of Diffusive Shock Acceleration and Stochastic Re-Acceleration

Kocharov

Laitinen

Vainio

et al. 2015

ApJ

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“…Some authors believe that FLRW is the main mechanism responsible for cross-field transport of charged cosmic particles. At least for situations in which particles follow magnetic field lines, the perpendicular transport parameters can directly be related to field line diffusion coefficients (see, for example, Webb et al 2006;Shalchi and Kourakis 2007c;Shalchi et al 2007Shalchi et al , 2009aWebb et al 2008;Weinhorst et al 2008).…”

Section: Discussionmentioning

confidence: 99%

“…The purpose in the theory of FLRW is to compute field line diffusion coefficients κ F L and field line mean square displacements (MSD's) ( x) 2 . The knowledge of these parameters is important for understanding fundamental properties of magnetic turbulence and the propagation of cosmic rays through the interplanetary or interstellar system (see, for example, Webb et al 2006Webb et al , 2008Shalchi and Kourakis 2007c;Shalchi et al 2007Shalchi et al , 2009aWeinhorst et al 2008). Field line wandering or random walk has been investigated in numerous papers (see, e.g., Jokipii and Parker 1969;Lerche 1973;Matthaeus et al 1995;Zimbardo et al 1995Zimbardo et al , 2000Ruffolo et al 2006;Shalchi andKourakis 2007a, 2007b;Shalchi and Weinhorst 2009).…”

Section: Introductionmentioning

confidence: 99%

Random walk of magnetic field lines: analytical theory versus simulations

Shalchi

Qin

2010

Astrophys Space Sci

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The analytical nonlinear theory of magnetic field line random walk predicts the existence of nondiffusive transport for certain forms of the turbulence spectrum. In the present article we use computer simulations to test these predictions made for well-established one-and twodimensional models of magnetic field fluctuations. For the first time it is shown by using simulations, that for a whole family of spectra a non-diffusive behavior of field line wandering can be found.

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“…Our result for κ F is similar to that of Chuvilgin and Ptuskin (1993), who studied particle transport in a random magnetic field, with multiple scales (in their case the effective bulk velocity can be identified with the Alfvén speed plus an effective drift speed). Shalchi et al (2009a) explore the role of field line random walk and advection, drifts and wave propagation effects on the cross-field transport of particles, with similar results to this paper. They give an extensive description of the statistics of the field line random walk…”

Section: Introductionmentioning

confidence: 57%

“…x 2 ∝ | z| α for the second moment for slab plus 2D turbulence and concentrate on the second moment of the pdf P ⊥ . Our paper concentrates more on a generalized form of the Chapman-Kolmogorov equation for cross-field transport and a detailed description of P ⊥ not addressed by Shalchi et al (2009a).…”

Section: Introductionmentioning

confidence: 99%

Compound and perpendicular diffusion of cosmic rays and random walk of the field lines: II. Non-parallel particle transport and drifts

Webb¹,

Kaghashvili²,

Roux³

et al. 2009

J. Phys. A: Math. Theor.

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Compound transport of energetic charged particles across the mean magnetic field due to field line random walk is investigated by means of a Chapman–Kolmogorov equation. The probability distribution function (pdf) for the particle transport across the field P⊥ is given as a convolution of the pdf for random walk of the magnetic field, PFRW, with the pdf Pp, for particle transport relative to the random walking field. The particle propagator Pp includes the effects of advection, drift, parallel diffusion and local perpendicular diffusion of particles relative to the random walking field. At early times, the particles sub-diffuse across the field due to field line random walk. At late times, the effective cross-field diffusion coefficient has the form κ⊥e = κ⊥ + κF. The diffusion coefficient κ⊥ is the local cross-field diffusion coefficient due to particle scattering in the random magnetic field. The diffusion coefficient κF is due to coherent particle advection parallel to the mean magnetic field B0 coupled with transverse random walk of the magnetic field. Estimates of cross-field diffusion due to field line random walk, advection and drift are obtained both near to the heliospheric current sheet at Earth and at higher helio-latitudes. Cross-field diffusion due to field line random walk and advection is shown to be an important transport mechanism for low-energy particles near the current sheet, where the effects of drifts are negligible. Drift effects and field line random walk are also assessed at higher helio-latitudes off the current sheet, for a model interplanetary magnetic field, with a flat current sheet in the helio-equatorial plane.

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Compound perpendicular transport of charged particles with drift, advection, wave propagation effects, and an arbitrary turbulence spectrum

Cited by 7 publications

References 23 publications

Solar Interacting Protons Versus Interplanetary Protons in the Core Plus Halo Model of Diffusive Shock Acceleration and Stochastic Re-Acceleration

Solar Interacting Protons Versus Interplanetary Protons in the Core Plus Halo Model of Diffusive Shock Acceleration and Stochastic Re-Acceleration

Random walk of magnetic field lines: analytical theory versus simulations

Compound and perpendicular diffusion of cosmic rays and random walk of the field lines: II. Non-parallel particle transport and drifts

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