### Abstract

We consider the transport of charged particles in a stochastic magnetic field using a method based on the velocity correlation function 〈v_{i}(0)v_{j}(t)〉 developed by R. Kubo. This can be used under very general conditions to evaluate the corresponding spatial diffusion coefficients, if the fluctuations are statistically homogeneous in space and time. Although Kubo's theory is quite general, it is not obvious how it can be applied to describe compound diffusion when particles are strictly tied to the magnetic field lines and perpendicular transport results solely from the random walk of the field lines. This motion is non-Markovian and leads to a slower 〈Δx^{2}〉 ∝ t^{1/2} diffusion in contrast to the 〈Δx^{2}〉 ∝ t dependence of the standard diffusion. We demonstrate how compound diffusion fits into Kubo's formalism. As intuitively as can be anticipated, the non-Markovian nature of the motion results in a long-term anticorrelation in 〈v_{j}(0)v_{i}(t)〉, which causes the ordinary spatial diffusion coefficient to vanish identically. The 〈Δx^{2}〉 ∝ t^{1/2} dependence of the compound diffusion can also be recovered from the Laplace transform of the velocity correlation function. Some implications of the long-term anticorrelation are discussed.

Original language | English (US) |
---|---|

Pages (from-to) | 1067-1070 |

Number of pages | 4 |

Journal | Astrophysical Journal |

Volume | 531 |

Issue number | 2 PART 1 |

State | Published - Mar 10 2000 |

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### Keywords

- Acceleration of particles
- Cosmic rays
- Diffusion
- Turbulence

### ASJC Scopus subject areas

- Space and Planetary Science

### Cite this

*Astrophysical Journal*,

*531*(2 PART 1), 1067-1070.

**Velocity correlation and the spatial diffusion coefficients of cosmic rays : Compound diffusion.** / Kóta, J.; Jokipii, J. Randy.

Research output: Contribution to journal › Article

*Astrophysical Journal*, vol. 531, no. 2 PART 1, pp. 1067-1070.

}

TY - JOUR

T1 - Velocity correlation and the spatial diffusion coefficients of cosmic rays

T2 - Compound diffusion

AU - Kóta, J.

AU - Jokipii, J. Randy

PY - 2000/3/10

Y1 - 2000/3/10

N2 - We consider the transport of charged particles in a stochastic magnetic field using a method based on the velocity correlation function 〈vi(0)vj(t)〉 developed by R. Kubo. This can be used under very general conditions to evaluate the corresponding spatial diffusion coefficients, if the fluctuations are statistically homogeneous in space and time. Although Kubo's theory is quite general, it is not obvious how it can be applied to describe compound diffusion when particles are strictly tied to the magnetic field lines and perpendicular transport results solely from the random walk of the field lines. This motion is non-Markovian and leads to a slower 〈Δx2〉 ∝ t1/2 diffusion in contrast to the 〈Δx2〉 ∝ t dependence of the standard diffusion. We demonstrate how compound diffusion fits into Kubo's formalism. As intuitively as can be anticipated, the non-Markovian nature of the motion results in a long-term anticorrelation in 〈vj(0)vi(t)〉, which causes the ordinary spatial diffusion coefficient to vanish identically. The 〈Δx2〉 ∝ t1/2 dependence of the compound diffusion can also be recovered from the Laplace transform of the velocity correlation function. Some implications of the long-term anticorrelation are discussed.

AB - We consider the transport of charged particles in a stochastic magnetic field using a method based on the velocity correlation function 〈vi(0)vj(t)〉 developed by R. Kubo. This can be used under very general conditions to evaluate the corresponding spatial diffusion coefficients, if the fluctuations are statistically homogeneous in space and time. Although Kubo's theory is quite general, it is not obvious how it can be applied to describe compound diffusion when particles are strictly tied to the magnetic field lines and perpendicular transport results solely from the random walk of the field lines. This motion is non-Markovian and leads to a slower 〈Δx2〉 ∝ t1/2 diffusion in contrast to the 〈Δx2〉 ∝ t dependence of the standard diffusion. We demonstrate how compound diffusion fits into Kubo's formalism. As intuitively as can be anticipated, the non-Markovian nature of the motion results in a long-term anticorrelation in 〈vj(0)vi(t)〉, which causes the ordinary spatial diffusion coefficient to vanish identically. The 〈Δx2〉 ∝ t1/2 dependence of the compound diffusion can also be recovered from the Laplace transform of the velocity correlation function. Some implications of the long-term anticorrelation are discussed.

KW - Acceleration of particles

KW - Cosmic rays

KW - Diffusion

KW - Turbulence

UR - http://www.scopus.com/inward/record.url?scp=0034628770&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0034628770&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0034628770

VL - 531

SP - 1067

EP - 1070

JO - Astrophysical Journal

JF - Astrophysical Journal

SN - 0004-637X

IS - 2 PART 1

ER -