### Abstract

The standard paradigm for the transport and acceleration of cosmic rays and other fast charged particles is based on the well-established Parker equation. The Parker equation can be demonstrated to be a good approximation if the particle distribution function is nearly isotropic in pitch angle, even in the presence of discontinuities in the flow such as shocks and current sheets. However, there are many situations, such as MHD reconnection where the fluid flow velocity is nearly incompressible. In these cases the Parker equation predicts little or no particle acceleration since the energy change is proportional to the divergence of the flow velocity. This energy-change rate is independent of spatial or temporal scales, for isotropic angular distributions. One approach to accelerating particles in nearly incompressible flows is to extend the Parker equation by invoking small-scale propgating waves - giving rise to the venerable 2nd-order Fermi acceleration. A second possibility is to invoke large pitch-angle anisotropies. A third possibility is considered in this paper. I examine the effects of fluid flow acceleration and shear, both of which also accelerate charged particles. The resulting transport equation is Parker's equation augmented by terms proportional to the fluid acceleration and shear, which can be non-zero in incompressible flow. These new terms are of second order in the fluid flow speed U, and hence are generally small. Nonetheless, they will be important in considerations of charged-particle acceleration in nearly incompressible flows such as reconnection. A synthesized divergence-free fluid velocity U(x,y chosen to be similar to that found in reconnection is used to illustrate the acceleration. The acceleration rate is estimated for the inner heliosphere and shown to be greater than the adiabatic cooling rate in the expanding solar wind.

Original language | English (US) |
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Title of host publication | Proceedings of the 32nd International Cosmic Ray Conference, ICRC 2011 |

Publisher | Institute of High Energy Physics |

Pages | 232-235 |

Number of pages | 4 |

Volume | 10 |

DOIs | |

State | Published - 2011 |

Event | 32nd International Cosmic Ray Conference, ICRC 2011 - Beijing, China Duration: Aug 11 2011 → Aug 18 2011 |

### Other

Other | 32nd International Cosmic Ray Conference, ICRC 2011 |
---|---|

Country | China |

City | Beijing |

Period | 8/11/11 → 8/18/11 |

### Fingerprint

### ASJC Scopus subject areas

- Nuclear and High Energy Physics

### Cite this

*Proceedings of the 32nd International Cosmic Ray Conference, ICRC 2011*(Vol. 10, pp. 232-235). Institute of High Energy Physics. https://doi.org/10.7529/ICRC2011/V10/0082

**Fast charged-particle acceleration in incompressible flows.** / Jokipii, J. Randy.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*Proceedings of the 32nd International Cosmic Ray Conference, ICRC 2011.*vol. 10, Institute of High Energy Physics, pp. 232-235, 32nd International Cosmic Ray Conference, ICRC 2011, Beijing, China, 8/11/11. https://doi.org/10.7529/ICRC2011/V10/0082

}

TY - GEN

T1 - Fast charged-particle acceleration in incompressible flows

AU - Jokipii, J. Randy

PY - 2011

Y1 - 2011

N2 - The standard paradigm for the transport and acceleration of cosmic rays and other fast charged particles is based on the well-established Parker equation. The Parker equation can be demonstrated to be a good approximation if the particle distribution function is nearly isotropic in pitch angle, even in the presence of discontinuities in the flow such as shocks and current sheets. However, there are many situations, such as MHD reconnection where the fluid flow velocity is nearly incompressible. In these cases the Parker equation predicts little or no particle acceleration since the energy change is proportional to the divergence of the flow velocity. This energy-change rate is independent of spatial or temporal scales, for isotropic angular distributions. One approach to accelerating particles in nearly incompressible flows is to extend the Parker equation by invoking small-scale propgating waves - giving rise to the venerable 2nd-order Fermi acceleration. A second possibility is to invoke large pitch-angle anisotropies. A third possibility is considered in this paper. I examine the effects of fluid flow acceleration and shear, both of which also accelerate charged particles. The resulting transport equation is Parker's equation augmented by terms proportional to the fluid acceleration and shear, which can be non-zero in incompressible flow. These new terms are of second order in the fluid flow speed U, and hence are generally small. Nonetheless, they will be important in considerations of charged-particle acceleration in nearly incompressible flows such as reconnection. A synthesized divergence-free fluid velocity U(x,y chosen to be similar to that found in reconnection is used to illustrate the acceleration. The acceleration rate is estimated for the inner heliosphere and shown to be greater than the adiabatic cooling rate in the expanding solar wind.

AB - The standard paradigm for the transport and acceleration of cosmic rays and other fast charged particles is based on the well-established Parker equation. The Parker equation can be demonstrated to be a good approximation if the particle distribution function is nearly isotropic in pitch angle, even in the presence of discontinuities in the flow such as shocks and current sheets. However, there are many situations, such as MHD reconnection where the fluid flow velocity is nearly incompressible. In these cases the Parker equation predicts little or no particle acceleration since the energy change is proportional to the divergence of the flow velocity. This energy-change rate is independent of spatial or temporal scales, for isotropic angular distributions. One approach to accelerating particles in nearly incompressible flows is to extend the Parker equation by invoking small-scale propgating waves - giving rise to the venerable 2nd-order Fermi acceleration. A second possibility is to invoke large pitch-angle anisotropies. A third possibility is considered in this paper. I examine the effects of fluid flow acceleration and shear, both of which also accelerate charged particles. The resulting transport equation is Parker's equation augmented by terms proportional to the fluid acceleration and shear, which can be non-zero in incompressible flow. These new terms are of second order in the fluid flow speed U, and hence are generally small. Nonetheless, they will be important in considerations of charged-particle acceleration in nearly incompressible flows such as reconnection. A synthesized divergence-free fluid velocity U(x,y chosen to be similar to that found in reconnection is used to illustrate the acceleration. The acceleration rate is estimated for the inner heliosphere and shown to be greater than the adiabatic cooling rate in the expanding solar wind.

UR - http://www.scopus.com/inward/record.url?scp=84899514422&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84899514422&partnerID=8YFLogxK

U2 - 10.7529/ICRC2011/V10/0082

DO - 10.7529/ICRC2011/V10/0082

M3 - Conference contribution

AN - SCOPUS:84899514422

VL - 10

SP - 232

EP - 235

BT - Proceedings of the 32nd International Cosmic Ray Conference, ICRC 2011

PB - Institute of High Energy Physics

ER -