Determination of Electron Flows

(2.234) |

(2.235) |

(2.237) | ||

(2.238) | ||

(2.239) |

Making use of Equations (2.197), (2.198), and (2.216), and only retaining terms up to first order in the small parameter , we get

where Here use has been made of Equations (2.209)–(2.211), (2.217), and (2.218).It follows from Equations (2.165), (2.166), (2.170), (2.181)–(2.185), (2.236), and (2.240)–(2.242) that

(2.255) | ||

(2.256) |

(2.257) | ||

(2.258) |

In the circular magnetic flux-surface limit, Equations (2.255) and (2.256) reduce to

whereas Equations (2.257)–(2.258) yield(2.261) | ||

(2.262) |

Expressions (2.259)–(2.262) have many features in common with the corresponding expressions, (2.226)–(2.229), for the ions, despite being much more complicated in nature. In particular, the E-cross-B velocity makes no contribution to the poloidal component of the electron fluid velocity. Moreover, the poloidal component of the electron fluid velocity is similar in magnitude to a diamagnetic velocity, whereas the parallel component is larger by a factor .