## Abstract

An approximate analytic theory is developed and implemented numerically for calculating the space charge limited current and electric field of a thin cylindrical beam or current sheet between two wide parallel electrodes. The flow is confined by a sufficiently strong magnetic field. Assuming that the potential and current density are almost homogeneous in the direction transversal to the flow, the beam current and its profile are computed by a variational method. The average current density scales as the reciprocal of the beam width when the latter becomes very small. The total cylindrical beam current thus decreases proportionly to its diameter while the total current of a sheet becomes almost independent of the width in this regime.

Original language | English (US) |
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Pages (from-to) | 4559-4563 |

Number of pages | 5 |

Journal | Physics of Plasmas |

Volume | 11 |

Issue number | 10 |

DOIs | |

State | Published - Oct 2004 |

## All Science Journal Classification (ASJC) codes

- Condensed Matter Physics