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Two-dimensional axisymmetric Child–Langmuir scaling law

Phys. Plasmas 16, 103102 (2009); doi:10.1063/1.3243474

Published 6 October 2009

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Benjamin Ragan-Kelley,1 John Verboncoeur,2 and Yang Feng2
1Applied Science and Technology, University of California, Berkeley, California 94720, USA
2Nuclear Engineering, University of California, Berkeley, California 94720, USA
The classical one-dimensional (1D) Child–Langmuir law was previously extended to two dimensions by numerical calculation in planar geometries. By considering an axisymmetric cylindrical system with axial emission from a circular cathode of radius r, outer drift tube radius R>r, and gap length L, we further examine the space charge limit in two dimensions. Simulations were done with no applied magnetic field as well as with a large (100 T) longitudinal magnetic field to restrict motion of particles to 1D. The ratio of the observed current density limit JCL2 to the theoretical 1D value JCL1 is found to be a monotonically decreasing function of the ratio of emission radius to gap separation r/L. This result is in agreement with the planar results, where the emission area is proportional to the cathode width W. The drift tube in axisymmetric systems is shown to have a small but measurable effect on the space charge limit. Strong beam edge effects are observed with J(r)/J(0) approaching 3.5. Two-dimensional axisymmetric electrostatic particle-in-cell simulations were used to produce these results. ©2009 American Institute of Physics
History: Received 21 April 2009; accepted 14 September 2009; published 6 October 2009
Permalink: http://link.aip.org/link/?PHPAEN/16/103102/1
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KEYWORDS and PACS

Keywords
PACS
  • 52.80.-s
    Electric discharges
  • 52.65.Rr
    Particle-in-cell method (plasma simulation)
  • YEAR: 2009

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ISSN:
1070-664X (print)   1089-7674 (online)
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REFERENCES (19)
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