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Notwithstanding the recent conjecture that the upper bound on the time-averaged current across a space-charge-limited diode is equal to the steady state Child-Langmuir limit ( J CL ), Zhu and Ang used a one-dimensional (1D) particle in cell (PIC) code to show that in the regime where space charge effects limit the current to only a few electrons at a time, the time-averaged current can exceed J CL by up to 13% (Y. Zhu and L. K. Ang, Appl. Phys. Lett. 98 , 051502 (2011)). These results are, in fact, verified using our own 1D PIC code. However, the increase in the current is due to special boundary conditions that pertain in this regime and not to the time dependence of the current. To rule out discreteness effects, the conjecture on the upper bound may be reformulated to include only the case when the electric field at the cathode does not fall below zero.

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Amended conjecture on an upper bound to time-dependent space-charge limited current

Griswold, M. E.; Fisch, N. J.; Wurtele, J. S.
Physics of Plasmas , Volume 19 (2)
American Institute of PhysicsFeb 1, 2012

More Info

  • Publisher American Institute of Physics
  • Copyright Copyright © 2012 American Institute of Physics
  • ISSN 1070-664X
  • eISSN 1089-7674
  • D.O.I. 10.1063/1.3671961
  • Publisher site Get PDF  

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