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

M. E. Griswold, N. J. Fisch, J. S. Wurtele

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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.

Original languageEnglish (US)
Article number024502
JournalPhysics of Plasmas
Issue number2
StatePublished - Feb 2012

All Science Journal Classification (ASJC) codes

  • Condensed Matter Physics


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