Comment on “Power loss in open cavity diodes and a modified Child-Langmuir law” [Phys. Plasmas 12, 093102 (2005)]

Abstract

In this Comment, it is shown that no modification of the Child-Langmuir law [Phys. Rev.32, 492 (1911); Phys. Rev. 2, 450 (1913)] is necessary to treat the space-charge-limited flow from a diode with an open boundary as reported in Phys. Plasmas 12, 093102 (2005). The open boundary condition in their simulations can be represented by a voltage source and a resistor whose value is the vacuum-wave impedance of the opening. The diode can be represented as a variable resistor whose value depends on the voltage drop across the diode (as measured by the line integral of E across the diode gap). This is a simple voltage-divider circuit whose analysis shows that the real diode voltage drops as the vacuum-wave impedance increases. Furthermore, it is shown that in equilibrium, the voltage drop between the anode and cathode is independent of the path chosen for the line integral of the electric field so that E=−∇Φ is valid. In this case, the equations of electrostatics are applicable. This clearly demonstrates that the electric field is electrostatic and static fields DO NOT RADIATE. It is shown that the diode voltage drops as the vacuum wave impedance increases and the current drops according to the Child-Langmuir law. Therefore, the observed drop in circuit current can be explained by a real drop in voltage across the diode and not an effective drop as claimed by the authors.

Radiation from a space charge dominated linear electron beam

“…8 When the N charges move together as a single unit as in case of a linear beam below the space charge limit, the multiplying factor is in fact N 2 . 6,7,12,13 In Ref. Thus, for a beam of electrons, the macroparticle has a charge q = Ne and mass M = Nm 0 , where e and m 0 are the charge and mass of an electron.…”

Response to “Comment on ‘Power loss in open cavity diodes and a modified Child-Langmuir law' ” [Phys. Plasmas 14, 094701 (2007)]

“…As stated in the Comment 4 and by us earlier, 1 electromagnetic power loss may be expressed in terms of an impedance. In terms of energy conservation, this implies that the energy gained by the electrons…”

“…In the preceding Comment, 4 the authors have constructed an identical electrostatic potential V D by subtracting out the power loss in terms of the impedance Z 0 of the open window ͑V loss = Z 0 I D , I D is the diode current͒ rather than the power P rad leaking out ͑V loss = P rad / I TR , I TR = I D ͒. The Comment is therefore largely a reconfirmation of our results 1 in terms of lumped circuit parameters, except that it also takes recourse to ͑misleading͒ semantics and calls this effective electrostatic potential the real potential drop across the diode.…”

“…As E =−ٌV holds only in electrostatics, it is obvious that V eff or V D is only an electrostatic equivalent and not the true or actual potential across the diode as claimed in the Comment. 4 Insistence on V D being the true voltage drop can in fact lead to unphysical consequences. As Z 0 is considered external to the simulation region in the Comment, 4 it follows that the energy entering the simulation region is eV D , which is entirely transferred to the electrons as it travels from the cathode to the anode.…”

“…4 Insistence on V D being the true voltage drop can in fact lead to unphysical consequences. As Z 0 is considered external to the simulation region in the Comment, 4 it follows that the energy entering the simulation region is eV D , which is entirely transferred to the electrons as it travels from the cathode to the anode. It follows from the Comment, therefore, that accelerated electrons do not radiate, for if they did, energy conservation would be violated.…”