Ion current losses in the convolute and inner magnetically insulated transmission line of the Z machine

Abstract

We introduce a 1D planar static model to elucidate the underlying mechanism of large ion current losses in the vacuum convolute and the inner magnetically insulated transmission line (MITL) of the Z machine. We consider E × B electron flow, parallel to the electrodes, and ion motion across the vacuum gap, for given voltage V, gap distance d, anode magnetic field B a , and vacuum electron current ΔI. This model has been introduced and solved before by Desjarlais [Phys. Rev. Lett. 59, 2295 (1987)] for the applied magnetic field ion diode. Here we apply it to convolute and inner MITL ion losses of Z, relaxing the fix magnetic flux condition of that reference. In the absence of ions we show that the electron vacuum flow must be close to the anode if its current exceeds the value given by the local flow impedance, implying high electric fields there. We then introduce space charge limited ion emission from the anode, neglecting the magnetic force on ions. We obtain the solution of the steady state equations for two special cases: (a) when both the electric potential and the electric field are zero inside the gap, and there is a layer of electrons not carrying current that neutralizes the ion charge between the virtual and the electrode cathode, making that region electric field free, and (b) when the electric field is zero inside the gap, but the potential is not, and zero electron charge between that point and the physical cathode. For case (a) we obtain an ion current density which we conjecture is the maximum attainable for any electron charge distribution in the electron current carrying layer, given V; d; B a ; ΔI an ion species. We obtain the enhancement factor for both cases with respect to the ion-only Child-Langmuir ion current density, and show that it can be significantly larger than that of the electron saturated flow case. Furthermore, imposing electron current conservation as the flow enters the inner MITL from the four outer MITLs, we recover the well-known dependence j ion ∼ V 3=2 =d 2 , where voltage and gap are taken near the joining point of those outer MITLs. The implications and limitations of the proposed model are discussed.

Numerical simulations of enhanced ion current losses in the inner magnetically insulated transmission line of the Z accelerator

“…As discussed in Ref. [5], the enhancement of ion current with respect to the CL ion-only law, due to the presence of an E × B electron flow charge in the anode-cathode (AK) gap, goes back to the work of Desjarlais [9] for applied magnetic field ion diodes. In that research the saturated flow case is defined, such that for the appropriate constant electron charge density filling the gap, the enhancement factor η ¼ j i =j CL , where j i is the ion current density and j CL is the CL ion current density given in Eq.…”

“…We remark that neither Ref. [5] nor Ref. [10] address the interaction between magnetically and nonmagnetically insulated ion species, which is indeed one of the main subjects of this paper.…”

“…Experimental measurements and numerical simulations suggest significant current losses in the inner magnetically insulated transmission line (MITL) of the Z accelerator [1][2][3][4] at Sandia National Laboratories, although direct measurements of these losses has not been obtained to date. In a recently published paper [5], a model for enhanced ion current losses in the inner MITL of Z [6][7][8] was presented. The model assumes that vacuum electron flow close to the anode enhances the electric field, thereby increasing the realizable ion current emitted from the anode which results in ion current loss enhancements well in excess of the nominal Child-Langmuir (CL) limit for ions.…”

“…In the Appendix D a comparison between that formulation and that of Ref. [5] is provided. We remark that neither Ref.…”

“…A series of two-dimensional (2D), fully electromagnetic (EM) particle-in-cell simulations using CHICAGO [13] are compared directly with the model of Waisman, Desjarlais and Cuneo [5] in the "high-enhancement" (WDC-HE) limit. The simulations are operated in a quasi-equilibrium limit for easier comparison to the model of Ref.…”