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

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 Δ I. 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 ofmore » 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, Δ I 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.« less
Authors:
 [1] ;  [1] ;  [1]
  1. Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
Publication Date:
Report Number(s):
SAND-2019-0092J
Journal ID: ISSN 2469-9888; PRABCJ; 671321
Grant/Contract Number:
AC04-94AL85000; NA0003525
Type:
Published Article
Journal Name:
Physical Review Accelerators and Beams
Additional Journal Information:
Journal Volume: 22; Journal Issue: 3; Journal ID: ISSN 2469-9888
Publisher:
American Physical Society (APS)
Research Org:
Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
Sponsoring Org:
USDOE National Nuclear Security Administration (NNSA)
Country of Publication:
United States
Language:
English
Subject:
70 PLASMA PHYSICS AND FUSION TECHNOLOGY
OSTI Identifier:
1501737
Alternate Identifier(s):
OSTI ID: 1502450

Waisman, Eduardo M., Desjarlais, M. P., and Cuneo, M. E.. Ion current losses in the convolute and inner magnetically insulated transmission line of the Z machine. United States: N. p., Web. doi:10.1103/PhysRevAccelBeams.22.030402.
Waisman, Eduardo M., Desjarlais, M. P., & Cuneo, M. E.. Ion current losses in the convolute and inner magnetically insulated transmission line of the Z machine. United States. doi:10.1103/PhysRevAccelBeams.22.030402.
Waisman, Eduardo M., Desjarlais, M. P., and Cuneo, M. E.. 2019. "Ion current losses in the convolute and inner magnetically insulated transmission line of the Z machine". United States. doi:10.1103/PhysRevAccelBeams.22.030402.
@article{osti_1501737,
title = {Ion current losses in the convolute and inner magnetically insulated transmission line of the Z machine},
author = {Waisman, Eduardo M. and Desjarlais, M. P. and Cuneo, M. E.},
abstractNote = {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 Δ I. 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, Ba, Δ I 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 jion ~ V3/2 / d2, where voltage and gap are taken near the joining point of those outer MITLs. The implications and limitations of the proposed model are discussed.},
doi = {10.1103/PhysRevAccelBeams.22.030402},
journal = {Physical Review Accelerators and Beams},
number = 3,
volume = 22,
place = {United States},
year = {2019},
month = {3}
}

Works referenced in this record:

Steady-state modeling of current loss in a post-hole convolute driven by high power magnetically insulated transmission lines
journal, December 2013
  • Madrid, E. A.; Rose, D. V.; Welch, D. R.
  • Physical Review Special Topics - Accelerators and Beams, Vol. 16, Issue 12, Article No. 120401
  • DOI: 10.1103/PhysRevSTAB.16.120401