Skip to main content
banner image
No data available.
Please log in to see this content.
You have no subscription access to this content.
No metrics data to plot.
The attempt to load metrics for this article has failed.
The attempt to plot a graph for these metrics has failed.
The full text of this article is not currently available.
T. P. Hughes, R. E. Clark, and S. S. Yu, “Three-dimensional calculations for a 4-kA, 3.4 MV, 2 microsecond injector with asymmetric power feed,” Phys. Rev. Spec. Top.–Accel. Beams 2, 110401 (1999).
S. Humphries, “Trak charged particle toolkit,” Field Precision LLC, 2016, available at; accessed 2016.
C. Ekdahl, M. Greenspan, R. E. Kribel, J. Sethian, and C. B. Wharton, “Heating of a fully ionized plasma column by a relativistic electron beam,” Phys. Rev. Lett. 33(6), 346348 (1974).
C. A. Ekdahl, J. R. Freeman, G. T. Leifeste, R. B. Miller, W. A. Stygar, and B. B. Godfrey, “Axisymetric hollowing instability of an intense relativistic electron beam propagating in air,” Phys. Rev. Lett. 55(9), 935938 (1985).
C. Ekdahl, E. O. Abeyta, H. Bender, W. Broste, C. Carlson, L. Caudill, K. C. D. Chan, Y.-J. Chen, D. Dalmas, G. Durtschi, S. Eversole, S. Eylon, W. Fawley, D. Frayer, R. Gallegos, J. Harrison, E. Henestroza, M. Holzscheiter, T. Houck, T. Hughes, S. Humphries, D. Johnson, J. Johnson, K. Jones, E. Jacquez, B. T. McCuistian, A. Meidinger, N. Montoya, C. Mostrom, K. Moy, K. Nielsen, D. Oro, L. Rodriguez, P. Rodriguez, M. Sanchez, M. Schauer, D. Simmons, H. V. Smith, J. Studebaker, R. Sturgess, G. Sullivan, C. Swinney, R. Temple, C. Y. Tom, and S. S. Yu, “Initial electron-beam results from the DARHT-II linear induction accelerator,” IEEE Trans. Plasma Sci. 33, 892900 (2005).
I. Langmuir, “The effect of space charge and residual gases on thermionic currents in high vacuum,” Phys. Rev. 2(6), 450486 (1913).
I. Langmuir and K. B. Blodgett, “Currents limited by space charge between coaxial cylinders,” Phys. Rev. 22(4), 347356 (1923).
I. Langmuir and K. B. Blodgett, “Currents limited by space charge between concentric spheres,” Phys. Rev. 24, 4959 (1924).
I. Langmuir and K. T. Compton, “Electrical discharges in gases,” Rev. Mod. Phys. 3(2), 191257 (1931).
H. R. Jory and A. W. Trivelpiece, “Exact relativistic solution for the one-dimensional diode,” J. Appl. Phys. 40(10), 39243926 (1969).
J. E. Boers and D. Kelleher, “Exact solution of Poisson’s equation for space-charge-limited flow in a relativistic planar diode,” J. Appl. Phys. 40(6), 24092412 (1969).
B. V. Weber, D. Mosher, and P. F. Ottinger, “Fit functions for relativistic, single-species and bipolar, and space-charge-limited current densities,” IEEE Trans. Plasma. Sci. 42(6), 18191822 (2014).
I. M. Rittersdorf, P. F. Ottinger, R. J. Allen, and J. W. Schumer, “Current density scaling expressions for a bipolar space-charge-limited cylindrical diode,” IEEE Trans. Plasma Sci. 43(10), 36263636 (2015).
C. Ekdahl and S. Humphries, “Grid-focused diodes for radiography,” in IEEE Pulsed Power Conference, Monterey, CA, 2005.
R. B. Miller, Intense Charged Particle Beams (Plenum Press, New York, NY, 1985), p. 108 et seq.
C. Ekdahl, E. O. Abeyta, P. Aragon, R. Archuleta, G. Cook, D. Dalmas, K. Esquibel, R. Gallegos, R. Garnett, J. Harrison, J. Johnson, E. Jacquez, B. T. McCuistian, N. Montoya, S. Nath, K. Nielsen, D. Oro, L. Rowton, M. Sanchez, R. Scarpetti, M. Schauer, G. Seitz, V. Smith, R. Temple, R. Anaya, G. Caporaso, F. Chambers, Y.-J. Chen, S. Falabella, G. Guetlein, B. Raymond, R. Richardson, J. Watson, J. Weir, H. Bender, W. Broste, C. Carlson, D. Frayer, D. Johnson, C. Y. Tom, C. Trainham, J. Williams, B. Prichard, M. Schulze, T. Genoni, T. Hughes, and C. Thoma, “Electron beam dynamics in a long-pulse linear induction accelerator,” J. Korean Phys. Soc. 59, 34483452 (2011).

Data & Media loading...


Article metrics loading...



A simple approximation for the current-voltage characteristics of a relativistic electron diode is presented. The approximation is accurate from non-relativistic through relativistic electron energies. Although it is empirically developed, it has many of the fundamental properties of the exact diode solutions. The approximation is simple enough to be remembered and worked on almost any pocket calculator, so it has proven to be quite useful on the laboratory floor.


Full text loading...


Access Key

  • FFree Content
  • OAOpen Access Content
  • SSubscribed Content
  • TFree Trial Content
752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd