Theory and simulation of nonrelativistic elliptic-beam formation with one-dimensional Child-Langmuir flow characteristics

A theory of nonrelativistic, laminar, elliptic-beam formation is presented. The beam is shown to have the one-dimensional Child-Langmuir flow form. An analytic expression for the electrostatic potential outside the beam is derived. Equipotentials corresponding to electrode surfaces are computed numerically. The effectiveness of the electric field formed by the electrodes in focusing and preserving the elliptic, 1D Child-Langmuir flow beam is verified via 3D ray-tracing simulations.

[1]  Bruce E. Carlsten,et al.  Circular-to-planar transformations of high-perveance electron beams by asymmetric solenoid lenses , 2004 .

[2]  M. Reiser,et al.  Beam experiments in the extreme space-charge limit on the University of Maryland Electron Ring , 2003 .

[3]  C. K. Allen,et al.  Beam-halo in mismatched proton beams , 2004 .

[4]  Bruce E. Carlsten,et al.  Modal analysis and gain calculations for a sheet electron beam in a ridged waveguide slow-wave structure , 2002 .

[5]  Richard True,et al.  The MICHELLE three-dimensional electron gun and collector modeling tool: theory and design , 2002 .

[6]  John W. Luginsland,et al.  Beyond the Child–Langmuir law: A review of recent results on multidimensional space-charge-limited flow , 2002 .

[7]  Y. Lau,et al.  Simple theory for the two-dimensional Child-Langmuir law. , 2001, Physical review letters.

[8]  J. Luginsland,et al.  Two-dimensional space-charge-limited emission: beam-edge characteristics and applications. , 2001, Physical review letters.

[9]  John W. Luginsland,et al.  Current and current density of a finite-width, space-charge-limited electron beam in two-dimensional, parallel-plate geometry , 2001 .

[10]  Chi-ping Chen,et al.  Ideal matching of heavy ion beams , 2001 .

[11]  Chen,et al.  Cold-fluid equilibrium for a corkscrewing elliptic beam in a variably focusing channel , 2000, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[12]  John H. Booske,et al.  Two-plane focusing of high-space-charge sheet electron beams using periodically cusped magnetic fields , 1999 .

[13]  Jean-Luc Vay,et al.  New developments in WARP: Progress toward end-to-end simulation 1 1 Work performed under auspices of U.S. DoE by LLNL, NRL, and LBNL under contracts W-7405-ENG-48, DE-AI02-93ER40799, DE-AI02-94ER54232, and DE-AC03-765F00098. Proceedings of the 12th International Symposium on Heavy Ion Inertial Fusio , 1998 .

[14]  John W. Luginsland,et al.  Two-Dimensional Child-Langmuir Law. , 1996 .

[15]  A. Nakai.  A new method of the rectilinear strip beam formation under space-charge condition , 1967 .

[16]  P. A. Sturrock,et al.  Magnetic Deflection Focusing , 1959 .

[17]  D. E. Radley,et al.  The Theory of the Pierce Type Electron Gun , 1958 .

[18]  Irving Langmuir,et al.  The Effect of Space Charge and Initial Velocities on the Potential Distribution and Thermionic Current between Parallel Plane Electrodes , 1923 .