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Space-charge-limited 2D electron flow between two flat electrodes in a strong magnetic field
1Department of Mathematics, Rutgers University, Piscataway, New Jersey 08854-8019, USA.
Physical Review Letters
|October 4, 2003
Summary
This study presents an approximate analytic solution for space-charge-limited emission from cathodes with conducting ledges. The solution reveals current density growth near edges strongly depends on ledge width, providing an empirical formula for total current.
Area of Science:
- Plasma Physics
- Applied Electromagnetics
- Vacuum Electronics
Background:
- Space-charge-limited emission is crucial for vacuum electronic devices.
- Cathode geometry, particularly surrounding structures, significantly impacts emission characteristics.
- Accurate modeling is needed to optimize device performance.
Purpose of the Study:
- To develop an approximate analytic solution for 2D space-charge-limited emission.
- To investigate the influence of nonemitting conducting ledges on current density.
- To derive an empirical formula for total current based on ledge width.
Main Methods:
- Constructing an approximate analytic solution for the emission problem.
- Employing conformal mapping for an exact electrostatic solution in vacuum.
- Matching vacuum solution to a linearized problem in the space charge region.
- Utilizing a strong magnetic field to define sharp boundaries.
Main Results:
- The current density growth near cathode edges is highly sensitive to the conducting ledge width (Lambda).
- An empirical formula was derived relating total current to Lambda.
- The derived formula is applicable to more general cathode geometries.
Conclusions:
- The study provides a valuable analytical tool for understanding and predicting electron emission in complex cathode geometries.
- The findings are essential for the design and optimization of high-current vacuum electronic devices.
- The empirical formula offers a practical method for estimating total current based on geometric parameters.
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