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Virtual cathode behavior in a crossed-field gap
Ashmita Panda1, Jim Browning2, Allen L Garner3
1Purdue University, West Lafayette, School of Nuclear Engineering, Indiana 47907, USA.
Physical Review. E
|July 24, 2026
Summary
Virtual cathodes (VCs) behavior in crossed-field gaps is less understood than in nonmagnetic gaps. This study reveals VC formation depends on initial electron velocity and magnetic field strength relative to the Hull cutoff, differing from nonmagnetic cases.
Area of Science:
- Plasma physics
- Electron dynamics
- Applied electromagnetics
Background:
- Virtual cathode (VC) behavior in space-charge limited gaps without magnetic fields is well-established.
- Characterization of VCs in crossed-field gaps with perpendicular electric and magnetic fields is limited.
Purpose of the Study:
- To examine steady-state virtual cathode (VC) formation in a crossed-field gap below the magnetic insulation Hull cutoff field.
- To determine the influence of initial electron velocity and magnetic field strength on VC formation.
Main Methods:
- Theoretical analysis of electron motion in crossed electric and magnetic fields.
- Investigation of conditions for virtual cathode (VC) formation at critical current density (Jc).
Main Results:
- VC formation at critical current density (Jc) in crossed-field gaps is dependent on initial electron velocity (u0) and magnetic field strength (b=B/BH).
- A threshold magnetic field (b_VC) exists for VC formation; below it, VCs form at Jc, but not above. This contrasts with nonmagnetic diodes.
- In the absence of VC formation, electron density peaks near the anode, shifting the limiting current condition.
Conclusions:
- Virtual cathode (VC) formation in crossed-field gaps is not solely sufficient or necessary for the limiting current condition.
- The interplay between magnetic fields, initial electron velocity, and current density significantly alters VC behavior compared to nonmagnetic systems.
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