Collisional space-charge-limited current with monoenergetic velocity: From Child–Langmuir to Mott–Gurney

Journal Article · 03 March 2024 · Physics of Plasmas

DOI: https://doi.org/10.1063/5.0189406 · OSTI ID:2567545

Breen, Lorin I. ; Garner, Allen L.

All theories coupling electron emission theories ultimately approach the space-charge-limited current (SCLC) in vacuum, given by the Child–Langmuir (CL) law, for sufficiently high voltage, or the Mott–Gurney (MG) law for finite electron mobility and high (but not infinite) voltage. These analyses demonstrate the presence of an SCLC regime that cannot be described by either CL or MG. Here, we derive an exact solution for SCLC for general electron mobility and nonzero velocity. We recover the traditional CL with nonzero initial velocity at high voltage. For low mobility (or infinite collision frequency), we derive corrections to the MG law that depend on the ratio of initial velocity to the product of collision frequency and gap distance or initial velocity to drift velocity for low and high voltage, respectively. Increasing collisionality decreases the correction to SCLC for nonzero velocity, indicating that these corrections are less important for low-mobility materials (e.g., solids) than high-mobility materials (e.g., air or vacuum). For a given gap distance (collision frequency), increasing the collision frequency (gap distance) increases the voltage necessary to make the gap appear more like vacuum. These results provide a generalized SCLC for both collisionality and initial velocity when assessing the transitions between electron emission mechanisms.

• Research Organization: Sandia National Laboratories (SNL-NM), Albuquerque, NM (United States)
• Sponsoring Organization: USDOE; USDOE National Nuclear Security Administration (NNSA)
• Grant/Contract Number: NA0003525
• OSTI ID: 2567545
• Journal Information: Physics of Plasmas, Journal Name: Physics of Plasmas Journal Issue: 3 Vol. 31; ISSN 1070-664X
• Publisher: American Institute of PhysicsCopyright Statement
• Country of Publication: United States
• Language: English