Solution for Space-Charge-Limited Currents in Initially Monoenergetic Electron Vacuum Diodes in the Relativisitic Regime

Summary form only given. The space-charge-limited (SCL) currents play crucial role in classical discharge and bounded plasma devices. Child and Langmuir first derived the classic SCL in pure electron vacuum diode in their pioneering papers to predict the maximum possible operating currents, providing the initial electron velocities are neglected. The solution was obtained by zero steady state surface electric field. But, the finite initial electron velocities have a strong influence on the SCL flow, which has been well studied in classic regime. [3] Now we extend the solution for the SCL with uniform initial velocities to the relativistic regime. There are two types of solution found, where type I requires the steady state surface electric field to be zero but type II requires a finite surface electric field at the steady state. Our solution agrees to the classic results quite well in the classic regime but when either the applied voltage or the initial energy for electrons become to relativistic, the classic SCL is shown to be not useful anymore. For high applied voltage, the classic SCL expects a higher current than our solution, and for high initial energy, the classic SCL expects a lower current than our solution.