Coordinate System Invariant Formulation of Fractional‐Dimensional Child‐Langmuir Law for a Rough Cathode (Adv. Phys. Res. 7/2023)

SCL Current Imagine a current so intense it pushes the boundaries of what's possible in vacuum electronics, high-power microwave sources, ion thrusters, and plasma processing. This remarkable phenomenon, known as space-charge-limited (SCL) emission, is governed by the influential Child-Langmuir (CL) law, which determines the maximum current density in diodes. In article number 2200120, Muhammad Zubair, Muhammad Qasim Mehmood, Yehia Massoud, and co-workers unveil an exact analytical model incorporating fractional dimensions to explore the impact of surface roughness on SCL current in planar, cylindrical, and spherical diodes. This remarkable achievement bridges the gap between theory and practical applications, paving the way for cutting-edge advancements in these transformative fields.