The Child–Langmuir diode as a physical system exhibiting constant jerk motion

Abstract This study explores a physical system in which particle motion is characterized by linearly increasing acceleration and constant jerk over time. A vacuum planar electron diode operating under constant voltage in the space-charge-limited regime is analyzed. The derivation of the Child–Langmuir law is presented in detail. It is demonstrated that in such diode, all electrons travel from the cathode to the anode with constant jerk and the linearly increasing acceleration. Higher-order time derivatives of motion—snap (or jounce), crackle, and pop are all zero. An exact formula for the constant jerk is derived for the first time.