High energy devices are designed to work with extremely high electric and magnetic fields. As a consequence, these devices show non-linear phenomena and behaviour, such as magnetic insulation which alters electron trajectory. A mathematical analysis and review of magnetic insulation were carried out as a consequence of non-linearity to find frontier conditions and solutions to the problem. This paper was aimed at presenting the topic in a way which is easier for that part of the academic community which is unfamiliar with it to understand it. The paper gives a description of the phenomena developed by high electric and magnetic fields in a vacuum plane diode, some equations modelling the phenomenon, proves its existence and finds positive solutions based on upper and lower solutions for boundary limit problems and gives some practical applications.