Cyclotrons are technologies used to accelerate charged ions in a vacuum lying between two magnets with a strong magnetic field. The particles injected into the systems are either from internal or external sources. Each of the sources has specific benefits based on the functionality and behavior of the ionized particles. Typically, the particles move in circular orbits with the centripetal force acting on them mathematically modeled based on either relativistic or non-relativistic environments. Typically, in a relativistic environment, the ionized particles acquire centripetal forces due to the effects of the transverse magnetic field. The field, B goes through an angular displacement,Â w,Â mathematically expressed as Bqv. On the other hand, cyclotrons are designed to generate uninterrupted stream of a beam ionized particles. However, some limiting factors are related to the relativistic detuning and the behavior of the radial magnetic field. Therefore, ideal situations cannot be attained in the process. Large areas of magnetic fields are applied in restricting the moving ions during their translation from zero energy to new energy levels which are acquired at the output. As mentioned above a number of cyclotron machines have been designed for the specific purpose of accelerating charged particles. Some examples are discussed in the following document which details the mathematics of cyclotrons and the behavior of ions that form the main focus of the study.
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