Cyclotrons are a historical development that has gone through different development phase

Cyclotrons are a historical development that has gone through different development phases with a lot of scientific significance. Typically, a stream of particles is accelerated through a circular or closed orbit. The trajectory of the particles can be reflected by applying a force on the trajectory due to a magnetic field on the stream of ionized particles. Typically, these particles can be re-circulated to achieve higher levels of resonance while in orbit. As the particles continue passing through the same field repeatedly, ions acquire higher levels of energy and speed.

Different types of cyclotrons are characterized by different operational functionalities. One of the earlier cyclotron inventions was the uniform field cyclotron. Typically, the machine could work on a 15MeV capacity. The operational efficiency of the machine depends on the increase or decrease of the relativistic mass of the ionized particles. On the other hand, a number of cyclotrons have been developed and their operational efficiency examined depending on the strength of the magnetic field and other design factors. Typically, the ions keep moving and acquiring higher resonant capabilities based on the phases covered by the particles as detailed by(Sabaiduc, Du, Boiesan, Zhu, Suthanthiran, Johnson, Ladysmith, Gelbart & Conard, 3).

Two examples of the operating environment include a circular field and a linear polarized field. The relativistic motion of a moving charged particle is characterized by influencing factors that are inherently defined in the relation. Typically, the entire environment is integrative, be it polarized or not. On the other hand, the entire working environment is not integrative if the functional environment is non-relativistic. On the other hand, different approaches are used in viewing the particle behavior in either a relativistic or non-relativistic environment.

Either is mathematically related based on the variables of the operating environment. The mathematical relations are illustrated below as detailed by (Sabaiduc, Du, Boiesan, Zhu, Suthanthiran, Johnson, Ladysmith, Gelbart & Conard, 4).