please give the resonance condition and drawbacks of a cyclotron.
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A cyclotron is a type of particle accelerator that uses a constant magnetic field and alternating electric fields to accelerate a particle in a spiral motion. These types of particle accelerators were among the first devised and have several advantages over early linear accelerators, such as smaller size requirements. While advances in technology have made more complex types of particle accelerators possible, there are still some uses for cyclotrons in a number of different fields. A cyclotron can still be used in physics experimentation, especially as an early part of a multi-stage accelerator.
Developed in 1932, a cyclotron is a particle accelerator that uses circular motion, typically in an outward growing spiral, to accelerate particles for a number of different uses. Particle acceleration typically requires a fairly great distance to allow the particles to come to sufficient speed for use in experiments. The design of a cyclotron, however, allows for smaller accelerators to be used to great effect, since the particle moves in a circular motion and travels a great distance without requiring a long straight corridor for passage.
A cyclotron basically works by utilizing a pair of high powered electrodes, each shaped like a “D” with the flat sides toward each other, to create a complete circular shape. Beginning at the center of the circle, a particle begins to move away from the center, but by using attraction and repulsion, it is instead pulled into a circular motion. The diodes alternate charge between them so the particle is accelerated toward one, then curves around as it is pushed away by that one and attracted toward the other, then continues the pattern between the two electrodes. This would create a perfect circular motion if left alone, but a magnetic field is created between the two diodes, which is perpendicular to the circular motion of the particle.
This magnetic field slightly shifts the motion of the particle, so each time it passes between the two electrodes it is moved a bit away from the center of the circle. By moving the particle slightly outward, the path it takes during acceleration becomes an outward growing spiral rather than a circle. This allows the particle to eventually strike a target area on the inside of the containment unit, where it can then be redirected for further study or use.
One of the major drawbacks of a cyclotron is that the target area can only be used for a particle traveling at speeds that can be properly calculated using Newtonian physics. Higher speeds would cause relativistic effects to occur, and the target would not be struck properly, meaning a cyclotron cannot typically produce the levels of acceleration that newer, linear accelerators can. Isochronous cyclotrons have been developed, however, that can compensate for relativistic changes to the particle, and can be quite effective.
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