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The basic method for computing dynamic aperture involves the use of a tracking code. A model of the ring is built within the code that includes an integration routine for each magnetic element. The particle is tracked many turns and stability is determined.
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For the case of electrons, the electrons will radiate which causes a damping effect. This means that one typically only cares about stability over thousands of turns.
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In addition, there are other quantities that may be computed to characterize the dynamics, and can be related to the dynamic aperture. One example is the
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There have also been other proposals for approaches to enlarge dynamic aperture, such as:
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is the stability region of phase space in a circular accelerator.
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189:"W. Wan, J. Cary, "Method of enlarging dynamic aperture""
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Physical Review
Special Topics: Accelerators and Beams
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Physical Review
Special Topics: Accelerators and Beams
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In the case of protons or heavy ion accelerators, (or
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