The dynamic aperture is the stability region of phase space in a circular accelerator.
For hadrons
In the case of protons or heavy ion accelerators, (or
synchrotron
A synchrotron is a particular type of cyclic particle accelerator, descended from the cyclotron, in which the accelerating particle beam travels around a fixed closed-loop path. The magnetic field which bends the particle beam into its closed p ...
s, or
storage ring
A storage ring is a type of circular particle accelerator in which a continuous or pulsed particle beam may be kept circulating typically for many hours. Storage of a particular particle depends upon the mass, momentum and usually the charge of th ...
s), there is minimal
radiation
In physics, radiation is the emission or transmission of energy in the form of waves or particles through space or through a material medium. This includes:
* ''electromagnetic radiation'', such as radio waves, microwaves, infrared, visi ...
, and hence the dynamics is
symplectic.
For long term stability, tiny dynamical diffusion (or
Arnold diffusion
In applied mathematics, Arnold diffusion is the phenomenon of instability of integrable Hamiltonian systems. The phenomenon is named after Vladimir Arnold who was the first to publish a result in the field in 1964. More precisely, Arnold diffusio ...
) can lead an initially stable orbit slowly into an unstable region. This makes the dynamic aperture problem particularly challenging. One may be considering stability over billions of turns.
A scaling law for Dynamic aperture vs. number of turns has been proposed by Giovannozzi.
For electrons
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.
Methods to compute or optimize dynamic aperture
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.
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
tune shift with amplitude.
There have also been other proposals for approaches to enlarge dynamic aperture, such as:
References
{{Reflist
Accelerator physics
Dynamical systems