Degrees of Freedom Determination in Accelerator Physics Optimisation Problems Subject to Global Constraints

The determination of the number of degrees of freedom of a system is a common problem in physics. It is straightforward for the case of unbounded parameters. For global constraints cutting into the parameter space however, the determination is difficult. This problem occurs, for example, in the matching of beam lines where global constraints like aperture or maximum bend angle have to be respected. It is also relevant for fits of complex models to experimental data, where external information (e.g. positivity, maximum energy loss or measured momentum spread) is included in the form of constraints. This paper proposes a method to extract the effective number of degrees of freedom for a given system. Examples are discussed to illustrate the method.