A Few Words on Emittance Chris Rogers MICE vc 27/05/05

Abstract (written by ?) Authors Chris Rogers, Malcolm Ellis (Imperial College of Science and Technology, London) Presenter Chris Rogers (Imperial College of Science and Technology, London) Abstract Muon ionization cooling, an essential ingredient of a neutrino factory, will be demonstrated for the first time by the MICE experiment. The central part of MICE consists of a short section of a neutrino factory cooling channel and the emittance reduction achieved in this experiment is quite modest, 10% to 15%. In order to extrapolate the performance of a full cooling channel from these values, it is crucial for MICE to achieve an emittance measurement accuracy of 10^-3 absolute. So far, beam emittance has never been measured with such a high level of precision and normailzed emittance in its present definition is not even conserved to 10^-3 in the absence of dissipative forces. We present an improved definition of beam emittance and the requirements and constraints on MICE beam optics and spectrometers that are necessary to achieve the 10^-3 level of accuracy. Type of Presentation Poster Main Classification Single-Particle Beam Dynamics and Optics Sub Classification Nonlinear Dynamics, Resonances, Tracking, and Higher- Order Fields

Define Single Particle Emittance We define single particle emittance by (Holzer?) Then given some collection of SPEs, it can be shown that the bunch emittance for some arbritrary beam distribution is given by (in a 4D phase space)

Amplitude For a particle by particle experiment, it is desirable to define the single particle emittance without reference to a bunch. We write Where V m is the “machine”/design covariance matrix This is a generalisation of Greg Penn’s Combined Amplitude (MUCOOL note 71) Then the “bunch amplitude” is given by

Eg: effects of non-linearities This particle-by-particle definition enables us to study e.g. change in emittance due to non-linear optics independently of the non-linearities Here we see the change in single particle amplitude through the MICE magnetic lattice as a function of initial single particle amplitude for some typical selection of events –this is without any interactions with material/RF The input emittance for a typical NuFact channel is 12 mm so =48 mm

And then… Then go on to describe Malcolm’s work on spectrometer resolution etc There is some algebra to go with this work but I do not present it here