Ways to teach modelling—a 50 year study

This article describes a sequence of design research projects, some exploratory others more formal, on the teaching of modelling and the analysis of modelling skills. The initial motivation was the author’s observation that the teaching of applied mathematics in UK high schools and universities involved no active modelling by students, but was entirely focused on their learning standards models of a restricted range of phenomena, largely from Newtonian mechanics. This did not develop the numeracy/mathematical literacy that was so clearly important for future citizens. Early explorations started with modelling workshops with high school teachers and mathematics undergraduates, observed and analysed—in some case using video. The theoretical basis of this work has been essentially heuristic, though the Shell Centre studies included, for example, a detailed analysis of formulation processes that has not, as so often, been directly replicated. Recent work has focused on developing a formative assessment approach to teaching modelling that has proved both successful and popular. Finally, the system-level challenges in trying to establish modelling as an integral part of mathematics curricula are briefly discussed

Partial survival and inelastic collapse for a randomly accelerated particle

We present an exact derivation of the survival probability of a randomly accelerated particle subject to partial absorption at the origin. We determine the persistence exponent and the amplitude associated to the decay of the survival probability at large times. For the problem of inelastic reflection at the origin, with coefficient of restitution $r$, we give a new derivation of the condition for inelastic collapse, $r<r_c=e^{-\pi/\sqrt{3}}$, and determine the persistence exponent exactly.Comment: 6 page

Multi-TeV CLIC Photon Collider Option

Considerations for an option of gamma gamma collisions at multi-TeV energies are described, with focus on the 3 TeV CLIC machine, currently under study at CERN

Beam Lifetime and Beam Tails in LEP

Measurements of beam lifetime and non-Gaussian beam tails in LEP will be summarized. The measured beam lifetimes are compared to the lifetime expected from scattering processes. Non-Gaussian beam tails have been observed for colliding beams and on a much lower but still significant level also for single beams. The quantum lifetime was measured and compared with predictions

ELFE at CERN

A conceptual design for a recirculating electron accelerator with a maximum energy of 25 GeV and a continuous beam current of 0.1 mA on target has been prepared by a study group at CERN. The machine makes use of the super-conducting RF system and other components that will become available after the decommissioning of LEP. The beam will be accelerated in seven passes through a linac with an energy gain of 3.5 GeV per pass. The status of the study and the main design features are presented

Machine background common to all machines

General machine backgrounds relevant for linear colliders are described: Off momentum particles from beam-gas and Compton scattering on black body radiation, beam-tails, muons and synchrotron radiation. The discussion of these conventional machine backgrounds is largely based on experience with LEP

Energy dependence of beam-beam interactions at LEP

LEP has been operated for several years at beam energies around 45 GeV and more recently at beam energies of 65 and 86 GeV, thus covering about a factor of two in beam energies. Vertical beam-beam tune shifts exceeding 0.04 were reached at all energies. At the lower energies, emittance increase using wigglers was used successfully to avoid excessive beam blow-up and flip-flop from beam-beam interactions and allowed to operate safely at the beam-beam limit throughout fills lasting typically 10 hours. Significant non-Gaussian tails were observed in the vertical plane and have limited the maximum current in collisions. At the higher energies, the best performance in terms of luminosity and beam-beam tune shift demands higher currents per bunch and minimization of emittances. Vertical to horizontal emittance ratios below 0.5% have been achieved