*M. Cornacchia* `cornacchia@ssrl01.slac.stanford.edu`

SLAC3mm

The 12th Advanced ICFA Beam Dynamics Workshop on ``Nonlinear and Collective Phenomena in Beam Physics" was held in Arcidosso, Italy, from the 2nd to the 6th of September, 1996. The Workshop was sponsored by ICFA, the US Department of Energy, the National Institute for Nuclear Physics (INFN, Italy), the National Laboratory for High Energy Physics (KEK, Japan), the Lawrence Berkeley National Laboratory (USA), the Stanford Linear Accelerator Center (USA), the University of California at Los Angeles (USA) and the University of Rome ``La Sapienza''. It attracted 70 experts on beam dynamics in particle accelerators and mathematicians of non-linear dynamics. Arcidosso is a medieval town in Southern Tuscany, close to the city of Sienna. The meeting took place in the historically evocative scenario of the 11th century Aldobrandescan castle atop a hill dominating the nearby valley. The castle was restored in 1989, and preserves all the atmosphere and raggedness of medieval times.

The participants were presented with a choice of four groups, each addressing a particular problem. For each Group there was a Speaker, who gave the opening lecture, and a Coordinator, who led the discussions and presented a summary of the work on the last day.

The Workshop was organized in such a way as to leave as much time as possible to discussions and to minimize the number of formal plenary talks. There were four invited lectures on Monday the 2nd and four summary talks in the afternoon of Friday the 6th. Contributed plenary talks were not held and were replaced by exhibits in a Poster Room, displayed for the full duration of the meeting.

The Group on ''Single Particle Dynamics'' (Speaker: Katsunobu Oide, KEK; Coordinator: Alex Chao, SLAC) was charged with the review of the status and the discussion of new ideas on the nonlinear dynamics of a single particle (i.e. not including collective effects) in accelerators. In his plenary lecture, Oide gave an overview of the theory, methods and algorithms that are used to estimate the stability of charged particles in accelerators in presence of nonlinear perturbations. In his summary talk, Chao said that an impressive arsenal of analytical and semi- analytical tools have been developed, in the form of one turn maps and spectral line analysis. The Group discussed the suitability and shortcomings of each method to tackle various problems: fast tracking, detuning, resonance analysis, prediction of dynamic aperture. The long term dynamic aperture is of interest to the only large collider under construction, the LHC, and many contributions to the early prediction of long term dynamic aperture were devoted to this problem. The basic question is whether one can track for turns and predict the stability for turns. Several methods were proposed, including one where a constant in the Lyapunov condition is derived from the Henon map. Surprisingly, the computations suggest that the value of the constant so derived can be applied with good predictions to a complex nonlinear lattice like the LHC. Other indicators that were discussed include the computation of tune drifts measured over a ``small'' number of turns and the change of the quasi-invariant action. The relationship between short and long term dynamic aperture is important for the determination of the optimization methods. Here the conclusions at workshop was that correlation is probably good beyond turns, but often poor for less than turns, implying that the two may have different mechanism. Tracking studies and experimental results from the SPS indicate that modulation effects are important, but not yet well understood theoretically. The beam-beam effect did not receive a lot of attention this time. A semi-empirical law, derived by M. Bassetti (Laboratori di Frascati INFN), fits surprisingly well the measured beam-beam limits. In summarizing the work of the Group, Chao said that, in spite of the progress in theoretical and numerical tools, the mechanism of dynamic aperture limit is still elusive.

The Group on ``Production and Dynamics of High Brightness Beams'' (Speaker: Luca Serafini, Milan University; Coordinator: Richard Sheffield, LANL) covered the advances on production, acceleration, transport and monitoring of high brightness beams, including coherent and radiation effects. Radio-frequency photo-cathode guns, emittance compensation and preservation were the main topics of discussion of this Working Group. Reviewing the present status and understanding of experiments and computations, the Group agreed that an emittance of 2 p mm-mrad with 1 nano-Coulomb charge has been achieved and that, according to the results of simulations, an emittance of 0.5 to 1.0 p mm-mrad (still with 1 nano-Coulomb charge) must be expected to be the minimum achievable. The above numbers, it must be noted, refer to the total projected emittance of a bunch after linear emittance compensation. The latter was discussed and is well understood. The next step is the compensation of the nonlinear emittance dilution. Halo formation was also a topic of discussion: the best understanding of its formation, at the moment, is that it is due to overfocusing of the beam tail. Other aspects that were visited by the Group included frequency scaling, electron sources (beside photo-cathode guns, needles and plasmas), thermal emittance (need for new experimental data on promising cathode materials like Cs2Te, Cu, Mg and others). A topic of discussion that stirred considerable interest was that of emittance degradation in bends. This subject of was debated in joint sessions of Groups 2 and 4. The conclusions were that some of the approximations used in current theories are of somewhat doubtful validity, and that more rigorous approaches are needed. Many participants were confident that the effect can be tuned away with clever beam transport design, but that present understanding is not sufficient to produce such a design. Experiments are being planned that, in a year or so, should shed some experimental light on the phenomenon.

The Group on ``Beam Dynamics in Plasmas'' (Speaker: Thomas Katsuleas, University of Southern California; Coordinator: Francois Aminoroff (Ecole Politechnique, Paris) covered the subjects of Plasma Lenses, Electron Beam Driven Wakefields, Laser Wakefields, Self-Modulated Laser Wakefields, Crossed Beam Wakefields and the generation, acceleration, and focusing of low emittance, high energy, high current short pulses. The laser wakefield and guiding principle were reviewed, with discussions on how to increase the effective acceleration length by guiding the laser beam, on the emittance of the accelerated electron beam and on the practical applications. Experiments have been carried out over an acceleration length of one cm with power density of W/ and others are being proposed over a few cm and power densities of W/. (beat-wave) and up to of W/. (wakefields). Projects for 1 GeV laser-driven plasma accelerators are being planned in Japan, USA and France. On Electron Beam Driven Wakefield Accelerators, Aminoroff, in his summary talk, said the low energy gain proof of principle experiment has been done and that high energy and/or high current experiments are being proposed. Plasma lenses experiments have been done at low energy and low current and the need now is for experiments at higher energies and beam densities.

The charge to the Group on ``Plasma Phenomena in Beams'' (Speaker: Patrick Colestock, FNAL; Coordinator: Jonathan Wurtele, LBNL and UC Berkeley) was to survey the status and recent ideas on transverse and longitudinal oscillations in high density relativist beams, including parametric instabilities and filamentation. The longitudinal microwave instability was one of the main topics discussed, with questions and suggestions ranging from the confidence on predicting the threshold (requires knowledge of wake function, harder to achieve as the trend is for shorter and shorter bunches) to design criteria for increasing the threshold (strong longitudinal focusing was proposed by V. Litvinenko). Various new interesting theoretical approaches were proposed. Well controlled machine experiments are needed to shed light on the problem. Other instabilities that were discussed included ion-electron effects, with a report of observations at the ALS and discussions of its possible occurrence in single pass electron accelerators. A topic that kindled considerable interest was the observation of the ''longitudinal echo'' at the Antiproton Accelerator and the Tevatron (Fermilab) and at the SPS (CERN). This phenomenon was explained theoretically, and it was shown that it can be exploited as a powerful diagnostic tool for determining the charge and momentum spread distribution in the beam, as well as its diffusion time. The possibility of the existence and observation of an even more exotic phenomenon, ``solitons'', or space charge waves, was also raised.