Extracting dynamical frequencies from invariants of motion in finite-dimensional nonlinear integrable systems.

Integrable dynamical systems play an important role in many areas of science, including accelerator and plasma physics. An integrable dynamical system with n degrees of freedom possesses n nontrivial integrals of motion, and can be solved, in principle, by covering the phase space with one or more charts in which the dynamics can be described using action-angle coordinates. To obtain the frequencies of motion, both the transformation to action-angle coordinates and its inverse must be known in explicit form.

Transverse Beam Emittance Measurement by Undulator Radiation Power Noise.

Generally, turn-to-turn power fluctuations of incoherent spontaneous synchrotron radiation in a storage ring depend on the 6D phase-space distribution of the electron bunch. In some cases, if only one parameter of the distribution is unknown, this parameter can be determined from the measured magnitude of these power fluctuations. In this Letter, we report an absolute measurement (no free parameters or calibration) of a small vertical emittance (5-15 nm rms) of a flat beam by this method, under conditions, when it is unresolvable by a conventional synchrotron light beam size monitor.

Experimental demonstration of relativistic electron cooling.

We report on an experimental demonstration of electron cooling of high-energy antiprotons circulating in a storage ring. In our experiments, electron cooling, a well-established method at low energies (<500 MeV/nucleon), was carried out in a new region of beam parameters, requiring a multi-MeV dc electron beam and an unusual beam transport line. In this Letter, we present the results of the longitudinal cooling force measurements and compare them with theoretical predictions.

Circular modes, beam adapters, and their applications in beam optics.

In the optics of charged particle beams, circular transverse modes can be introduced; they provide an adequate basis for rotation-invariant transformations. A group of these transformations is shown to be identical to a group of the canonical angular momentum preserving mappings. These mappings and the circular modes are parametrized similar to the Courant-Snyder forms for the conventional uncoupled, or planar, case.