Laser-driven accelerators, in which particles are accelerated by the electric field of a plasma wave (the wakefield) driven by an intense laser, have demonstrated accelerating electric fields of hundreds of GV m(-1) (refs 1-3). These fields are thousands of times greater than those achievable in conventional radio-frequency accelerators, spurring interest in laser accelerators as compact next-generation sources of energetic electrons and radiation. To date, however, acceleration distances have been severely limited by the lack of a controllable method for extending the propagation distance of the focused laser pulse. The ensuing short acceleration distance results in low-energy beams with 100 per cent electron energy spread, which limits potential applications. Here we demonstrate a laser accelerator that produces electron beams with an energy spread of a few per cent, low emittance and increased energy (more than 10(9) electrons above 80 MeV). Our technique involves the use of a preformed plasma density channel to guide a relativistically intense laser, resulting in a longer propagation distance. The results open the way for compact and tunable high-brightness sources of electrons and radiation.

Guiding-center theory provides the reduced dynamical equations for the motion of charged particles in slowly varying electromagnetic fields, when the fields have weak variations over a gyration radius ͑or gyroradius͒ in space and a gyration period ͑or gyroperiod͒ in time. Canonical and noncanonical Hamiltonian formulations of guiding-center motion offer improvements over non-Hamiltonian formulations: Hamiltonian formulations possess Noether's theorem ͑hence invariants follow from symmetries͒, and they preserve the Poincaré invariants ͑so that spurious attractors are prevented from appearing in simulations of guiding-center dynamics͒. Hamiltonian guiding-center theory is guaranteed to have an energy conservation law for time-independent fields-something that is not true of non-Hamiltonian guiding-center theories. The use of the phase-space Lagrangian approach facilitates this development, as there is no need to transform a priori to canonical coordinates, such as flux coordinates, which have less physical meaning. The theory of Hamiltonian dynamics is reviewed, and is used to derive the noncanonical Hamiltonian theory of guiding-center motion. This theory is further explored within the context of magnetic flux coordinates, including the generic form along with those applicable to systems in which the magnetic fields lie on nested tori. It is shown how to return to canonical coordinates to arbitrary accuracy by the Hazeltine-Meiss method and by a perturbation theory applied to the phase-space Lagrangian. This noncanonical Hamiltonian theory is used to derive the higher-order corrections to the magnetic moment adiabatic invariant and to compute the longitudinal adiabatic invariant. Noncanonical guiding-center theory is also developed for relativistic dynamics, where covariant and noncovariant results are presented. The latter is important for computations in which it is convenient to use the ordinary time as the independent variable rather than the proper time. The final section uses noncanonical guiding-center theory to discuss the dynamics of particles in systems in which the magnetic-field lines lie on nested toroidal flux surfaces. A hierarchy in the extent to which particles move off of flux surfaces is established. This hierarchy extends from no motion off flux surfaces for any particle to no average motion off flux surfaces for particular types of particles. Future work in magnetically confined plasmas may make use of this hierarchy in designing systems that minimize transport losses.

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