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High intensity proton linacs (HIPLs) for applications such as Accelerator Driven Reactor Systems (ADRS) have serious beam dynamics issues related to beam halo formation. This can lead to particle loss and radioactivation of the surroundings which consequently limit the beam current. Beam halos are largely driven by the nonlinear space-charge force of the beam, which depends strongly on the beam distribution and also on the initial beam mismatch. We propose here the use of a higher order mode beam (HOMB), that has a weaker nonlinear force, to mitigate beam halos. We first show how the nonlinear space-charge force can itself be exploited in the presence of nonlinear solenoid fields, to produce a HOMB in the low energy beam transport (LEBT) line. We then study the transport of such a beam through a radio frequency quadrupole (RFQ), and show that the HOMB has a significant advantage in terms of emittance blow-up, halo formation and beam loss, over a Gaussian beam, even with a finite initial mismatch. For example, for the transport of a 30 mA beam through the RFQ, with an initial beam mismatch of 45%, the Gaussian beam sees an emittance blow-up of 125%, while the HOMB sees a blow-up of only 35% (relative to the initial emittance of 0.2π mm-mrad). Similarly, the beam halo parameter and beam loss are 0.95 and 25% respectively for a Gaussian beam, but only 0.35 and 15% for a HOMB. The beam dynamics of the HOMB agrees quite well with the particle-core model, because of the more linear space-charge force, while for the Gaussian beam there are additional particle loss mechanisms arising from nonlinear resonances. Therefore, the HOMB suppresses emittance blow-up and halo formation, and can make high current ADRS systems more viable.

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Three-dimensional simulation codes GENESIS and OPC are used to investigate the dependence of the resonator stability of free-electron laser (FEL) oscillators on the stability parameter, laser wavelength, outcoupling hole size and mirror tilt. We find that to have stable lasing over a wide range of wavelengths, the FEL cavity configuration should be carefully chosen. Broadly, the concentric configuration gives near-Gaussian modes and the best performance. At intermediate configurations the dominant mode often switches to a higher-order mode, which kills lasing. For the same reason, the outcoupled power can also be less. We have constructed a simple analytic model to study resonator stability which gives results that are in excellent agreement with the simulations. This suggests that modes in FEL oscillators are determined more by the cavity configuration and radiation propagation than by the details of the FEL interaction. We find (as in experiments at the CLIO FEL) that tilting the mirror can, for some configurations, lead to more outcoupled power than a perfectly aligned mirror because the mode is now a more compact higher-order mode, which may have implications for the mode quality for user experiments. Finally, we show that the higher-order mode obtained is usually a single Gauss-Laguerre mode, and therefore it should be possible to filter out the mode using suitable intracavity elements, leading to better FEL performance.