K.M. Hock

ALICE tomography section: measurements and analysis

The ALICE tomography section at Daresbury is a diagnostic setup in the injection line of EMMA, the worlds first non-scaling FFAG accelerator. We present our measurements and analysis of the transverse emittance, Twiss parameters and phase space distribution of the electron beam that is injected into EMMA. The measurements are carried out at 12 MeV, for bunch charges from 20 to 80 pC. Quadrupole scans and tomography are used. The results show that space charge effect does not change the beam emittance significantly over the length of the tomography section. Starting from projections of the beam images, the quadrupole scan technique can be applied to give the emittance and Twiss parameters. The same projections can be processed using tomography to give the phase space distribution. A careful treatment of the background noise is required to produce consistent emittances between quadrupole scans at different locations. Extending this in a natural way to tomography, we are also able to remove most of the the streaking artefacts from reconstructions obtained using the Filtered Back Projection technique.

Beam tomography research at Daresbury Laboratory

Beam tomography research at Daresbury Laboratory has focussed on the development of normalised phase space techniques—starting with the idea of sampling tomographic projections at equal phase advances. This idea has influenced the design and operation of the tomography sections at the Photo Injector Test Facility at Zeuthen (PITZ) and at the Accelerator and Lasers in Combined Experiments (ALICE) at Daresbury. We have studied the feasibility of using normalised phase space to measure the effect of space charge. Quadrupole scan measurements are carried out at two different parts of a beamline. Reconstructions at the same location give results that are clearly rotated with respect to each other in normalised phase space. We are able to show that a significant part of this rotation can be attributed to the effect of space charge. We show how the normalised phase space technique can be used to increase the reliability of the Maximum Entropy Technique (MENT). While MENT is known for its ability to work with just a few projections, the accuracy of its reconstructions has seldom been questioned. We show that for typical phase space distributions, MENT could produce results that look quite different from the original. We demonstrate that a normalised phase space technique could give results that are closer to the actual distribution. We also present simpler ways of deriving the phase space tomography formalism and the Maximum Entropy Technique.

Complementary split-ring resonator-based accelerating structure

We describe a novel particle accelerating structure consisting of Complementary Split-Ring Resonators (C-SRRs) etched into the lower and upper walls of a copper rectangular waveguide. Outer cylindrical cavities enclosing the C-SRR sections allow a vacuum to be maintained. The accelerating gradient of a 1 GHz cavity is simulated to be 8.76 MV/m, when referenced to the actual accelerating gap, for only 10.7 kW of input power. Particle simulation results confirm the efficacy of the proposed structure. A simple analytical model of the structure is given as a design aid to compute the relationship between the key geometrical parameters and the resonance frequency.

An elementary analysis of coupled-bunch instabilities

We reconsider the equations of motion of wake field coupled bunches in the light of recent developments in Delay Differential Equations. In the case of uniform resistive wall in a storage ring, we demonstrate an alternative way to characterize the growth modes. For each multibunch Fourier mode, an infinite number of time domain modes can arise from an exact solution of the equation of motion. The growth rate as it is commonly defined corresponds to only one of them. The amplitude of each Fourier mode can therefore evolve with time in a way that is not a simple exponential. This is a result that has been observed in simulations of wake field coupled bunches.