Abstract
A large-scale Vlasov simulation study of the microwave instability below transition energy in a beam confined between two barrier pulses is performed. Starting from a matched distribution function for the confined ion beam including the space charge impedance the stability threshold in the longitudinal impedance plane is obtained. A simple stability criterium is found to be in good agreement with the simulation results.
Highlights
The determination of reliable impedance budgets for the design of low energy, high current ring machines requires the inclusion of space charge in combination with the other ring impedance components
By extending the parabolic bunch model to a beam confined between two sinus half waves (‘‘sausage beam model’’) we arrive at the distribution function
The results presented in a later section will show that this is not the case in space charge dominated beams below transition
Summary
The determination of reliable impedance budgets for the design of low energy, high current ring machines requires the inclusion of space charge in combination with the other ring impedance components. Systematic studies of the coherent stability limits due to the longitudinal microwave instability were performed mostly for high energy bunches in conventional rf buckets For the microwave instability in space charge dominated low energy beams detailed studies exist for coasting beams (see, e.g., [3]). Barrier buckets are usually considered in low energy, high current ring machines in order to increase the transverse space charge limit [8]. PACS numbers: 29.27.Bd, 29.20.– c, 52.59.Sa causes a reduction of the peak current density and of the transverse space charge tune shift Another method to flatten the bunches is the installation of a secondharmonic rf system [9]. Besides the increased transverse space charge limit barrier buckets offer greater flexibility for bunch manipulations compared to conventional rf systems, especially for injection and accumulation (see, e.g., [14]).
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