Abstract
The drift motion of cooling electrons makes them able to respond to transverse perturbations of a cooled ion beam. This response may lead to dipole or quadrupole transverse instabilities at specific longitudinal wave numbers. While the dipole instabilities can be suppressed by a combination of the Landau damping, machine impedance, and the active damper, the quadrupole and higher order modes can lead to either emittance growth, or a lifetime degradation, or both. The growth rates of these instabilities are strongly determined by the machine x-y coupling. Thus, tuning out of the coupling resonance and/or reduction of the machine coupling can be an efficient remedy for these instabilities.
Highlights
Electron cooling is an effective method to increase phase space density of hadron beams
Since its invention by Budker [1], and experimental proof at NAP-M [2], it has been successfully used at many nonrelativistic ion storage rings, and recently 8:9 GeV=c antiprotons have been electron cooled at Recycler ring, Fermilab [5]
The ion beam does not need focusing elements inside the cooler, while the electron beam is focused by a homogeneous solenoidal magnetic field
Summary
Electron cooling is an effective method to increase phase space density of hadron beams. A tune shift by the space charge of the electron beam drives high-order resonances in the ion motion, and this incoherent effect may reduce a lifetime of the ions. This effect was first pointed out by Reistad [9], who suggested that as an explanation for reduction of the ion lifetime with the electron current, observed at CELSIUS ring [10], and called such kind of phenomena as ‘‘electron heating.’’. Coherent ion-electron interaction was theoretically considered in a model of transversely immobile, totally magnetized electrons [16]; the longitudinal and the transverse impedances introduced by the electron beam were calculated These impedances appeared to be too low for realistic parameters of electron coolers, indicating that the electron drift mobility should be taken into account. An important conclusion is that a straightforward remedy for all orders coherent ion-electron instabilities is tuning out of the coupling resonance and/or suppression of the machine coupling
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