Experimental study of coherent betatron resonances with a Paul trap

Abstract

Linear and nonlinear resonant instabilities of charged-particle beams traveling in periodic quadrupole focusing channels are studied experimentally with a compact non-neutral plasma trap. The present experiments are based on the idea that the collective motion of a beam in an accelerator is physically similar to that of a one-component plasma in a trap. A linear Paul trap system named ''S-POD'' (simulator for particle orbit dynamics) was developed to explore a variety of space-charge-induced phenomena. To emulate lattice-dependent effects, periodic perturbations are applied to quadrupole electrodes, which gives rise to additional resonance stop bands that shift depending on the plasma density. It is confirmed that an mth-order resonance takes place when the corresponding tune of an mth-order collective mode m is close to a half integer.

Experimental study of resonance crossing with a Paul trap

“…But in reality, we do have finite electrode misalignments that enhance the amplitudes of nonlinear multipole components. In case the rms displacement of the rods from the ideal positions is 50 m, the average strength of the third-order nonlinearity (sextupole) becomes 0.34% at the circular aperture of 5 mm in radius [22]. The higher-order nonlinearities are monotonically weakened; 0.19% for the fourth order and 0.13% for the fifth.…”

“…Each quadrupole rod of our ''multisectioned'' LPT is divided into five electrically isolated pieces, so that we can form a couple of axial potential wells simultaneously by applying different bias voltages to those pieces [22]. For the present experiments, ions are confined within the axial region of 75 mm long (much greater than the aperture size) in-between short quadrupole sections.…”

“…Since the sinusoidal focusing has a resonance nature very close to that of the FODO lattice, we can approximately model a circular machine if it is composed of identical doublet cells [22]. The nonscaling FFAG ''EMMA'' consisting of 42 doublets is one such example [4,26].…”

Sheet beam model for intense space charge: Application to Debye screening and the distribution of particle oscillation frequencies in a thermal equilibrium beam

“…Recent experiments and simulations supporting the reliability of the KV model as an aid to interpret space-charge effects for relatively weak spacecharge are presented in Ref. [9]. h Point 7.-Conversely to the weak space-charge case discussed in the point above, in the strong space-charge limit the KV model is expected to provide a poor approximation to smooth distributions.…”

“…Sacherer applied a self-consistent, 1D Kapchinskij-Vladimirskij (KV) model for a uniform density beam to analyze equilibrium and stability properties and applied his results to model space-charge induced effects on resonances in rings [6]. Various studies have applied and extended Sacherer's pioneering work in interpreting space-charge resonance effects in rings [7][8][9]. Anderson showed that in a cold, laminar beam limit all initial density perturbations on a uniform density sheet beam are transferred to velocity space in a quarter plasma oscillation period [10]; he also estimated emittance growth rates due to centroid displacements using a sheet-beam model [11].…”