Coherent Beam-Beam Tune Shift of Unsymmetrical Beam-Beam Interactions with Large Beam-Beam Parameter

Coherent beam-beam tune shift of unsymmetrical beam-beam interactions was studied experimentally and numerically in HERA where the lepton beam has a very large beam-beam parameter (up to $\xi_y=0.272$). Unlike the symmetrical case of beam-beam interactions, the ratio of the coherent and incoherent beam-beam tune shift in this unsymmetrical case of beam-beam interactions was found to decrease monotonically with increase of the beam-beam parameter. The results of self-consistent beam-beam simulation, the linearized Vlasov equation, and the rigid-beam model were compared with the experimental measurement. It was found that the coherent beam-beam tune shifts measured in the experiment and calculated in the simulation agree remarkably well but they are much smaller than those calculated by the linearized Vlasov equation with the single-mode approximation or the rigid-beam model. The study indicated that the single-mode approximation in the linearization of Vlasov equation is not valid in the case of unsymmetrical beam-beam interactions. The rigid-beam model is valid only with a small beam-beam parameter in the case of unsymmetrical beam-beam interactions.Comment: 32 pages, 13 figure

Method of projection operator for the study of angle-averaged distribution function of beam particles in hadron storage rings

Starting from the Vlasov equation for the single-particle phase-space distribution of beam particles in hadron storage rings, the angle-averaged distribution function of the action variables is studied by means of projection operator. It is shown that the angle-averaged distribution function is governed by a kinetic equation similar to the Fokker-Planck equation but with a memory integral. For localized nonlinear perturbations, this kinetic equation can be further reduced to a moment map which can be iterated numerically for studying the beam-size growth in hadron storage rings. To examine the validity of this treatment, the evolution of beam size is studied with examples of integrable and nonintegrable systems. It is found that the result from the moment map agrees very well with the exact solution for the integrable example or that from multiparticle tracking for the nonintegrable example when the system is not very close to low-order resonances. The angle-averaged distribution function is a promising tool to study the effect of the space charge and beam-beam interaction on high-intensity hadron beams

Phase space distribution of particles near an isolated difference resonance

We have studied the phase space distribution of beam particles near an isolated difference resonance. The numerical simulation has shown that the distribution can quickly settle down to a final state if its initial state is Gaussian. The final state can be treated as a stationary state as long as the high order fluctuation can be neglected. From the Liouville equation, the emittances of beam particles are calculated approximately. There is a good agreement between analytical and numerical results. 3 refs., 2 figs

Single-molecule detection of protein efflux from microorganisms using fluorescent single-walled carbon nanotube sensor arrays.

A distinct advantage of nanosensor arrays is their ability to achieve ultralow detection limits in solution by proximity placement to an analyte. Here, we demonstrate label-free detection of individual proteins from Escherichia coli (bacteria) and Pichia pastoris (yeast) immobilized in a microfluidic chamber, measuring protein efflux from single organisms in real time. The array is fabricated using non-covalent conjugation of an aptamer-anchor polynucleotide sequence to near-infrared emissive single-walled carbon nanotubes, using a variable chemical spacer shown to optimize sensor response. Unlabelled RAP1 GTPase and HIV integrase proteins were selectively detected from various cell lines, via large near-infrared fluorescent turn-on responses. We show that the process of E. coli induction, protein synthesis and protein export is highly stochastic, yielding variability in protein secretion, with E. coli cells undergoing division under starved conditions producing 66% fewer secreted protein products than their non-dividing counterparts. We further demonstrate the detection of a unique protein product resulting from T7 bacteriophage infection of E. coli, illustrating that nanosensor arrays can enable real-time, single-cell analysis of a broad range of protein products from various cell types