An augmented moment method for stochastic ensembles with delayed couplings: II. FitzHugh-Nagumo model

Dynamics of FitzHugh-Nagumo (FN) neuron ensembles with time-delayed couplings subject to white noises, has been studied by using both direct simulations and a semi-analytical augmented moment method (AMM) which has been proposed in a recent paper [H. Hasegawa, E-print: cond-mat/0311021]. For $N$-unit FN neuron ensembles, AMM transforms original $2N$-dimensional {\it stochastic} delay differential equations (SDDEs) to infinite-dimensional {\it deterministic} DEs for means and correlation functions of local and global variables. Infinite-order recursive DEs are terminated at the finite level $m$ in the level-$m$ AMM (AMM$m$), yielding $8(m+1)$-dimensional deterministic DEs. When a single spike is applied, the oscillation may be induced if parameters of coupling strength, delay, noise intensity and/or ensemble size are appropriate. Effects of these parameters on the emergence of the oscillation and on the synchronization in FN neuron ensembles have been studied. The synchronization shows the {\it fluctuation-induced} enhancement at the transition between non-oscillating and oscillating states. Results calculated by AMM5 are in fairly good agreement with those obtained by direct simulations.Comment: 15 pages, 3 figures; changed the title with correcting typos, accepted in Phys. Rev. E with some change

An augmented moment method for stochastic ensembles with delayed couplings: I. Langevin model

By employing a semi-analytical dynamical mean-field approximation theory previously proposed by the author [H. Hasegawa, Phys. Rev. E {\bf 67}, 041903 (2003)], we have developed an augmented moment method (AMM) in order to discuss dynamics of an $N$-unit ensemble described by linear and nonlinear Langevin equations with delays. In AMM, original $N$-dimensional {\it stochastic} delay differential equations (SDDEs) are transformed to infinite-dimensional {\it deterministic} DEs for means and correlations of local as well as global variables. Infinite-order DEs arising from the non-Markovian property of SDDE, are terminated at the finite level $m$ in the level-$m$ AMM (AMM$m$), which yields $(3+m)$-dimensional deterministic DEs. Model calculations have been made for linear and nonlinear Langevin models. The stationary solution of AMM for the linear Langevin model with N=1 is nicely compared to the exact result. The synchronization induced by an applied single spike is shown to be enhanced in the nonlinear Langevin ensemble with model parameters locating at the transition between oscillating and non-oscillating states. Results calculated by AMM6 are in good agreement with those obtained by direct simulations.Comment: 18 pages, 3 figures, changed the title with re-arranged figures, accepted in Phys. Rev. E with some change

New beam for the CERN fixed target heavy ion programme

The physicists of the CERN heavy ion community (SPS fixed target physics) have requested lighter ions than the traditional lead ions, to scale their results and to check their theories. Studies have been carried out to investigate the behaviour of the ECR4 for the production of an indium beam. Stability problems and the low melting point of indium required some modifications to the oven power control system which will also benefit normal lead ion production. Present results of the source behaviour and the ion beam characteristics will be presented

Options for upgrading the intensity of the CERN lead pre-injector ion source

CERN's heavy ion pre-injector has been in service since 1994, providing lead ions for fixed target collisions at 177 GeV per nucleon in the SPS. In the LHC era, heavy ion collisions require an increase in the beam brightness, compared to the present injector system of Linac 3, Proton Synchrotron Booster and the Proton Synchrotron. Stacking and cooling ions in a Low Energy Ion Ring should find the largest part of this increase. However, further improvements can be envisaged by upgrading the pre-injector and source. The performance and limitations of the present source and Linac 3 will be discussed, and options for increasing the source brightness will be presented. These options consist of upgrades of the ECR Source to higher frequencies, or its replacement with a Laser Ion Source

Studies on ECR4 for the CERN ion programme

The CERN heavy ion community, and some other high energy physics experiments, are starting to demand other ions, both heavy and light, in addition to the traditional lead ions. Studies of the behaviour of the afterglow for different operation modes of the ECR4 at CERN have been continued to try to understand the differences between pulsed afterglow and continuous operation, and their effect on ion yield and beam reproducibility. The progress in adapting the source and ion beam characteristics to meet the new demands will be presented, as will new information on voltage holding problems in the extraction

Electrical resistivity ofYb(Rh1-xCox)2Si2 single crystals at low temperatures

We report low-temperature measurements of the electrical resistivity of Yb(Rh1-xCox)2Si2 single crystals with 0 <= x <= 0.12. The isoelectronic substitution of Co on the Rh site leads to a decrease of the unit cell volume which stabilizes the antiferromagnetism. Consequently, the antiferromagnetic transition temperature increases upon Co substitution. For x = 0.07 Co content a subsequent low-temperature transition is observed in agreement with susceptibility measurements and results on YbRh2Si2 under hydrostatic pressure. Above the Neel transition the resistivity follows a non-Fermi liquid behavior similar to that of YbRh2Si2.Comment: 4 pages, submitted to SCES0

Effect of a Biased Probe on the Afterglow Operation of an ECR4 Ion Source

Various experiments have been performed on a 14.5 GHz ECR4 in order to improve the ion yield. The source runs in pulsed afterglow mode, and provides currents ~120 emA of Pb27+ to the CERN Heavy Ion Facility on an operational basis. In the search for higher beam intensities, the effects of a pulsed biased disk on axis at the injection side were investigated with different pulse timing and voltage settings. No proof for absolute higher intensities was seen for any of these modifications. However, the yield from a poorly tuned/low-performing source could be improved and the extracted pulse was less noisy with bias voltage applied. The fast response on the bias implies that increases/decreases are not due to ionisation processes. A good tune for high yield of high charge states during the afterglow coincides with a high plasma potential

Operation of the GTS-LHC Source for the Hadron Injector at CERN

The GTS-LHC ion source, designed and build by CEA Grenoble, was installed and commissioned at CERN in 2005. Since than the source has delivered oxygen and lead ion beams (O4+ and Pb27+ from the source, Pb54+ from the linac) for the commissioning of the Low Energy Ion Ring (LEIR). Results of this operation and attempts to improve the source performance and reliability, and the linac performance will be presented in this paper