Estimates for Long-term stability for the LHC

Since about 10 years survival plots have been used to evaluate single-particle long-term stability. In a recent paper (M. Giovannozzi et al.) this concept has been reviewed, using a dynamic aperture (Dyn.Aper.) definition based on the average over different ratios of emittances. It has been shown that the survival times evaluated according to this procedure decay with the inverse of the logarithm of the number of turns in several different systems. In this paper the validity of this conjecture is tested in the case of the latest LHC lattice which has been studied extensively. The inverse log conjecture also predicts a non-zero Dyn.Aper. at infinite times called $D_{\infty}$. The tracking data are analysed for the LHC lattice to determine the relation between $D_{\infty}$ and the onset of chaos determined through Lyapunov exponents. Two different methods to automate the prediction of the Lyapunov exponent are tested and are compared with $D_{\infty}$

Dynamic aperture studies for the LHC version 4

The limitations of the dynamic aperture due to field errors of the super-conducting magnets is a notorious problem for the LHC. Given the large amount of independent studies performed by a sizeable research team it becomes necessary to define a common tracking strategy. The emphasis is placed on an elaborate on - and off - line processing of the tracking data making use of all tools presently available. To manage the very time-comsuming investigations our approach is two-fold: firstly we are maximising the computing power running optimised code on state of the art equipment which is continuously upgraded and secondly we speed up the studies by using reliable and automated early indicators for long-term losses. The procedure is exemplified with a series of tracking runs for the LHC version 4 at injection

Speeding up Cylindrical Algebraic Decomposition by Gr\"obner Bases

Gr\"obner Bases and Cylindrical Algebraic Decomposition are generally thought of as two, rather different, methods of looking at systems of equations and, in the case of Cylindrical Algebraic Decomposition, inequalities. However, even for a mixed system of equalities and inequalities, it is possible to apply Gr\"obner bases to the (conjoined) equalities before invoking CAD. We see that this is, quite often but not always, a beneficial preconditioning of the CAD problem. It is also possible to precondition the (conjoined) inequalities with respect to the equalities, and this can also be useful in many cases.Comment: To appear in Proc. CICM 2012, LNCS 736

Parity of the Pairing Bosons in a High-Temperature Superconductor

We report the observation of a novel effect in the bilayer Pb-Bi2212 high-TC superconductor by means of angle-resolved photoemission with circularly polarized excitation. Different scattering rates, determined as a function of energy separately for the bonding and antibonding copper-oxygen bands, strongly imply that the dominating scattering channel is odd with respect to layer exchange within a bilayer. This is inconsistent with a phonon-mediated scattering and favours the participation of the odd collective spin excitations in the scattering mechanism in near-nodal regions of the k-space, suggesting a magnetic nature of the pairing mediator.Comment: 5 RevTex pages, 4 eps figure

Campholenic aldehyde ozonolysis: a mechanism leading to specific biogenic secondary organic aerosol constituents

In the present study, campholenic aldehyde ozonolysis was performed to investigate pathways leading to specific biogenic secondary organic aerosol (SOA) marker compounds. Campholenic aldehyde, a known α-pinene oxidation product, is suggested to be a key intermediate in the formation of terpenylic acid upon α-pinene ozonolysis. It was reacted with ozone in the presence and absence of an OH radical scavenger, leading to SOA formation with a yield of 0.75 and 0.8, respectively. The resulting oxidation products in the gas and particle phases were investigated employing a denuder/filter sampling combination. Gas-phase oxidation products bearing a carbonyl group, which were collected by the denuder, were derivatised by 2,4-dinitrophenylhydrazine (DNPH) followed by liquid chromatography/negative ion electrospray ionisation time-of-flight mass spectrometry analysis and were compared to the gas-phase compounds detected by online proton-transfer-reaction mass spectrometry. Particle-phase products were also analysed, directly or after DNPH derivatisation, to derive information about specific compounds leading to SOA formation. Among the detected compounds, the aldehydic precursor of terpenylic acid was identified and its presence was confirmed in ambient aerosol samples from the DNPH derivatisation, accurate mass data, and additional mass spectrometry (MS² and MS³ fragmentation studies). Furthermore, the present investigation sheds light on a reaction pathway leading to the formation of terpenylic acid, involving α-pinene, α-pinene oxide, campholenic aldehyde, and terpenylic aldehyde. Additionally, the formation of diaterpenylic acid acetate could be connected to campholenic aldehyde oxidation. The present study also provides insights into the source of other highly functionalised oxidation products (e.g. <i>m</i> / <i>z</i> 201, C₉H₁₄O₅ and <i>m</i> / <i>z</i> 215, C₁₀H₁₆O₅), which have been observed in ambient aerosol samples and smog chamber-generated monoterpene SOA. The <i>m</i> / <i>z</i> 201 and 215 compounds were tentatively identified as a C₉- and C₁₀-carbonyl-dicarboxylic acid, respectively, based on reaction mechanisms of campholenic aldehyde and ozone, as well as detailed interpretation of mass spectral data, in conjunction with the formation of corresponding DNPH derivatives

Terpenylic acid and related compounds: precursors for dimers in secondary organic aerosol from the ozonolysis of α- and β-pinene

In the present study, we have characterized the structure of a higher-molecular weight (MW) 358 α- and β-pinene dimeric secondary organic aerosol (SOA) product that received ample attention in previous molecular characterization studies and has been elusive. Based on mass spectrometric evidence for deprotonated molecules formed by electrospray ionization in the negative ion mode and chemical considerations, it is suggested that diaterpenylic acid is a key monomeric intermediate for dimers of the ester type. It is proposed that cis-pinic acid is esterified with the hydroxyl-containing diaterpenylic acid, which can be explained through acid-catalyzed hydrolysis of the recently elucidated lactone-containing terpenylic acid and/or diaterpenylic acid acetate, both first-generation oxidation products. To a minor extent, higher-MW 358 and 344 diester products are formed containing other terpenoic acids as monomeric units, i.e., diaterpenylic acid instead of cis-pinic acid, and diaterebic acid instead of diaterpenylic acid. It is shown that the MW 358 diester and related MW 344 compounds, which can be regarded as processed SOA products, also occur in ambient fine (PM2.5) rural aerosol collected at night during the warm period of the 2006 summer field campaign conducted at K-puszta, Hungary, a rural site with coniferous vegetation. This indicates that, under ambient conditions, the higher-MW diesters are formed in the particle phase over a longer time-scale than that required for gas-to-particle partitioning of their monomeric precursors in laboratory α-/β-pinene ozonolysis experiments

Measurements of Collision Offsets and Difference in vertical Dispersion at the LEP Interaction Points

The beam overlap at the EP interaction points is optimized by monitoring the change in the Bhabha rate during the variation of an electrostatic bump amplitude. A new method has been developed and implemented to measure the difference of the residual vertical dispersion of electrons and positrons at the interaction points based on beam separation measurements at two different beam energies