scholarly journals Linearized method for the study of transverse instabilities driven by electron clouds

2020 ◽  
Vol 23 (8) ◽  
Author(s):  
Giovanni Iadarola ◽  
Lotta Mether ◽  
Nicolas Mounet ◽  
Luca Sabato
Keyword(s):  
Electron Clouds

scholarly journals Incoherent Effects of Electron Clouds in Proton Storage Rings

2006 ◽  
Vol 97 (3) ◽  
Author(s):  
E. Benedetto ◽  
G. Franchetti ◽  
F. Zimmermann
Keyword(s):  
Storage Rings ◽  
Proton Storage Rings ◽  
Electron Clouds

Electronic Warfare: Electrophilic Substitution

Reactions ◽  
2011 ◽  
Author(s):  
Peter Atkins
Keyword(s):  
Sulfuric Acid ◽  
Nitric Acid ◽  
Electrophilic Substitution ◽  
Proton Acceptor ◽  
Acid Molecule ◽  
Electronic Warfare ◽  
Hexagonal Ring ◽  
Initial Outcome ◽  
Concentrated Sulfuric Acid ◽  
Electron Clouds

Benzene, 1, is a hard nut to crack. The hexagonal ring of carbon atoms each with one hydrogen atom attached has a much greater stability than its electronic structure, with an alternation of double and single carbon–carbon bonds, might suggest. But for reasons fully understood by chemists, that very alternation, corresponding to a continuous stabilizing cloud of electrons all around the ring, endows the hexagon with great stability and the ring persists unchanged through many reactions. The groups of atoms attached to the ring, though, may come and go, and the reaction type responsible for replacing them is commonly ‘electrophilic substitution’. Whereas the missiles of Reaction 15 sniff out nuclei by responding to their positive electric charge shining through depleted regions of electron clouds, electrophiles, electron lovers, are missiles that do the opposite. They sniff out the denser regions of electron clouds by responding to their negative charge. Let’s suppose you want to make, for purposes you are perhaps unwilling to reveal, some TNT; the initials denote trinitrotoluene. You could start with the common material toluene, which is a benzene ring with a methyl group (–CH3) in place of one H atom, 2. Your task is to replace three of the remaining ring H atoms with nitro groups, –NO2, to achieve 3. And not just any of the H atoms: you need the molecule to have a symmetrical array of these groups because other arrangements are less stable and therefore dangerous. It is known that a mixture of concentrated nitric and sulfuric acids contains the species called the ‘nitronium ion’, NO2+, 4, and this is the reagent you will use. Before we watch the reaction itself, it is instructive to see what happens when concentrated sulfuric acid and nitric acid are mixed. If we stand, suitably protected, in the mixture, we see a sulfuric acid molecule, H2SO4, thrust a proton onto a neighbouring nitric acid molecule, HNO3. (Funnily enough, according to the discussion in Reaction 2, nitric ‘acid’ is now acting as a base, a proton acceptor! I warned you of strange fish in deep waters.) The initial outcome of this transfer is unstable; it spits out an H2O molecule which wanders off into the crowd. We see the result: the formation of a nitronium ion, the agent of nitration and the species that carries out the reaction for you.

Average value of the shape and direction factor in the equation of refractive index

2017 ◽  
Vol 31 (29) ◽  
pp. 1750263 ◽  
Author(s):  
Tao Zhang
Keyword(s):  
Refractive Index ◽  
Theoretical Calculation ◽  
Calculation Method ◽  
Electromagnetic Induction ◽  
Optical Materials ◽  
Electron Cloud ◽  
Refractive Indices ◽  
Average Value ◽  
Electron Clouds ◽  
Induction Energy

The theoretical calculation of the refractive indices is of great significance for the developments of new optical materials. The calculation method of refractive index, which was deduced from the electron-cloud-conductor model, contains the shape and direction factor [Formula: see text]. [Formula: see text] affects the electromagnetic-induction energy absorbed by the electron clouds, thereby influencing the refractive indices. It is not yet known how to calculate [Formula: see text] value of non-spherical electron clouds. In this paper, [Formula: see text] value is derived by imaginatively dividing the electron cloud into numerous little volume elements and then regrouping them. This paper proves that [Formula: see text] when molecules’ spatial orientations distribute randomly. The calculations of the refractive indices of several substances validate this equation. This result will help to promote the application of the calculation method of refractive index.

Effective Ion Mobility Calculations for Macromolecules by Scattering on Electron Clouds

2014 ◽  
Vol 118 (34) ◽  
pp. 6763-6772 ◽  
Author(s):  
Yuri Alexeev ◽  
Dmitri G. Fedorov ◽  
Alexandre A. Shvartsburg
Keyword(s):  
Ion Mobility ◽  
Electron Clouds
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