Hilbert space models commodity exchanges

It is argued that the vector space measures used to measure closeness of market prices to predictors for market prices are invalid because of the observed metric of commodity space. An alternative representation in Hilbert space within which such measures do apply is proposed. It is shown that commodity exchanges can be modeled by the application of unitary operators to this space

Plasma density from Cerenkov radiation, betatron oscillations, and beam steering in a plasma wakefield experiment at 30 GeV

A method for using Cerenkov radiation near atomic spectral lines to measure plasma source properties for plasma wakefield applications has been discussed and experimentally verified. Because the radiation co-propagates with the electron beam, the radiation samples the source properties exactly along the path of interest with perfect temporal synchronization. Observation wavelengths were chosen with respect to the atomic resonances of the plasma source, where the relative change in the index of refraction strongly affects the Cerenkov cone angle, and permits flexible diagnostic design. The Cerenkov spatial profiles were systematically studied for a Lithium heat pipe oven as a function of oven temperature and observation wavelength. Neutral densities and plasma densities were extracted from the measurements

Transverse envelope dynamics of a 28.5 GeV electron beam in a long plasma

The transverse dynamics of a 28.5 GeV electron beam propagating in a 1.4 m long, 0-2 x 10^14 cm^-3 plasma are studied experimentally in the underdense or blow-out regime. The transverse component of the wake field excited by the short electron bunch focuses the bunch, which experiences multiple betatron oscillations as the plasma density is increased. The spot size variations are observed using optical transition radiation and Cherenkov radiation. In this regime, the behavoir of the spot size as a function of the plasma density is well described by a simple beam envelope model. Dynamic changes of the beam envelope are observed by time resolving the Cherenkov light