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The equations below assume a beam with a circular cross-section at all values of z; this can be seen by noting that a single transverse dimension, r, appears.Beams with elliptical cross-sections, or with waists at different positions in z for the two transverse dimensions (astigmatic beams) can also be described as Gaussian beams, but with distinct values of w 0 and of the z = 0 location for ...
Full width at half maximum. In a distribution, full width at half maximum (FWHM) is the difference between the two values of the independent variable at which the dependent variable is equal to half of its maximum value. In other words, it is the width of a spectrum curve measured between those points on the y-axis which are half the maximum ...
A molecular beam is produced by allowing a gas at higher pressure to expand through a small orifice into a chamber at lower pressure to form a beam of particles (atoms, free radicals, molecules or ions) moving at approximately equal velocities, with very few collisions between the particles.
This class applies molecular dynamic calculations that are able to analyze both low and high energy physical interactions taking place in the ion beam analysis. A key and popular feature that accompanies such techniques is the possibility for the computations to be incorporated in real time with the ion beam analysis experiment itself.
The crossed molecular beam technique was developed by Dudley Herschbach and Yuan T. Lee, for which they were awarded the 1986 Nobel Prize in Chemistry. [3] While the technique was demonstrated in 1953 by Taylor and Datz of Oak Ridge National Laboratory, [4] Herschbach and Lee refined the apparatus and began probing gas-phase reactions in unprecedented detail.
A theoretical plate in many separation processes is a hypothetical zone or stage in which two phases, such as the liquid and vapor phases of a substance, establish an equilibrium with each other.
This discards the overall phase information that would be needed for calculation of interference with other beams. Note that all Jones vectors and matrices in this article employ the convention that the phase of the light wave is given by ϕ = k z − ω t {\displaystyle \phi =kz-\omega t} , a convention used by Eugene Hecht . [ 2 ]
Euler–Bernoulli beam theory (also known as engineer's beam theory or classical beam theory) [1] is a simplification of the linear theory of elasticity which provides a means of calculating the load-carrying and deflection characteristics of beams. It covers the case corresponding to small deflections of a beam that is subjected to lateral ...