Functions Of Transverse Coordinate Research Articles

Initial Conditions with Flow from a McLerran Venugopalan model with Transverse Dynamics

Using a recursive solution of the Yang-Mills equation, we calculate analytic expressions for the gluon fields created in ultra-relativistic heavy ion collisions at small times τ. We have worked out explicit solutions for the fields and the energy momentum tensor up to 4th order in an expansion in τ. We generalize the McLerran-Venugopalan model to allow for a systematic treatment of averaged charge densities μ2 that vary as a function of transverse coordinates. This allows us to calculate radial, elliptic and directed flow of gluon fields. Our results can serve as initial conditions for hydrodynamic simulations of nuclear collisions that include initial flow.

Calculation of Layered Shells by the Pseudogeometrical–Nonlinearity Method

The problem of determining the stress—strain state of a multilayered shell is solved. It is assumed that the layer material is nonlinearly elastic and the strain—displacement relations are nonlinear. The displacements are expanded in terms of the functions of transverse coordinate that contain unknown parameters. The governing equations are derived with the use of the Lagrange variational principle. A technique for minimizing the energy functional is proposed. An example of a three–layered beam is considered, calculation results are compared with the exact solution, and the specific features of the approach proposed are analyzed.

Transverse phase space mapping of relativistic electron beams using optical transition radiation

Optical transition radiation (OTR) has proven to be a versatile and effective diagnostic for measuring the profile, divergence, and emittance of relativistic electron beams with a wide range of parameters. Diagnosis of the divergence of modern high brightness beams is especially well suited to OTR interference (OTRI) techniques, where multiple dielectric or metal foils are used to generate a spatially coherent interference pattern. Theoretical analysis of measured OTR and OTRI patterns allows precise measurement of electron beam emittance characteristics. Here we describe an extension of this technique to allow mapping of divergence characteristics as a function of transverse coordinates within a measured beam. We present the first experimental analysis of the transverse phase space of an electron beam using all optical techniques. Comparing an optically masked portion of the beam to the entire beam, we measure different angular spread and average direction of the particles. Direct measurement of the phase-space ellipse tilt angle has been demonstrated using this optical masking technique.