Inferred electron beam radius via a thermodynamic model of target expansion*

Flash x-ray radiography with Intense relativistic electron beams (IREBs) is used in several application areas.

In typical usage, an intense electron beam ($>1$kA, typical) rapidly impinges a high-Z converter target and

produces \emph{bremsstrahlung} radiation for imaging.

This process rapidly deposits significant energy into the target material which heats and expands due to internal pressure.

Previous estimates attempt to use ideal gas relationships to describe the state of the expanding target.

For high-Z materials, however, significant complications arise because of changing ionization fraction.

This work constructs a thermodynamic description of the target material using ionization balance and excited states

determined by the collisional-radiative code FLYCHK[1].

A simple fluid expansion is then modeled using isochoric heating and adiabatic expansion steps.

Velocity is determined by momentum balance an an entropy limit.

Experiments varying beam time by a factor of two show a change in terminal velocity from 2.5--6 km/s of an expanding

Mo foil.

Inferred beam spot-sizes radii range from 350-650$\mu$m.

[1] H.-K. Chung, \emph{et al.}, \emph{High Energy Density Phys.} \textbf{1} (2005) 3--12.