On the delay time for the onset of radiographic spot size growth

We have revisited the physical mechanisms, which lead to a time delay of the onset of the undesirable spot size growth in high-dose X-ray radiography. In our theoretical model, the delay time is partially due to the time needed for the electron beam to thermally ionize the target spot resulting in target ions and partially due to the time needed for the ions to form a column of at least a quarter of the betatron wavelength of the electron beam, Based on our model, an analytic formula is derived, and it has been found to be consistent with experimental observations for different target materials and beam parameters. Our analysis shows that the delay time is directly proportional to the beam spot size at the target and inversely proportional to the beam current. Our calculations further show the spot size of the DARHT-1 beam with 2 kA current should be stable because the delay time of about 69 ns is longer then the beam pulse length.