On the Use of Crystals with an Asymmetric Reflection Geometry to Measure the Parameters of Electron Beams

Use of parametric X-ray radiation of electrons in crystals to determine the parameters of imaging-plates

“…In this case, the only unknown parameter requiring experimental determination is 𝜉 IP . A comparison of the measurement and calculation results for different crystal orientations, carried out using an IPU-type IP, showed a difference in the shape of the experimental and calculated dependences in the center of the distributions [15]; that is, not all the conditions necessary for an accurate determination of 𝜂(𝜔 𝑖 (𝜃 𝑥 , 𝜃 𝑦 )) are executed. Therefore, the required parameters that must be determined from the measurement results are not only 𝜉 IP but also the yield of photo-stimulated radiation per photon incident on the plate (i.e., 𝜒 IP (𝜔 𝑖 (𝜃 𝑥 , 𝜃 𝑦 )) = 𝜂(𝜔 𝑖 (𝜃 𝑥 , 𝜃 𝑦 ))𝜉 IP ).…”

“…The quantity 𝜒 IP ( ω𝑖 ) = 𝜂( ω𝑖 ) 𝜉 IP , where ω𝑖 is the average energy radiation for the 𝑖th order of reflection, can be estimated using the least-squares method by minimizing the difference between the experimental and calculated dependences [15]:…”

“…Studies of the parameters for the plates were carried out for the (111) reflection plane and for a 0.5 m distance between the crystal and the detector to reduce absorption in the air and increase the intensity of the recorded radiation. In addition, we analyzed the measurement results presented in previous works [5,15,16] and those obtained using the IPU-type IP.…”

“…As noted above, to compare the measurement results with calculations and thereby determine the parameters describing the second and third stages of radiation registration using an IP, it is necessary to consider all mechanisms and orders of reflection, the electron beam sizes [14,15], the radiation absorption along the path from the crystal to the detector, and the results of the first stage.…”

“…The values of photo-stimulated emission yields 𝜒 IP ( ω𝑖 ) per photon, obtained by fitting the measurement results and calculating vertical angular distributions for the reflecting plane (111), are given in table 1 for all studied plates. The values of 𝜒 IPU ( ω𝑖 ) for an IPU plate and all previously studied crystal orientations [5,15,16] are also presented here. Errors are statistical and do not include normalization and calculation model errors.…”