Spatial and Temporal Coherence Effects in Parametric X-ray Radiation

8 Sept 2015, 18:00
1h 30m
Poster 3. Parametric X- Radiation Poster Section

Speaker

Alexander Potylitsyn (National Research Tomsk Polytechnic University)

Description

Coherent emission from an electron bunch moving in magnetic fields is described using the phase shift for each electron in a bunch [1] $\varphi^{(i)}_{SR}=\exp\left \{i~\mathit{\mathbf{k~r}}_i \right \}$, where $\mathbf k$ the wave vector, $\mathbf r_i= \left\{x_i,y_i,z_i\right\}$ is radius-vector of $i$-th electron. For such radiation mechanism as parametric X-ray radiation (PXR) for which atom electrons from crystallographic plane are emission sources the time dependence has to be included into phase shift: $$ \varphi^{(i)}_{PXR}=\exp\left \{i\left(\mathit{\mathbf{k~r}}^{(i)}_{pl}-\omega~t^{(i)} \right)\right \},~~~~~~~~~(1) $$ Here $\mathit{\mathbf{r}}^{(i)}_{pl}$ is radius-vector characterizing the point at the plane where $i$-th electron crosses it, $t^{(i)}$ is the time interval characterizing time of this crossing. The first term in (1) is responsible for spatial coherence, the second one - for temporal. If a crystallographic plane is tilted at the angle $\theta_B$ relative to the electron beam then we have: $$ \mathit{\mathbf{r}}^{(i)}_{pl}=\left \{x_i,y_i,z_i/\tan\theta_B\right \}, \omega t^{(i)}=\frac{2 \pi}{\beta\lambda}\left (x_i/\tan \theta_B-z_i\right ) $$ Influence of both terms on characteristics of coherent PXR produced by microbunched beams is considered in the report. [1] Y.Shibata, K.Ishi, T.Ohsaka et al. NIM A 301(1991) 161-166

Author

Alexander Potylitsyn (National Research Tomsk Polytechnic University)

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