Synchrotron radiation interferometry for beam size measurement at low current and in large dynamic range

The Synchrotron Radiation Interferometry (SRI) has become a widely used technique to measure the small transverse size of the electron beam in the storage ring. In a typical SRI system for the routine storage ring operation, synchrotron radiation from a dipole magnet is used to illuminate a double slit with a small slit opening and a relatively large slit separation to form a large number of interference fringes on the observation plane. However, a different type of SRI is needed for intrabeam scattering (IBS) research to measure the beam size at ultralow currents and in a wide dynamic range. Such a system requires a double slit with a large slit opening to increase the light input while having the capability of accurately measuring the beam size with a range of visibility. By examining the impact of the nonuniform wave amplitude of synchrotron radiation and that of the varying visibility (due to a changing beam size) on the beam size measurement, we propose a new physics model for this type of SRI. This new model is validated using simulation, showing significantly improved results when compared with the conventional model. Based on this new model, we have developed and tested an SRI system dedicated to the IBS study on the Duke storage ring. This system has been used successfully to measure electron beams with about $10\mu \mathrm{A}$ of current and with a higher current but a variable size. This new physics model can also improve the measurement accuracy and consistency of the conventional SRIs, especially at low visibility.

Figure 1

Illustration of interference patterns simulated using the Synchrotron Radiation Workshop (srw) with two different double slits. (a) Simulated for a conventional SRI measurement system with a large number of interference fringes inside the main diffraction envelope. The slit separation is 5 mm and the slit opening is 0.4 mm. (b) Simulated for an SRI system with a large slit opening and a relatively small slit separation: only a few interference fringes are present inside the main diffraction envelope. The slit separation is 5 mm and the slit opening is 1.8 mm. For each subplot, the inset shows the image of the interference fringes. In each subplot, the projection of the simulated intensity distribution is shown with the data from a red rectangle in the inserted image. The $x$ axis is scaled to be equal in both plots.

Figure 2

Optical layout of an SRI-based electron beam size measurement system. Synchrotron radiation from the electron beam propagates through a double slit and a focusing lens, producing an interference pattern on the image plane of the lens, which is captured by a digital camera. A linear polarizer with its polarizing axis aligned horizontally and a narrow bandpass filter are used to improve the system performance.

Figure 3

Distribution of the synchrotron radiation intensity (blue curve) on the double slit, showing the nonuniformity light illumination over each single slit.

Figure 4

Illustration of the shifting of the single-slit diffraction envelope on the image plane due to the change of the electron’s vertical position. On the left side, the red dashed lines show the opening angle (${\theta }_{\mathrm{sr}}$) of synchrotron radiation from an in-plane electron ($y_e=0$). The purple dash-dotted lines show the angle (${\theta }_D$) subtended by the two slits. On the right side, the red and blue solid curves represent the single-slit diffraction patterns produced by an in-plane and off-plane ($y_e={\sigma }_y$) electron, respectively, with the red dotted curve showing the double-slit interference pattern for the in-plane case.

Figure 5

Comparison of fitting simulated fringe data with three models: the old model (black line), the modified old model (blue rectangle line), and the new model (the red circle dash line). It shows that the modified old model and the new model provide reasonable fittings while the old model fails. The srw simulation data are the simulated vertical intensity distribution of measurement using a $D=5\mathrm{mm}$ and $d=2\mathrm{mm}$ double-slit plate for a 1000 MeV beam with $32.1\mu \mathrm{m}$ vertical beam size.

Figure 6

Simulation results for a fixed size beam using a double slit with a fixed slit separation but a varying slit opening. (a) The relative difference between the fit beam size and the actual beam size. The blue solid line is the result using the old modified model; the red dashed line is the result based on the new model. (b) The effective slit separation $D_y^{\mathrm{eff}}$ and visibility $V$ extracted from the fit parameters in the new model. The beam energy is 1000 MeV, ${\sigma }_y=32.1\mu \mathrm{m}$, $D_y=5\mathrm{mm}$, $L_1=2\mathrm{m}$, $L_2=2\mathrm{m}$, and a $\lambda =340\mathrm{nm}$ wavelength filter is used in the simulation.

Figure 7

Simulation results using a double slit with a fixed slit separation and a fixed slit opening for beams with varying sizes. (a) The relative difference between the fit beam size and the actual beam size. The blue solid line is the result of the old modified model and the red dashed line is the result of the new model. (b) The effective separation $D_y^{\mathrm{eff}}$ and the visibility $V$ extracted from the fit parameters using the new model. The beam energy is 1000 MeV, $D_y=5\mathrm{mm}$, $d=2\mathrm{mm}$, $L_1=2\mathrm{m}$, $L_2=2\mathrm{m}$, and a 340-nm wavelength filter is used in the simulation.

Figure 8

Beam size measurement for a low current beam at the Duke storage ring. The main plot shows the projected vertical intensity distribution of the image. The blue stars are the average value of the image intensity in the selected area shown as a red rectangle in the inserted image and the red solid line is the fit curve using Eq. (17). The inset shows the average image of 22 images taken using a CMOS camera with the same exposure time (1s) and a constant gain with the background subtracted. The beam current is determined to be $12.5\pm 0.2\mu \mathrm{A}$ using an imaging technique, and the beam size is measured to be $14.6\pm 0.4\mu \mathrm{m}$. The storage ring is operated at 562 MeV in a multibunch mode

Figure 9

Beam size measurements with a varying vertical size using setups of the storage ring lattices with different emittance coupling. (a) For each of the eight sets of measurements, a representative intensity distribution (blue stars) and fitting curve (red lines) are shown, selected from one of the ten images. (b) The measured beam size with the statistical error based on ten images for each set of measurements. (c) The effective slit separation and measured visibility versus the measured beam size. All the measurements are performed with a single beam operated at 562 MeV with a current of about 10 mA.