Measurement of the Positive Muon Anomalous Magnetic Moment to 0.20 ppm.

We present a new measurement of the positive muon magnetic anomaly, a_{µ}≡(g_{µ}-2)/2, from the Fermilab Muon g-2 Experiment using data collected in 2019 and 2020. We have analyzed more than 4 times the number of positrons from muon decay than in our previous result from 2018 data. The systematic error is reduced by more than a factor of 2 due to better running conditions, a more stable beam, and improved knowledge of the magnetic field weighted by the muon distribution, ω[over ˜]_{p}^{'}, and of the anomalous precession frequency corrected for beam dynamics effects, ω_{a}. From the ratio ω_{a}/ω[over ˜]_{p}^{'}, together with precisely determined external parameters, we determine a_{µ}=116 592 057(25)×10^{-11} (0.21 ppm). Combining this result with our previous result from the 2018 data, we obtain a_{µ}(FNAL)=116 592 055(24)×10^{-11} (0.20 ppm). The new experimental world average is a_{µ}(exp)=116 592 059(22)×10^{-11} (0.19 ppm), which represents a factor of 2 improvement in precision.

Synchrotron radiation transmission by two coupled flat microchannel plates: new opportunities to control the focal spot characteristics.

An improved theoretical model to calculate the focal spot properties of coherent synchrotron radiation (SR) soft X-ray beams by combining and aligning two microchannel plates (MCPs) is presented. The diffraction patterns of the radiation behind the MCP system are simulated in the framework of the electrodynamical model of the radiation emission from two-dimensional finite antenna arrays. Simulations show that this particular optical device focuses the soft X-ray radiation in a circular central spot with a radius of ∼4 µm. The study points out that such MCP-based devices may achieve micrometre and sub-micrometre spot sizes as required by many applications in the soft X-ray range. Finally, based on experimental and theoretical results of the radiation transmission by this MCP-based device, a new method to characterize the spatial properties of brilliant SR sources is discussed.

Measurement of the Positive Muon Anomalous Magnetic Moment to 0.46 ppm.

We present the first results of the Fermilab National Accelerator Laboratory (FNAL) Muon g-2 Experiment for the positive muon magnetic anomaly a_{µ}≡(g_{µ}-2)/2. The anomaly is determined from the precision measurements of two angular frequencies. Intensity variation of high-energy positrons from muon decays directly encodes the difference frequency ω_{a} between the spin-precession and cyclotron frequencies for polarized muons in a magnetic storage ring. The storage ring magnetic field is measured using nuclear magnetic resonance probes calibrated in terms of the equivalent proton spin precession frequency ω[over ˜]_{p}^{'} in a spherical water sample at 34.7 °C. The ratio ω_{a}/ω[over ˜]_{p}^{'}, together with known fundamental constants, determines a_{µ}(FNAL)=116 592 040(54)×10^{-11} (0.46 ppm). The result is 3.3 standard deviations greater than the standard model prediction and is in excellent agreement with the previous Brookhaven National Laboratory (BNL) E821 measurement. After combination with previous measurements of both µ^{+} and µ^{-}, the new experimental average of a_{µ}(Exp)=116 592 061(41)×10^{-11} (0.35 ppm) increases the tension between experiment and theory to 4.2 standard deviations.

Wave propagation and focusing of soft X-rays by spherical bent microchannel plates.

Synchrotron radiation sources have been used to study the focusing properties and angular distribution of X-ray radiation at the exit of spherically bent microchannel plates (MCPs). In this contribution it is shown how soft X-ray radiation at energies up to 1.5 keV can be focused by spherically bent MCPs with curvature radii R of 30 mm and 50 mm. For these devices, a focus spot is detectable at a distance between the detector and the MCP of less than R/2, with a maximum focusing efficiency up to 23% of the flux illuminating the MCP. The soft X-ray radiation collected at the exit of microchannels of spherically bent MCPs are analyzed in the framework of a wave approximation. A theoretical model for the wave propagation of radiation through MCPs has been successfully introduced to explain the experimental results. Experimental data and simulations of propagating radiation represent a clear confirmation of the wave channeling phenomenon for the radiation in spherically bent MCPs.

Excitation and propagation of X-ray fluorescence through thin devices with hollowed ordered structures: comparison of experimental and theoretical spectra.

The lack of models describing the propagation of X-rays in waveguides and the interference mechanism between incident and reflected radiation waves hamper the understanding and the control of wave propagation phenomena occurring in many real systems. Here, experimental spectra collected at the exit of microchannel plates (MCPs) under the total X-ray reflection condition are presented. The results are discussed in the framework of a theoretical model in which the wave propagation is enhanced by the presence of a transition layer at the surface. The angular distributions of the propagating radiation at the exit of these MCPs with microchannels of ∼3 µm diameter will also be presented and discussed. These spectra show contributions associated with the reflection of the primary monochromatic beam and with the fluorescence radiation originating from the excitation of atoms composing the surface of the microchannel. The soft X-ray fluorescence spectra collected at the exit of microcapillaries were analyzed in the framework of a wave approximation while diffraction contributions observed at the exit of these hollow X-ray waveguides have been calculated using the Fraunhofer diffraction model for waves in the far-field domain. Data collected at the Si L-edge show that in glassy MCPs the fluorescence radiation can be detected only when the energy of the primary monochromatic radiation is above the absorption edge for grazing angles higher than half of the critical angle of the total reflection phenomenon. Experimental data and simulations of the propagating radiation represent a clear experimental confirmation of the channeling phenomenon of the excited fluorescence radiation inside a medium and point out that a high transmission can be obtained in waveguide optics for parameters relevant to X-ray imaging.

Elemental mapping and microimaging by x-ray capillary optics.

Recently, many experiments have highlighted the advantage of using polycapillary optics for x-ray fluorescence studies. We have developed a special confocal scheme for micro x-ray fluorescence measurements that enables us to obtain not only elemental mapping of the sample but also simultaneously its own x-ray imaging. We have designed the prototype of a compact x-ray spectrometer characterized by a spatial resolution of less than 100 microm for fluorescence and less than 10 microm for imaging. A couple of polycapillary lenses in a confocal configuration together with a silicon drift detector allow elemental studies of extended samples (approximately 3 mm) to be performed, while a CCD camera makes it possible to record an image of the same samples with 6 microm spatial resolution, which is limited only by the pixel size of the camera. By inserting a compound refractive lens between the sample and the CCD camera, we hope to develop an x-ray microscope for more enlarged images of the samples under test.

Wave-field formation in a hollow x-ray waveguide.

Diffraction and refraction phenomena at the entrance of a hollow x-ray waveguide with weakly absorbing dielectric cladding layers are investigated using two independent approaches: (a) analytical and (b) numerical solutions of the wave equation in the paraxial (parabolic) approximation. It is shown that the wave penetrating through the cladding material substantially modifies the wave field near the waveguide entrance. It results in a significant increase of the total energy flux inside the guiding layer and in additional spatial modulation of the electromagnetic field.

Experimental study for the feasibility of a crystalline undulator.

We present an idea for creation of a crystalline undulator and report its first realization. One face of a silicon crystal was given periodic microscratches (grooves) by means of a diamond blade. The x-ray tests of the crystal deformation due to a given periodic pattern of surface scratches have shown that a sinusoidal-like shape is observed on both the scratched surface and the opposite (unscratched) face of the crystal; that is, a periodic sinusoidal-like deformation goes through the bulk of the crystal. This opens up the possibility for experiments with high-energy particles channeled in a crystalline undulator, a novel compact source of radiation.

Coherent and incoherent components of a synchrotron radiation spot produced by separate capillaries.

We discuss soft-x-ray focusing properties of separate capillaries. It is shown that a nonnegligible fraction of the synchrotron radiation beam transmitted by the capillary is modal. Experimental and theoretical data are discussed to explain the superposition pattern of x rays in the focal plane due to the interference phenomena of electromagnetic radiation propagating through separate capillaries.

Single-reflection regime of X rays that travel into a monocapillary.

We present an analysis of the transmission of x rays through a single monocapillary under the single-reflection regime. Because ray tracing does not provide an explanation for experimental data, we give a qualitative interpretation of the observed behavior within the framework of wave theory.

Observation of Interference Effects at the Focus of an X-ray Lens.

During an experiment on synchrotron radiation focusing with a capillary lens, an interference structure was observed at the focal spot of the lens, despite the fact that the lens capillary diameter is about a million times greater than the wavelength of the X-ray photons (600 mum and 8 A, respectively). The width of the central peak is close to the capillary diameter. At the same time the synchrotron radiation concentration increased by more than one hundred times. Analysis shows that the capillary lens acts in many respects as a macroscopic crystal. The observed effect is accounted for by wave theory. This phenomenon may have important practical effects in many fields.