We present a new measurement of the positive muon magnetic anomaly, a µ ≡ (gµ − 2)/2, from the Fermilab Muon g −2 Experiment based on data collected in 2019 and 2020. We have analyzed more than four 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 two due to better running conditions, a more stable beam, and improved knowledge of the magnetic field weighted by the muon distribution, ω′ p , and of the anomalous precession frequency corrected for beam dynamics effects, ωa. From the ratio ωa/ω ′ 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 aµ(Exp) = 116 592 059(22) × 10 −11 (0.19 ppm), which represents a factor of two improvement in precision.

We present an idea for creation of a crystalline undulator and report its first realization. One face of a silicon crystal was given periodic micro-scratches (trenches) by means of a diamond blade. The X-ray tests of the crystal deformation due to given periodic pattern of surface scratches have shown that a sinusoidal shape is observed on both the scratched surface and the opposite (unscratched) face of the crystal, that is, a periodic sinusoidal deformation goes through the bulk of the crystal. This opens up the possibility for experiments with high-energy particles channeled in crystalline undulator, a novel compact source of radiation. The wavelength λ of a photon emitted in an undulator is in proportion to the undulator period L and in inverse proportion to the square of the particle Lorentz factor γ. The minimal period L achieved presently with the electromagnetic undulators is limited to several millimeters [1], with respective restriction on the photon energy in the order of ћω=2πћγ 2 c/L. The crystalline undulators (CU) with periodically deformed crystallographic planes offer huge electromagnetic fields and could provide a quite short period L of an undulator in sub-millimeter range. This way one can also arrange for substantial amplitudes A of oscillation for the particles channeled through the undulator and thus increase the intensity of the radiation.Currently, bent crystals are largely used for channeling extraction of 70-GeV protons at IHEP (Protvino) with efficiency reaching 85% at intensity well over 10 12 particle With a strong world-wide attention to novel sources of radiation, there has been broad theoretical interest to compact crystalline undulators, with some approaches covering also nanotechnology to make use of nanotubes to guide radiating particles [4][5][6][7][8][9][10][11][12] In bent crystal channeling experiments at IHEP Protvino with 70-GeV protons, it was found that accidental micro-scratches on a crystal surface caused a deformation of the crystallographic planes to substantial depths, down to a few hundred microns as depicted in Fig. 1(a). The picture of the plane parallelism violation can be reconstructed through analysis of the profile data of 70-GeV protons channeled in crystals (ref.[15], p.120). This analysis shows that the protons in the vicinity of scratches are retained in channeling mode but do experience a substantial angular deviation following the deformation of the crystal planes. Therefore, this effect could be profitably used for creation of CU by making a periodic series of micro trenches on the crystal surface as shown on Fig. 1(b).For the first experimental proof of the method, a special diamond blade scratched one face of a silicon plate by a set of parallel trenches (grooves). A sample with dimensions of 50 x 17 x 0.48 mm 3 was prepared from commercial silicon wafer. The large polished faces of the sample were parallel to crystallographic planes (0 0 1), other faces were parallel to planes (0 1 1) and (0 1 -1). On one of the large faces of the sample, ...

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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.

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.