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Understanding and predicting complex dynamics in accelerators is necessary for their successful operation. A grand challenge in accelerator physics is to develop predictive virtual accelerators that mitigate design cost and schedule risk. Data-driven techniques greatly appeal to generating virtual accelerators due to their limited dimensionality compared with first-principle simulation, yet require significant up-front investment and lack interpretability in the context of governing equations. This paper uses an alternative, interpretable, data-driven technique called Sparse Identification of Nonlinear Dynamics (SINDy) developed by University of Washington researchers to study nonlinear beam centroid dynamics excited by realistic beam injection. We propose evolution equations based solely on data analysis and intuition of the underlying lattice structure, without recourse to an underlying first-principles centroid model nor the actual lattice forcing functions. We do this to mimic an application environment where analytic models are inadequate or where detailed lattice forcing functions are unknown. In the context of the accurate centroid model, we report and interpret SINDy's beam evolution equations learned from the training data and show favorable prediction results. We compare with an alternative machine learning model used on the same training data and contrast its prediction ability, computational expense, and interpretability with SINDy's results.

Terawatt x-ray free-electron lasers (XFELs) represent the frontier in further development of x-ray sources and require high current densities with strong transverse focusing. In this paper, we investigate the implications/potentialities of TW XFELs on the generation of harmonics at still shorter wavelengths and higher photon energies with variable polarization. The simulations indicate that significant power levels are possible at high harmonics of the XFEL resonance and that these XFELs can be an important coherent source of hard x-rays through the gamma ray spectrum. For this purpose, we use the MINERVA simulation code which self-consistently includes harmonic generation. Both helical and planar undulators are discussed in which the fundamental is at 1.5 {\AA} and study the associated harmonic generation. While tapered undulators are needed to reach TW powers at the fundamental, the taper does not enhance the harmonics because the taper must start before saturation of the fundamental, while the harmonics saturate before this point is reached. Nevertheless, the harmonics reach substantial powers. Simulations indicate that, for the parameters under consideration, peak powers of the order of 180 MW are possible at the fifth harmonic with a photon energy of about 41 keV and still high harmonics may also be generated at substantial powers. Such high harmonic powers are certain to enable a host of enhanced applications, Comment: 7 pages, 12 figures

High peak and average power free-electron lasers (FELs) in the terahertz region (THz) require small diameter, low-emittance, and high voltage electron beams. This paper presents two 1.5-2 MV, 100-200 A, thermionic cathode electron source approaches for compact megawatt range peak power, multi-kilowatt average power, high repetition rate, THz FELs. The preferred beam generation system includes grading electrodes and is quite compact compared to the other standard diode gun approaches. Both provide highly compressed beams at the waist having low values of normalized rms emittance. In particular, the new injector approach with grading electrodes, operating at a body voltage of 1.5-2 MV and 100 A, has a normalized rms emittance of roughly 10 mm-mrad at the beam waist. Power supply switching considerations are considered in the paper as well as considerations for very high-voltage multi-stage depressed collectors for device efficiency enhancement. Based on these designs, we provide performance estimates for FELs operating in the THz spectral region.

Students at Colorado College and cadets at the US Air Force Academy have conducted an experimental test of gravitational time dilation. This relativistic effect, highlighted in the movie Interstellar, causes clocks to tick more slowly near massive objects. A measurement of gravitational time dilation was made by comparing signals generated by a GPS frequency standard, which is based on sea-level time, to a cesium-beam frequency standard located at three different elevations above sea level. The effect is small but observable; for the highest elevation studied (4302 m on the summit of Pikes Peak), a local clock ticks only 41 ns/day faster than a sea-level clock. Our results are consistent with the predictions of general relativity. We also discuss implications of gravitational time dilation on GPS operations., Comment: 3 pages, 2 figures

General relativity predicts that clocks run more slowly near massive objects. The effect is small---a clock at sea level lags behind one 1000 m above sea level by only 9.4 ns/day. Here, we demonstrate that a measurement of this effect can be done by undergraduate students. Our paper describes an experiment conducted by undergraduate researchers at Colorado College and the United States Air Force Academy to measure gravitational time dilation. The measurement was done by comparing the signals generated by a GPS frequency standard (sea-level time) to a Cs-beam frequency standard at seven different altitudes above sea level. We found that our measurements are consistent with the predictions of general relativity.