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This paper addresses the problem of determining the optimum shape for a beer glass that minimizes the heat transfer while the liquid is consumed, thereby keeping it cold for as long as possible. The proposed solution avoids the use of insulating materials. The glass is modeled as a body of revolution generated by a smooth curve, constructed from a material with negligible thermal resistance, but insulated at the base. The ordinary differential equation describing the problem is derived from the first law of Thermodynamics applied to a control volume encompassing the liquid. This is an inverse optimization problem, aiming to find the shape of the glass (represented by curve $S$) that minimizes the heat transfer rate. In contrast, the direct problem aims to determine the heat transfer rate for a given geometry. The solution obtained here is analytic, and the resulting function describing the relation between height ans radius of the glass, is in closed form, providing a family of optimal glass shapes that can be manufactured by conventional methods. Special attention is payed to the dimensions and the capacity of the resulting shapes., Comment: 16 pages, 8 figures. arXiv admin note: substantial text overlap with arXiv:2402.18544

Since the invention of the laser nonlinear effects such as filamentation, Rabi-cycling and collective emission have been explored in the optical regime leading to a wide range of scientific and industrial applications. X-ray free electron lasers (XFELs) have led to the extension of many optical techniques to X-rays for their advantages of angstrom scale spatial resolution and elemental specificity. One such example is XFEL driven population inversion of 1s core hole states resulting in inner-shell K${\alpha}$ (2p to 1s) X-ray lasing in elements ranging from neon to copper, which has been utilized for nonlinear spectroscopy and development of next generation X-ray laser sources. Here we show that strong lasing effects, similar to those observed in the optical regime, can occur at 1.5 to 2.1 angstrom wavelengths during high intensity (> ${10^{19}}$ W/cm${^{2}}$) XFEL driven inner-shell lasing and superfluorescence of copper and manganese. Depending on the temporal substructure of the XFEL pump pulses, the resulting inner-shell X-ray laser pulses can exhibit strong spatial inhomogeneities as well as spectral inhomogeneities and broadening. Through 3D Maxwell Bloch theory we show that the observed spatial inhomogeneities result from X-ray filamentation, and that the spectral broadening is driven by Rabi cycling with sub-femtosecond periods. These findings indicate that we have generated Angstrom-wavelength x-ray pulses (containing ${10^{6}}$ - ${10^{8}}$ photons) in the strong lasing regime, some of them with pulse lengths of less than 100 attoseconds.

This paper addresses the problem of determining the optimum shape for a beer glass that minimizes the heat transfer while the liquid is consumed, thereby keeping it cold for as long as possible. The proposed solution avoids the use of insulating materials. The glass is modelled as a body of revolution generated by a smooth curve S, constructed from a material with negligible thermal resistance at the revolution surface but insulated at the bottom. The ordinary differential equation describing the problem is derived from the first law of Thermodynamics applied to a control volume encompassing the liquid. This is an inverse optimization problem, aiming to find the shape of the glass (represented by curve S) that minimizes the heat transfer rate. In contrast, the direct problem aims to determine the heat transfer rate for a given geometry. The solution obtained is analytic, and the resulting expression for S is in closed form, providing a family of optimal glass shapes that can be manufactured using conventional methods., Comment: 10 pages, 7 figures

In a recent paper we proposed to build an x-ray laser oscillator (XLO) in the 6-10 keV range providing intense, stable, transform-limited, x-ray pulses based on population inversion driven by an x-ray pulse train generated by an x-ray free-electron laser (XFEL) operated at a repetition rate of about 100 Hz. Here we present an analysis of recent experimental results on x-ray lasing with population inversion, damage caused by the pump on the lasing medium, and optical cavities, together with theoretical/numerical simulations. Our findings suggest that it is possible to build and operate a second-generation x-ray laser oscillator, XLO-II, operating at up to 125 kHz repetition rate. XLO-II will be pumped by 6-10 keV x-ray SASE pulses, generated by the new LCLS-II-HE XFEL now under construction at SLAC National Accelerator Laboratory, utilizing a CW superconducting linac and capable of running at 1 MHz repetition rate. XLO-II will generate transform-limited, coherent x-ray pulses with an average power in the tens of mW range. It will open new experimental capabilities, for instance in fields like imaging, interferometry, and quantum x-ray optics. The main characteristics of XLO-II and its main components, including the optical cavity, will be discussed.

Coherent nonlinear spectroscopies and imaging in the X-ray domain provide direct insight into the coupled motions of electrons and nuclei with resolution on the electronic length and time scale. The experimental realization of such techniques will strongly benefit from access to intense, coherent pairs of femtosecond X-ray pulses. We have observed phase-stable X-ray pulse pairs containing more thank 3 x 10e7 photons at 5.9 keV (2.1 Angstrom) with about 1 fs duration and 2-5 fs separation. The highly directional pulse pairs are manifested by interference fringes in the superfluorescent and seeded stimulated manganese K-alpha emission induced by an X-ray free-electron laser. The fringes constitute the time-frequency X-ray analogue of the Young double-slit interference allowing for frequency-domain X-ray measurements with attosecond time resolution., Comment: 39 pages, 13 figures, to be published

Novel emergent phenomena are expected to occur under conditions exceeding the QED critical electric field, where the vacuum becomes unstable to electron-positron pair production. The required intensity to reach this regime, $\sim10^{29}\,\mathrm{Wcm^{-2}}$, cannot be achieved even with the most intense lasers now being planned/constructed without a sizeable Lorentz boost provided by interactions with ultrarelativistic particles. Seeded laser-laser collisions may access this strong-field QED regime at laser intensities as low as $\sim10^{24}\,\mathrm{Wcm^{-2}}$. Counterpropagating e-beam--laser interactions exceed the QED critical field at still lower intensities ($\sim10^{20}\,\mathrm{Wcm^{-2}}$ at $\sim10\,\mathrm{GeV}$). Novel emergent phenomena are predicted to occur in the "QED plasma regime", where strong-field quantum and collective plasma effects play off one another. Here the electron beam density becomes a decisive factor. Thus, the challenge is not just to exceed the QED critical field, but to do so with high quality, approaching solid-density electron beams. Even though laser wakefield accelerators (LWFA) represent a very promising research field, conventional accelerators still provide orders of magnitude higher charge densities at energies $\gtrsim10\,\mathrm{GeV}$. Co-location of extremely dense and highly energetic electron beams with a multi-petawatt laser system would therefore enable seminal research opportunities in high-field physics and laboratory astrophysics. This white paper elucidates the potential scientific impact of multi-beam capabilities that combine a multi-PW optical laser, high-energy/density electron beam, and high-intensity x rays and outlines how to achieve such capabilities by co-locating a 3-10 PW laser with a state-of-the-art linear accelerator., Comment: 3 pages

We show the feasibility of generating X-ray pulses in the 4 to 8 keV fundamental photon energy range with 0.65 TW peak power, 15 fs pulse duration, $9\times10^{-5}$ bandwidth, using the LCLS-II copper linac and hard X-ray (HXR) undulator. Third harmonic pulses with 8-12 GW peak power and narrow bandwidth are also generated. High power and small bandwidth X-rays are obtained using two electron bunches separated by about 1 ns, one to generate a high power seed signal, the other to amplify it by tapering the magnetic field of the HXR undulator. The bunch delay is compensated by delaying the seed pulse with a four crystals monochromator. The high power seed leads to higher output power and better spectral properties, with $>$94\% of the X-ray power being within the near transform limited bandwidth. We discuss some of the experiments made possible by X-ray pulses with these characteristics, like single particle imaging and high field physics.

We outline the fundamental coherent radiation emission processes from a bunched charged particles beam. In contrast to spontaneous emission of radiation from a random electron beam that is proportional to the number of particles, a pre-bunched electron beam can emit spontaneously coherent radiation proportional to the number of particles - squared, through the process of (spontaneous) superradiance (SP-SR) (in the sense of Dicke's). The coherent SP-SR emission of a bunched electron beam can be even further enhanced by a process of stimulated-superradiance (ST-SR) in the presence of a seed injected radiation field. In this review, these coherent radiation emission processes for both single bunch and periodically bunched beams are considered in a model of radiation mode expansion. The general model of coherent spontaneous emission is extended to the nonlinear regime, particularly for undulator (wiggler) interaction: Tapering-Enhanced Stimulated Superradiant Amplification (TESSA). Processes of SP-SR and TESSA take place in tapered wiggler seed-injected FELs. In such FELs, operating in the X-Ray regime, these processes are convoluted with other effects. However these fundamental emission concepts are useful guidelines for the strategy of wiggler tapering efficiency and power enhancement. Based on this model, we review previous theories and experiments on coherent radiation sources based on SP-SR (coherent undulator radiation, synchrotron radiation, Smith-Purcell radiation etc.), in the THz regime and on-going works on tapered wiggler efficiency-enhancement concepts in all optical frequency regimes up to X-Rays., Comment: 109 pages, 34 figures

Bruno Touschek's life as a physicist spanned the period from World War II to the 1970s. He was a key figure in the developments of electron-positron colliders, storage rings, and gave important contributions to theoretical high energy physics. Storage rings, initially developed for high energy physics, are being widely used in many countries as synchrotron radiation sources and are a tool for research in physics, chemistry, biology environmental sciences and cultural heritage studies. We describe Touschek's life in Austria, where he was born, Germany, where he participated to the construction of a betatron during WWII, and Italy, where he proposed and led to completion the first electron-positron storage ring in 1960, in Frascati. We highlight how his central European culture influenced his life style and work, and his main contributions to physics, such as the discovery of the Touschek effect and beam instabilities in the larger storage ring ADONE., Comment: 24 pages, 17 figure, invited article submitted for publication in Reviews of Accelerator Science and Technology

We study high efficiency, multi-terawatt peak power, few angstrom wavelength, X-ray Free Electron Lasers (X-ray FELs). To obtain these characteristics we consider an optimized undulator design: superconducting, helical, with short period and built-in strong focusing. This design reduces the length of the breaks between modules, decreasing diffraction effects, and allows using a stronger transverse electron focusing. Both effects reduce the gain length and the overall undulator length. The peak power and efficiency depend on the transverse electron beam distribution and on time dependent effects, like synchrotron sideband growth. The last effect is identified as the main cause for reduction of electron beam microbunching and FEL peak power. We show that the optimal functional form for the undulator magnetic field tapering profile, yielding the maximum output power, depends significantly on these effects. The output power achieved when neglecting time dependent effects for an LCLS-like X-ray FEL with a 100 m long tapered undulator is 7.3 TW, a 14 $\%$ electron beam energy extraction efficiency. When these effects are included the highest peak power is achieved reducing the tapering rate, thus minimizing the reduction in electron micro-bunching due to synchrotron sideband growth. The maximum efficiency obtained for this case is 9 $\%$, corresponding to 4.7 TW peak radiation power. Possible methods to suppress the synchrotron sidebands, and further enhance the FEL peak power, up to about 6 TW by increasing the seed power, are discussed.

We study the tapering optimization scheme for a short period, less than two cm, superconducting undulator, and show that it can generate 4 keV X-ray pulses with peak power in excess of 1 terawatt, using LCLS electron beam parameters. We study the effect of undulator module length relative to the FEL gain length for continous and step-wise taper profiles. For the optimal section length of 1.5m we study the evolution of the FEL process for two different superconducting technologies NbTi and Nb3Sn. We discuss the major factors limiting the maximum output power, particle detrapping around the saturation location and time dependent detrapping due to generation and amplification of sideband modes.

Multidimensional optimization schemes for TW hard X-Ray free electron lasers are applied to the cases of transversely uniform and parabolic electron beam distributions and compared to examples of transversely Gaussian beams. The optimizations are performed for a $200$m undulator and a resonant wavelength of $\lambda_r=1.5\AA $ using the fully 3-dimensional FEL particle code GENESIS. Time dependent simulations showed that the maximum radiation power is larger for flatter transverse distributions due to enhanced optical guiding in the tapered section of the undulator. For a transversely Gaussian beam the maximum output power was found to be $\text{P}_{max}$=$1.56$ TW compared to $2.26$ TW for the parabolic case and $2.63$ TW for the uniform case. Spectral data also showed a 30-70$\%$ reduction in energy deposited in the sidebands for the uniform and parabolic beams compared with a Gaussian. An analysis of the maximum power as a function of detuning from resonance shows that redshifting the central wavelength by $\Delta \lambda / \lambda <\rho$ increases the power for all three transverse electron distributions.