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Under the U.S. High Luminosity LHC Accelerator Upgrade Project (HL-LHC AUP), the 150 mm bore, high-field Nb3Sn low-\b{eta} MQXFA quadrupole magnets are being fabricated, assembled and tested, in the context of the CERN Hi-Luminosity LHC (HL-LHC) upgrade. These magnets have 4.2 m magnetic length and 4.56 m long iron yoke. To date, eight MQXFA magnets have been tested. One of the magnets additionally underwent a successful endurance test with 40 triggered quenches, and two magnets did not perform as expected. This work summarizes for the first time the available strain gauge data from eight identical Nb3Sn MQXFA tested magnets, focusing on the endurance test, and on a possible cause of underperformance of the two magnets that did not pass the vertical test. We applied methods to prevent this from happening in future MQXFA magnets, which shown to be effective for last two tested magnets.

The increase in luminosity, and consequent higher backgrounds, of the LHC upgrades require improved rejection of fake tracks in the forward region of the ATLAS Muon Spectrometer. The New Small Wheel upgrade of the Muon Spectrometer aims to reduce the large background of fake triggers from track segments that are not originated from the interaction point. The New Small Wheel employs two detector technologies, the resistive strip Micromegas detectors and the "small" Thin Gap Chambers, with a total of 2.45 Million electrodes to be sensed. The two technologies require the design of a complex electronics system given that it consists of two different detector technologies and is required to provide both precision readout and a fast trigger. It will operate in a high background radiation region up to about 20 kHz/cm$^{2}$ at the expected HL-LHC luminosity of $\mathcal{L}$=7.5$\times10^{34}$cm$^{-2}$s$^{-1}$. The architecture of the system is strongly defined by the GBTx data aggregation ASIC, the newly-introduced FELIX data router and the software based data handler of the ATLAS detector. The electronics complex of this new detector was designed and developed in the last ten years and consists of multiple radiation tolerant Application Specific Integrated Circuits, multiple front-end boards, dense boards with FPGA's and purpose-built Trigger Processor boards within the ATCA standard. The New Small Wheel has been installed in 2021 and is undergoing integration within ATLAS for LHC Run 3. It should operate through the end of Run 4 (December 2032). In this manuscript, the overall design of the New Small Wheel electronics is presented., Comment: 61 pages

A detailed analysis is given of the effects of common and recurring approximations used in conventional superconductivity theories on the condensation energy values, whose magnitudes are notoriously smaller than those of other energies as the superconducting energy gap and the chemical potential. These approximations come from using the density of states $N(\epsilon)$ and the chemical potential $\mu(T)$ either constant or temperature-dependent, respectively. We use these approximations, a total of three, to calculate the critical temperature $T_{c}$, the superconductor energy gap $\Delta(T)$, the chemical potential $\mu(T)$ and the thermodynamic potential $\Omega(T)$ which are needed to obtain the condensation energy, and compare them with the exact case, i.e., where no approximations are used. To do this, we use a ternary Boson-Fermion theory of superconductivity composed of unbound electrons (or holes) as fermions plus two-electron and two-hole Cooper pairs, both as bosons. Although all these approximations lead to reasonable values of $T_{c}$ and $\Delta(T)$, the resulting thermodynamic and chemical potentials are quite different, so that the condensation energy value could be incorrect. However, when $N(\epsilon)$ and $\mu(T)$ variables are used, together with a correct physical interpretation of the condensation energy as the sum of the thermodynamic and chemical potential differences, it leads to a better agreement with reported experimental data, compared to the one obtained when taking them as constants, particularly so for low temperatures., Comment: 10 pages, 11 figures

Influence of the temperature dependent chemical potential on the condensation energy from a ternary Boson-Fermion model of superconductivity is reported, it consist of unbound electrons/holes which are fermions plus two-electron and two-hole Cooper pairs which are bosons. When solving simultaneously the set of equations of the mixture (two gap-like equations, one for electron pairs and another one for hole pairs, plus the particle number conservation equation) within the weak-coupling (BCS regime), the resulting superconducting chemical potential shows a shift from its normal state counterpart, which is related to both the magnitude of the temperature-dependent superconducting gap and to the Fermi energy of the superconductor. As predicted by van der Marel in the early 1990s we also find that the superconducting chemical potential has a prominent kink at critical temperature $T_c$, which in turn coincides with the normal state chemical potential. Also there is discontinuity in its first derivative which directly affects the magnitude in the specific heat jump. We show that the difference between the superconducting and normal state chemical potentials is of the same order of magnitude as the corresponding difference between the thermodynamic potentials for the mixture, and must therefore be accounted for in the condensation energy calculations instead of ignoring it as is done often. The condensation energy obtained here shows very good agreement with experimental data for elemental superconductors.

We present a generalized expression for the transfer matrix of finite and infinite one-dimensional spin chains within a magnetic field with spin pair interaction $J/r^p$, where $r\ = 1,2,\ldots,n_v$ is the distance between two spins, $n_v$ is the number of nearest neighbors reached by the interaction, and $p \in [1,2]$. With this generalized expression, we calculate the partition function, the Helmholtz free energy, and the specific heat for both finite and infinite ferromagnetic 1D Ising models within a zero external magnetic field. We focus on the temperature $T_{\text{max}}$ where specific heat reaches its maximum. We calculate $J/(k_B T_{\text{max}})$ numerically for every values of $n_v \in \{ 1,2,\ldots, 25\}$, which we interpolate and then extrapolate up to the critical temperature as a function of $p$, using a novel functional approach. Two different procedures are used to reach the infinite spin chain with an infinite interaction range: increasing the chain size and the interaction range by the same amount, and increasing the interaction range for the infinite chain. As we expected, both extrapolations lead to the same critical temperature, although by two different concurrent curves. Our critical temperatures as a function of $p$ fall within the upper and lower bounds reported in the literature and show a better coincidence with many existing approximations for $p$ close to 1 than for the $p$ values near 2. We report an averaged inverse critical temperature $J/(k_BT_c) = 0.532$ for the one-dimensional spin chain with $p=2$. It is worth mentioning that the well-known cases for near (original Ising model) and next-near neighbor interactions are recovered doing $n_v = 1$ and $n_v = 2$, respectively., Comment: 10 pages, 10 figures, 4 tables

We report on a novel structural Superfluid-Mott Insulator (SF-MI) quantum phase transition for an interacting one-dimensional Bose gas within permeable multi-rod lattices, where the rod lengths are varied from zero to the lattice period length. We use the ab-initio diffusion Monte Carlo method to calculate the static structure factor, the insulation gap, and the Luttinger parameter, which we use to determine if the gas is a superfluid or a Mott insulator. For the Bose gas within a square Kronig-Penney (KP) potential, where barrier and well widths are equal, the SF-MI coexistence curve shows the same qualitative and quantitative behavior as that of a typical optical lattice with equal periodicity but slightly larger height. When we vary the width of the barriers from zero to the length of the potential period, keeping the height of the KP barriers, we observe a new way to induce the SF-MI phase transition. Our results are of significant interest, given the recent progress on the realization of optical lattices with a subwavelength structure that would facilitate their experimental observation., Comment: 6 pages, 4 figures, accepted for publication in Phys. Rev. A

We use Coronal Multi-channel Polarimeter (CoMP) observations of propagating waves in the solar corona and Bayesian analysis to assess the evidence of models with resonant damping and foot-point wave power asymmetries. Two nested models are considered. The reduced model considers resonant damping as the sole cause of the measured discrepancy between outward and inward wave power. The larger model contemplates an extra source of asymmetry with origin at the foot-points. We first compute probability distributions of parameters conditional on the models and the observed data. The obtained constraints are then used to calculate the evidence for each model in view of data. We find that we need to consider the larger model to explain CoMP data and to accurately infer the damping ratio, hence, to better assess the possible contribution of the waves to coronal heating., Comment: Accepted in A&A

We report on ground state properties of a one-dimensional, weakly-interacting Bose gas constrained by an infinite multi-rods periodic structure at zero temperature. We solve the stationary Gross-Pitaevskii equation (GPE) to obtain the Bloch wave functions from which we give a semi-analytical solution for the density profile, as well as for the phase of the wave function in terms of the Jacobi elliptic functions, and the incomplete elliptic integrals of the first, second and third kind. Then, we determine numerically the energy of the ground state, the chemical potential and the compressibility of the condensate and show their dependence on the potential height, as well as on the interaction between the bosons. We show the appearance of loops in the energy band spectrum of the system for strong enough interactions, which appear at the edges of the first Brillouin zone for odd bands and at the center for even bands. We apply our model to predict the energy band structure of the Bose gas in an optical lattice with subwavelength spatial structure. To discuss the density range of the validity of the GPE predictions, we calculate the ground state energies of the free Bose gas using the GPE, which we compare with the Lieb-Liniger exact energies., Comment: 20 pages, 9 figures; introduction extended; references added; revised argument and new equations in Section II, results unchanged; fixed x-label in figures 5, 7b, and 8

A classic application of coronal seismology uses transverse oscillations of waveguides to obtain estimates of the magnetic field strength. The procedure requires information on the density of the structures. Often, it ignores the damping of the oscillations. We computed marginal posteriors for parameters such as the waveguide density; the density contrast; the transverse inhomogeneity length-scale; and the magnetic field strength, under the assumption that the oscillations can be modelled as standing magnetohydrodynamic (MHD) kink modes damped by resonant absorption. Our results show that the magnetic field strength can be properly inferred, even if the densities inside and outside the structure are largely unknown. Incorporating observational estimates of plasma density further constrains the obtained posteriors. The amount of information one is willing to include (a priori) for the density and the density contrast influences their corresponding posteriors, but very little the inferred magnetic field strength. The decision to include or leave out the information on the damping and the damping time-scales have a minimal impact on the obtained magnetic field strength. In contrast to the classic method which provides with numerical estimates with error bars or possible ranges of variation for the magnetic field strength, Bayesian methods offer the full distribution of plausibility over the considered range of possible values. The methods are applied to available datasets of observed transverse loop oscillations, can be extended to prominence fine structures or chromospheric spicules and implemented to propagating waves in addition to standing oscillations., Comment: 16 pages, A&A accepted

High resolution observations have permitted to resolve the solar prominences/filaments as sets of threads/fibrils. However, the values of the physical parameters of these threads and their structuring remain poorly constrained. We use prominence seismology techniques to analyse transverse oscillations in threads through the comparison between magnetohydrodynamic (MHD) models and observations. We apply Bayesian methods to obtain two different types of information. We first infer the marginal posterior distribution of physical parameters, such as the magnetic field strength or the length of the thread, when a totally filled tube, a partially filled tube, and three damping models (resonant absorption in the Alfv\'en continuum, resonant absorption in the slow continuum, and Cowling's diffusion) are considered as certain. Then, we compare the relative plausibility between alternative MHD models by computing the Bayes factors. Well constrained probability density distributions can be obtained for the magnetic field strength, the length of the thread, the density contrast, and parameters associated to damping models. When comparing the damping models of resonant absorption in the Alfv\'en continuum, resonant absorption in the slow continuum and Cowling's diffusion due to partial ionisation of prominence plasma, the resonant absorption in the Alfv\'en continuum is the most plausible mechanism in explaining the existing observations. Relations between periods of fundamental and first overtone kink modes with values around 1 are better explained by expressions of the period ratio in the long thread approximation, while the rest of the values are more probable in the short thread limit for the period ratio. Our results show that Bayesian analysis offers valuable methods for performing parameter inference and model comparison in the context of prominence seismology., Comment: 12 pages

Bose-Einstein condensation in a Bose gas is studied analytically, in any positive dimensionality ($d>0$) for identical bosons with any energy-momentum positive-exponent ($s>0$) plus an energy gap $\Delta$ between the ground state energy $\varepsilon_0$ and the first excited state, i.e., $\varepsilon=\varepsilon_0$ for $k=0$ and $\varepsilon=\varepsilon_0 +\Delta+ c_sk^s$, for $k>0$, where $\hbar \mathbf{k}$ is the particle momentum and $c_s$ a constant with dimensions of energy multiplied by a length to the power $s > 0$. Explicit formula with arbitrary $d/s$ and $\Delta$ are obtained and discussed for the critical temperature and the condensed fraction, as well as for the equation of state from where we deduce a generalized $\Delta$ independent thermal de Broglie wavelength. Also the internal energy is calculated from where we obtain the isochoric specific heat and its jump at $T_c$. When $\Delta > 0$, a Bose-Einstein critical temperature $T_c \neq 0$ exists for any $d > 0$ at which the internal energy shows a peak and the specific heat shows a jump. Both the critical temperature and the specific heat jump increase as functions of the gap but they decrease as of $d/s$. At sufficiently high temperatures $\Delta$- independent classical results are recovered. However, for temperatures below the critical one the gap effects are predominant. For $\Delta = 0$ we recover previous reported results., Comment: 8 pages, 9 figures

We present a method to assess the plausibility of alternative mechanisms to explain the damping of magnetohydrodynamic (MHD) transverse waves in solar coronal loops. The considered mechanisms are resonant absorption of kink waves in the Alfv\'en continuum, phase-mixing of Alfv\'en waves, and wave leakage. Our methods make use of Bayesian inference and model comparison techniques. We first infer the values for the physical parameters that control the wave damping, under the assumption of a particular mechanism, for typically observed damping time-scales. Then, the computation of marginal likelihoods and Bayes factors enable us to quantify the relative plausibility between the alternative mechanisms. We find that, in general, the evidence is not large enough to support a single particular damping mechanism as the most plausible one. Resonant absorption and wave leakage offer the most probable explanations in strong damping regimes, while phase mixing is the best candidate for weak/moderate damping. When applied to a selection of 89 observed transverse loop oscillations, with their corresponding measurements of damping times scales and taking into account data uncertainties, we find that only in a few cases positive evidence for a given damping mechanism is available.

We calculate and discuss the effects on the thermodynamic properties of a 3D Bose gas caused by a gap $\Delta$ in the energy of the particles constituting the gas that without the gap behaves like an ideal Bose gas. Explicit formulae with arbitrary $\Delta$ values are discussed for: the critical temperature which increases as the gap grows; the condensate fraction; the internal energy; and the constant-volume specific heat found to possess a jump-discontinuity for any $\Delta$ different from zero. Three dimensional infinite ideal Bose gas results are recovered when we the energy gap goes to zero., Comment: 5 pages and 5 eps figures

We adapt the Boson-Fermion superconductivity model to include layered systems such as underdoped cuprate superconductors. These systems are represented by an infinite layered structure containing a mixture of paired and unpaired fermions. The former, which stand for the superconducting carriers, are considered as noninteracting zero spin composite-bosons with a linear energy-momentum dispersion relation in the CuO$_2$ planes where superconduction is predominant, coexisting with the unpaired fermions in a pattern of stacked slabs. The inter-slab, penetrable, infinite planes are generated by a Dirac comb potential, while paired and unpaired electrons (or holes) are free to move parallel to the planes. Composite-bosons condense at a critical temperature at which they exhibit a jump in their specific heat. These two values are assumed to be equal to the superconducting critical temperature $T_c$ and the specific heat jump reported for YBa$_{2}$Cu$_{3}$O$_{6.80}$ to fix our model parameters namely, the plane impenetrability and the fraction of superconducting charge carriers. We then calculate the isochoric and isobaric electronic specific heats for temperatures lower than $T_c$ of both, the composite-bosons and the unpaired fermions, which matches recent experimental curves. From the latter, we extract the linear coefficient ($\gamma_n$) at $T_c$, as well as the quadratic ($\alpha T^2$) term for low temperatures. We also calculate the lattice specific heat from the ARPES phonon spectrum, and add it to the electronic part, reproducing the experimental total specific heat at and below $T_c$ within a $5 \%$ error range, from which the cubic ($\ss T^3$) term for low temperatures is obtained. In addition, we show that this model reproduces the cuprates mass anisotropies., Comment: 13 pages, 6 figures

For an ideal Bose-gas within a multi-slab periodic structure, we discuss the effect of the spatial distribution of the gas on its Bose-Einstein condensation critical temperature $T_c$, as well as on the origin of its dimensional crossover observed in the specific heat. The multi-slabs structure is generated by applying a Kronig-Penney potential to the gas in the perpendicular direction to the slabs of width $b$ and separated by a distance $a$, and allowing the particles to move freely in the other two directions. We found that $T_c$ decreases continuously as the potential barrier height increases, becoming inversely proportional to the square root of the barrier height when it is large enough. This behavior is {\it universal} as it is independent of the width and spacing of the barriers. The specific heat at constant volume shows a crossover from 3D to 2D when the height of the potential or the barrier width increase, in addition to the well known peak related to the Bose-Einstein condensation. These features are due to the trapping of the bosons by the potential barriers, and can be characterized by the energy difference between the energy bands below the potential height., Comment: 8 pages with four figures

Disorder effects in the thermodynamic properties of a ideal Bose gas confined in a semi-infinite multi-layer structure %described by $M$ permeable barriers within a box of thickness $L$ and infinite lateral extent, are analyzed. The layers are first modeled by a periodic array of $M$ Dirac delta-functions of equal intensity. Then, we introduce structural and compositional disorder, as well as a random set of layer vacancies in the system to calculate the internal energy, chemical potential and the specific heat for different configurations. Whereas structural and compositional disorder does not reveal a significant change, a dramatic increase in the maximum of the specific heat is observed when the system is depleted a fraction of the order of $0.1$ to $0.2$ of random layers compared to the original, fully periodic array. Furthermore, this maximum, which is reminiscent of a Bose-Einstein condensation for an infinite array, occurs at higher temperatures., Comment: Six pages and 8 eps figures

The specific heat for an ideal Bose gas confined in semi-infinite multifilament cables is analyzed. We start with a Bose gas inside a semi-infinite tube of impenetrable walls and finite rectangular cross section. The internal filament structure is created by applying to the gas two, mutually perpendicular, Kronig-Penney delta-potentials along the tube cross section, while particles are free to move perpendicular to the cross section. The energy spectrum accessible to the particles is obtained and introduced into the grand potential to calculate the specific heat of the system as a function of temperature for different values of the periodic structure parameters such as: the cross section area, the wall impenetrability and the number of filaments. The specific heat as a function of temperature shows at least two maxima and one minimum. The main difference with respect to the infinite case is that the peak associated with the BE condensation becomes a smoothed maximum or in other words, there is not a jump in the specific heat derivative, whose temperature no longer represents a critical point.

The collective excitations that minimize the Helmholtz free energy of a population-imbalanced mixture of a $^{6}$Li gas loaded in a quasi one-dimensional optical lattice are obtained. These excitations reveal a rotonic branch after solving the Bethe-Salpeter equation under a generalized random phase approximation based on a single-band Hubbard Hamiltonian. The phase diagram describing stability regions of Fulde-Farrell-Larkin-Ovchinnikov and Sarma phases is also analyzed., Comment: Six pages and 3 figures

We report the thermodynamic properties of Bose and Fermi ideal gases immersed in periodic structures such as penetrable multilayers or multitubes simulated by one (planes) or two perpendicular (tubes) external Dirac comb potentials, while the particles are allowed to move freely in the remaining directions. Although the bosonic chemical potential is a constant for $T < T_c$, a non decreasing with temperature anomalous behavior of the fermionic chemical potential is confirmed and monitored as the tube bundle goes from 2D to 1D when the wall impenetrability overcomes a critical value. In the specific heat curves dimensional crossovers are very noticeable at high temperatures for both gases, where the system behavior goes from 3D to 2D and latter to 1D as the wall impenetrability is increased., Comment: Six pages and 4 figures

For an ideal Bose-gas within a multi-slabs periodic structure, we report a dimensional crossover and discuss whether a BEC transition at $T_c \neq 0$ disappears or not. The multi-slabs structure is generated via a Kronig-Penney potential perpendicular to the slabs of width $a$ and separated by a distance $b$. The ability of the particles to jump between adjacent slabs is determined by the hight $V_0$ and width $b$ of the potential barrier. Contrary to what happens in the boson gas inside a zero-width multilayers case, where the critical temperature diminishes and goes up again as a function of the wall separation, here the $T_c$ decreases continuously as the potential barrier height and the cell size $a+b$ increase. We plot the surface $T_c = 10^{-6}$ showing two prominent regions in the parameters space, which suggest a phase transition BEC-NOBEC at $T \neq 0$. %The position of the phase transition surface is almost independent of the ratio $r=b/a$ while the cell size $a+b$ is almost proportional to the square root of the height of the potential barriers. The specific heat shows a crossover from 3D to 2D when the height of the potential or the barrier width increase, in addition to the well known peak related to the Bose-Einstein condensation., Comment: Five pages with four figures

We study fermion pairing in a population-imbalanced mixture of $^{6}$Li atomic gas loaded in a three-dimensional lattice at very low temperatures. Using the number equation for each population, the gap equation and the equation for the Helmholtz free energy, we determine the gap, chemical potentials and pair-momentum as functions of polarization. These parameters define the stability regions for: a Fulde-Ferrell-Larkin-Ovchinnikov phase; a phase separation region where BCS and normal phases coexist; a Sarma phase when the pair-momentum vanishes, and the transition to the normal phase when the gap disappears. The collective-mode energies are then calculated using a Bethe-Salpeter approach in the generalized random phase approximation assuming that the system is well described by the single-band Hubbard model. A novel result is that this fermionic gas has a superfluid phase revealed by rotonlike minima in the asymmetric collective-mode energy spectrum., Comment: 8 pages, 5 figures

We model cuprate superconductors as an infinite layered lattice structure which contains a fluid of paired and unpaired fermions. Paired fermions, which are the superconducting carriers, are considered as noninteracting zero spin bosons with a linear energy-momentum dispersion relation, which coexist with the unpaired fermions in a series of almost two dimensional slabs stacked in their perpendicular direction. The inter-slab penetrable planes are simulated by a Dirac comb potential in the direction in which the slabs are stacked, while paired and unpaired electrons (or holes) are free to move parallel to the planes. Paired fermions condense at a BEC critical temperature at which a jump in their specific heat is exhibited, whose values are assumed equal to the superconducting critical temperature and the specific heat jump experimentally reported for YBaCuO_(7-x) to fix our model parameters: the plane impenetrability and the fraction of superconducting charge carrier. We straightforwardly obtain, near and under the superconducting temperature Tc, the linear (\gamma_e T) and the quadratic (\alpha T^2) electronic specific heat terms, with \gamma_e and \alpha, of the order of the latest experimental values reported. After calculating the lattice specific heat (phonons) Cl from the phonon spectrum data obtained from inelastic neutron scattering experiments, and added to the electronic (paired plus unpaired) Ce component, we qualitatively reproduce the total specific heat below Tc, whose curve lies close to the experimental one, reproducing its exact value at Tc., Comment: 11 pages, 9 figures

We report the thermodynamic properties of an ideal boson gas confined in an infinite periodic array of channels modeled by two, mutually perpendicular, Kronig-Penney delta-potentials. The particle's motion is hindered in the x-y directions, allowing tunneling of particles through the walls, while no confinement along the z direction is considered. It is shown that there exists a finite Bose- Einstein condensation (BEC) critical temperature Tc that decreases monotonically from the 3D ideal boson gas (IBG) value $T_{0}$ as the strength of confinement $P_{0}$ is increased while keeping the channel's cross section, $a_{x}a_{y}$ constant. In contrast, Tc is a non-monotonic function of the cross-section area for fixed $P_{0}$. In addition to the BEC cusp, the specific heat exhibits a set of maxima and minima. The minimum located at the highest temperature is a clear signal of the confinement effect which occurs when the boson wavelength is twice the cross-section side size. This confinement is amplified when the wall strength is increased until a dimensional crossover from 3D to 1D is produced. Some of these features in the specific heat obtained from this simple model can be related, qualitatively, to at least two different experimental situations: $^4$He adsorbed within the interstitial channels of a bundle of carbon nanotubes and superconductor-multistrand-wires Nb$_{3}$Sn., Comment: 9 pages, 10 figures, submitted

We study electron pairing in a one-dimensional (1D) fermion gas at zero temperature under zero- and finite-range, attractive, two-body interactions. The binding energy of Cooper pairs (CPs) with zero total or center-of-mass momentum (CMM) increases with attraction strength and decreases with interaction range for fixed strength. The excitation energy of 1D CPs with nonzero CMM display novel, unique properties. It satisfies a dispersion relation with \textit{two} branches: a\ phonon-like \textit{linear }excitation for small CP CMM; this is followed by roton-like \textit{quadratic} excitation minimum for CMM greater than twice the Fermi wavenumber, but only above a minimum threshold attraction strength. The expected quadratic-in-CMM dispersion \textit{in vacuo }when the Fermi wavenumber is set to zero is recovered for \textit{any% } coupling. This paper completes a three-part exploration initiated in 2D and continued in 3D., Comment: 12 pages, 6 figures