High order time integrators for the simulation of charged particle motion in magnetic quadrupoles

Magnetic quadrupoles are essential components of particle accelerators like the Large Hadron Collider. In order to study numerically the stability of the particle beam crossing a quadrupole, a large number of particle revolutions in the accelerator must be simulated, thus leading to the necessity to preserve numerically invariants of motion over a long time interval and to a substantial computational cost, mostly related to the repeated evaluation of the magnetic vector potential. In this paper, in order to reduce this cost, we first consider a specific gauge transformation that allows to reduce significantly the number of vector potential evaluations. We then analyze the sensitivity of the numerical solution to the interpolation procedure required to compute magnetic vector potential data from gridded precomputed values at the locations required by high order time integration methods. Finally, we compare several high order integration techniques, in order to assess their accuracy and efficiency for these long term simulations. Explicit high order Lie methods are considered, along with implicit high order symplectic integrators and conventional explicit Runge Kutta methods. Among symplectic methods, high order Lie integrators yield optimal results in terms of cost/accuracy ratios, but non symplectic Runge Kutta methods perform remarkably well even in very long term simulations. Furthermore, the accuracy of the field reconstruction and interpolation techniques are shown to be limiting factors for the accuracy of the particle tracking procedures.Comment: 39 pages, 18 figure

Numerical methods for the simulation of particle motion in electromagnetic fields

In this thesis we study numerical methods for the approximate solution of problems arising in electromagnetism. Its main motivations come from applications to the modelling of high-energy particle accelerators. In this framework, we first compare the efficiency of several numerical methods for the omputation of particle trajectories in the design of a magnetic quadrupole for the High Luminosity - Large Hadron Collider (HL-LHC) project and we analyse the use of a specific vector potential gauge to reduce the computational cost. The results from this first comparison motivate the subsequent investigation of the accuracy of the numerical approximation of the field. We therefore develop a new type of discretization for the reconstruction of the magnetic scalar potential in cylindrical domains and we apply it to the field reconstruction from a realistic measurement process in a Bayesian framework. We compare this method with the reconstruction obtained by a more classical method based on the separation of variables, highlighting the benefits of the new type of discretization and its applicability to the reconstruction process. Motivated by the need of efficient methods for the description of electromagnetic fields, we extend the study to other types of problems for axisymmetric domains, which have a high practical relevance in particle accelerator applications. In this context, we propose the use of a method based on the Fourier basis and IsoGeometric Analysis (IGA) to exploit, on one hand, the computational efficiency that can be achieved thanks to the symmetry of the domain and, on the other, the exact representation of the geometry and the good approximation properties achievable in a IGA framework. Moreover, the proposed method forms a de Rham complex, which is a crucial property that allows to obtain a stable method which produces physically correct approximations. We finally apply the method to the computation of resonant modes of an accelerating TESLA cavity

IsoGeometric approximations for electromagnetic problems in axisymmetric domains

We propose a numerical method for the solution of electromagnetic problems on axisymmetric domains, based on a combination of a spectral Fourier approximation in the azimuthal direction with an IsoGeometric Analysis (IGA) approach in the radial and axial directions. This combination allows to blend the flexibility and accuracy of IGA approaches with the advantages of a Fourier representation on axisymmetric domains. It also allows to reduce significantly the computational cost by decoupling of the computations required for each Fourier mode. We prove that the discrete approximation spaces employed constitute a closed and exact de Rham sequence. Numerical simulations of relevant benchmarks confirm the high order convergence and other computational advantages of the proposed method

Accurate and Efficient Tracking in Electromagnetic Quadrupoles

Accelerator physics needs advanced modeling and simulation techniques, in particular for beam stability studies. A deeper understanding of the effects of magnetic fields nonlinearities will greatly help in the improvement of future colliders design and performance. This paper presents a study of quadrupole tracking using realistic field maps and measured or simulated longitudinal harmonics. The main goal is to describe the effect of the longitudinal dependence of high order non-homogeneity of the field in the case of the HL-LHC inner triplet

Airway pressure release ventilation during acute hypoxemic respiratory failure: a systematic review and meta-analysis of randomized controlled trials

Abstract Background Airway pressure release ventilation (APRV) has been considered a tempting mode of ventilation during acute respiratory failure within the concept of open lung ventilation. We performed a systematic review and meta-analysis to verify whether adult patients with hypoxemic respiratory failure have a higher number of ventilator-free days at day 28 when ventilated in APRV compared to conventional ventilation strategy. Secondary outcomes were difference in PaO2/FiO2 at day 3, ICU length of stay (LOS), ICU and hospital mortality, mean arterial pressure (MAP), risk of barotrauma and level of sedation. We searched MEDLINE, Scopus and Cochrane Central Register of Controlled Trials database until December 2018. Results We considered five RCTs for the analysis enrolling a total of 330 patients. For ventilatory-free day at day 28, the overall mean difference (MD) between APRV and conventional ventilation was 6.04 days (95%CI 2.12, 9.96, p = 0.003; I 2 = 65%, p = 0.02). Patients treated with APRV had a lower ICU LOS than patients treated with conventional ventilation (MD 3.94 days [95%CI 1.44, 6.45, p = 0.002; I 2 = 37%, p = 0.19]) and a lower hospital mortality (RD 0.16 [95%CI 0.02, 0.29, p = 0.03; I 2 = 0, p = 0.5]). PaO2/FiO2 at day 3 was not different between the two groups (MD 40.48 mmHg [95%CI − 25.78, 106.73, p = 0.23; I 2 = 92%, p < 0.001]). MAP was significantly higher during APRV (MD 5 mmHg [95%CI 1.43, 8.58, p = 0.006; I 2 = 0%, p = 0.92]). Then, there was no difference regarding the onset of pneumothorax under the two ventilation strategies (RR 1.94 [95%CI 0.54, 6.94, p = 0.31; I 2 = 0%, p = 0.74]). ICU mortality and sedation level were not included into quantitative analysis. Conclusion This study showed a higher number of ventilator-free days at 28 day and a lower hospital mortality in acute hypoxemic patients treated with APRV than conventional ventilation, without any negative hemodynamic impact or higher risk of barotrauma. However, these results need to be interpreted with caution because of the low-quality evidence supporting them and the moderate heterogeneity found. Other well-designed RCTs need to be conducted to confirm our findings

Evaluation of two neck ultrasound measurements as predictors of difficult direct laryngoscopy: A prospective observational study

Unpredictable difficult laryngoscopy remains a challenge for anaesthesiologists, especially if difficult ventilation occurs during standard laryngoscopy. Accurate airway assessment should always be performed, but the common clinical screening tests have shown low sensitivity and specificity with a limited predictive value. Ultrasound-based airway assessment has been proposed recently as a useful, simple, noninvasive bedside tool as an adjunct to clinical methods, but to date, few studies are available about the potential role of ultrasound in difficult airway evaluation, and these are mostly limited to specific groups of patients

Association between sublingual microcirculation, tissue perfusion and organ failure in major trauma: A subgroup analysis of a prospective observational study

INTRODUCTION: Previous studies described impaired microvascular perfusion and tissue oxygenation as reliable predictors of Multiple Organ Failure in major trauma. However, this relationship has been incompletely investigated. The objective of this analysis is to further evaluate the association between organ dysfunction and microcirculation after trauma. MATERIALS AND METHODS: This is a retrospective subgroup analysis on 28 trauma patients enrolled for the Microcirculation DAIly MONitoring in critically ill patients study (NCT 02649088). Patients were divided in two groups according with their Sequential Organ Failure Assessment (SOFA) score at day 4. At admission and every 24 hours, the sublingual microcirculation was evaluated with Sidestream Darkfield Imaging (SDF) and peripheral tissue perfusion was assessed with Near Infrared Spectroscopy (NIRS) and Vascular Occlusion Test (VOT). Simultaneously, hemodynamic, clinical/laboratory parameters and main organ supports were collected. RESULTS: Median SOFA score at Day 4 was 6.5. Accordingly, patients were divided in two groups: D4-SOFA ≤6.5 and D4-SOFA >6.5. The Length of Stay in Intensive Care was significantly higher in patients with D4-SOFA>6.5 compared to D4-SOFA≤6.5 (p = 0.013). Total Vessel Density of small vessels was significantly lower in patients with high D4-SOFA score at Day 1 (p = 0.002) and Day 2 (p = 0.006) after admission; the Perfused Vessel Density was lower in patients with high D4-SOFA score at Day 1 (p = 0.007) and Day 2 (p = 0.033). At Day 1, NIRS monitoring with VOT showed significantly faster tissue oxygen saturation downslope (p = 0.018) and slower upslope (p = 0.04) in patients with high D4-SOFA. DISCUSSION: In our cohort of major traumas, sublingual microcirculation and peripheral microvascular reactivity were significantly more impaired early after trauma in those patients who developed more severe organ dysfunctions. Our data would support the hypothesis that restoration of macrocirculation can be dissociated from restoration of peripheral and tissue perfusion, and that microvascular alterations can be associated with organ failure