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The last 22.5 orbits of the Cassini mission brought the spacecraft to less than 3000 km from Saturn's 1-bar surface. These close encounters offered an unprecedented view of Saturn's magnetic field, including contributions from the internal dynamo, the ionosphere, and the magnetosphere. In this chapter, we highlight the new picture of Saturn's magnetic field from the Cassini mission including the persistent yet time-varying low-latitude field-aligned currents, Alfv\'en waves planet-ward of the D-ring, extreme axisymmetry, and high-degree magnetic moments. We then discuss the implications and new questions raised for Saturn's innermost magnetosphere, equatorial ionosphere, and interior. We conclude this chapter with an outlook for the future exploration of Saturn and other giant planets., Comment: Peer reviewed and accepted for publication as Chapter 5 of a multi-volume work edited by Kevin Baines, Michael Flasar, Norbert Krupp, and Thomas Stallard, entitled Cassini at Saturn: The Grand Finale, to be published by Cambridge University Press. 15 pages, 10 figures

Coherent anti-Stokes Raman Spectroscopy (CARS) is a laser-based measurement technique widely applied across many science and engineering disciplines to perform non-intrusive gas diagnostics. CARS is often used to study combustion, where the measured spectra can be used to simultaneously recover multiple flow parameters from the reacting gas such as temperature and relative species mole fractions. This is typically done by using numerical optimization to find the flow parameters for which a theoretical model of the CARS spectra best matches the actual measurements. The most commonly used theoretical model is the CARSFT spectrum calculator. Unfortunately, this CARSFT spectrum generator is computationally expensive and using it to recover multiple flow parameters can be prohibitively time-consuming, especially when experiments have hundreds or thousands of measurements distributed over time or space. To overcome these issues, several methods have been developed to approximate CARSFT using a library of pre-computed theoretical spectra. In this work we present a new approach that leverages ideas from the machine learning literature to build an adaptively smoothed kernel-based approximator. In application on a simulated dual-pump CARS experiment probing a $H_2/$air flame, we show that the approach can use a small number library spectra to quickly and accurately recover temperature and four gas species' mole fractions. The method's flexibility allows fine-tuned navigation of the trade-off between speed and accuracy, and makes the approach suitable for a wide range of problems and flow regimes., Comment: 14 pages, 6 figures

In recent decades the analysis of data has become increasingly computational. Correspondingly, this has changed how scientific and statistical work is shared. For example, it is now commonplace for underlying analysis code and data to be proffered alongside journal publications and conference talks. Unfortunately, sharing code faces several challenges. First, it is often difficult to take code from one computer and run it on another. Code configuration, version, and dependency issues often make this challenging. Secondly, even if the code runs, it is often hard to understand or interact with the analysis. This makes it difficult to assess the code and its findings, for example, in a peer review process. In this review we describe the combination of two computing technologies that help make analyses shareable, interactive, and completely reproducible. These technologies are (1) analysis containerization, which leverages virtualization to fully encapsulate analysis, data, code and dependencies into an interactive and shareable format, and (2) code notebooks, a literate programming format for interacting with analyses. The fusion of these two technologies offers significant advantages over using either individually. This review surveys how the combination enhances the accessibility and reproducibility of code, analyses, and ideas., Comment: 22 pages, 6 figures

The Cassini mission entered the Grand Finale phase in April 2017 and executed 22.5 highly inclined, close-in orbits around Saturn before diving into the planet on September 15th 2017. Here we present our analysis of the Cassini Grand Finale magnetometer (MAG) dataset, focusing on Saturn's internal magnetic field. These measurements demonstrate that Saturn's internal magnetic field is exceptionally axisymmetric, with a dipole tilt less than 0.007 degrees (25.2 arcsecs). Saturn's magnetic equator was directly measured to be shifted northward by ~ 0.0468 +/- 0.00043 (1-sigma) $R_S$, 2820 +/- 26 km, at cylindrical radial distances between 1.034 and 1.069 $R_S$ from the spin-axis. Although almost perfectly axisymmetric, Saturn's internal magnetic field exhibits features on many characteristic length scales in the latitudinal direction. Examining Br at the a=0.75 $R_S$, c=0.6993 $R_S$ isobaric surface, the degrees 4 to 11 contributions correspond to latitudinally banded magnetic perturbations with characteristic width similar to that of the off-equatorial zonal jets observed in the atmosphere of Saturn. Saturn's internal magnetic field beyond 60 degrees latitude, in particular the small-scale features, are less well constrained by the available measurements, mainly due to incomplete spatial coverage in the polar region. A stably stratified layer thicker than 2500 km likely exists above Saturn's deep dynamo to filter out the non-axisymmetric internal magnetic field. A heat transport mechanism other than pure conduction, e.g. double diffusive convection, must be operating within this layer to be compatible with Saturn's observed luminosity. The latitudinally banded magnetic perturbations likely arise from a shallow secondary dynamo action with latitudinally banded differential rotation in the semi-conducting layer., Comment: Accepted for publication in Icarus

Measuring scattered light is central to many laser-based gas diagnostic techniques, e.g., coherent anti-Stokes Raman spectroscopy (CARS) and filtered Rayleigh scattering (FRS). To produce quantitative measurements with such techniques, a computational model of the scattered spectral lineshape is necessary. While accurate, these models are often quite computationally demanding and thus cannot be used in situations where computational speed matters. To overcome this, approximations of these spectral lineshape models can be used instead. In this paper, we develop a method called support vector spectrum approximation (SVSA). This method uses machine learning to create efficient and accurate approximations of any existing spectral lineshape model. The SVSA framework improves upon existing methods by allowing efficient approximations of spectral lineshapes to be calculated in arbitrary flow regimes. We demonstrate the efficacy of SVSA in approximating coherent and spontaneous Rayleigh-Brillioun spectra. We also show that SVSA reduces the computational cost of a simulated filtered Rayleigh scattering experiment by a factor of 300.