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1. Guiding-centre Lagrangian and quasi-symmetry

   https://doi.org/10.1017/s0022377825000133  

   Jacobson, Ted (April 2025, Journal of Plasma Physics)

   A charged particle in a suitably strong magnetic field spirals along the field lines while slowly drifting transversely. This note provides a brief derivation of an effective Lagrangian formulation for the guiding-centre approximation that captures this dynamics without resolving the gyro motion. It also explains how the effective Lagrangian may, for special magnetic fields, admit a ‘quasi-symmetry’ which can give rise to a conserved quantity helpful for plasma confinement in fields lacking a geometric isometry. The aim of this note is to offer a pedagogical introduction and some perspectives on this well-established subject. 

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2. Variational formulation of higher-order guiding-center Vlasov–Maxwell theory

   https://doi.org/10.1063/5.0161171  

   Brizard, Alain J. (October 2023, Physics of Plasmas)

   Extended guiding-center Vlasov–Maxwell equations are derived under the assumption of time-dependent and inhomogeneous electric and magnetic fields that obey the standard guiding-center space-timescale orderings. The guiding-center Vlasov–Maxwell equations are derived up to second order, which contains dipole and quadrupole contributions to the guiding-center polarization and magnetization that include finite-Larmor-radius corrections. Exact energy-momentum conservation laws are derived from the variational formulation of these higher-order guiding-center Vlasov–Maxwell equations. 

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3. Discovery of a nearby 1700 km/s star ejected from the Milky Way by Sgr A*

   https://doi.org/10.1093/mnras/stz3081  

   Koposov, Sergey E; Boubert, Douglas; Li, Ting S; Erkal, Denis; Da Costa, Gary S; Zucker, Daniel B; Ji, Alexander P; Kuehn, Kyler; Lewis, Geraint F; Mackey, Dougal; et al (January 2020, Monthly Notices of the Royal Astronomical Society)

   Abstract We present the serendipitous discovery of the fastest Main Sequence hyper-velocity star (HVS) by the Southern Stellar Stream Spectroscopic Survey (S5). The star S5-HVS1 is a ∼2.35 M⊙ A-type star located at a distance of ∼9 kpc from the Sun and has a heliocentric radial velocity of 1017 ± 2.7  km s−1 without any signature of velocity variability. The current 3-D velocity of the star in the Galactic frame is 1755 ± 50  km s−1. When integrated backwards in time, the orbit of the star points unambiguously to the Galactic Centre, implying that S5-HVS1 was kicked away from Sgr A* with a velocity of ∼1800  km s−1 and travelled for 4.8 Myr to its current location. This is so far the only HVS confidently associated with the Galactic Centre. S5-HVS1 is also the first hyper-velocity star to provide constraints on the geometry and kinematics of the Galaxy, such as the Solar motion Vy, ⊙ = 246.1 ± 5.3  km s−1 or position R0 = 8.12 ± 0.23 kpc. The ejection trajectory and transit time of S5-HVS1 coincide with the orbital plane and age of the annular disk of young stars at the Galactic centre, and thus may be linked to its formation. With the S5-HVS1 ejection velocity being almost twice the velocity of other hyper-velocity stars previously associated with the Galactic Centre, we question whether they have been generated by the same mechanism or whether the ejection velocity distribution has been constant over time. 

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4. Modelling CN Zeeman effect observations of the envelopes of a low-mass protostellar disc and a massive protostar

   https://doi.org/10.1093/mnras/stad3753  

   Mazzei, Renato; Li, Zhi-Yun; Chen, Che-Yu; Tu, Yisheng; Fissel, Laura; Klein, Richard I. (December 2023, Monthly Notices of the Royal Astronomical Society)

   ABSTRACT We use the polaris radiative transfer code to produce simulated circular polarization Zeeman emission maps of the cyanide (CN) J = 1–0 molecular line transition for two types of protostellar envelope magnetohydrodynamic simulations. Our first model is a low-mass disc envelope system (box length L = 200 au), and our second model is the envelope of a massive protostar (L = 104 au) with a protostellar wind and a CN-enhanced outflow shell. We compute the velocity-integrated Stokes I and V, as well as the implied V/I polarization percentage, for each detector pixel location in our simulated emission maps. Our results show that both types of protostellar environments are in principle accessible with current circular polarization instruments, with each containing swaths of envelope area that yield percentage polarizations that exceed the 1.8 per cent nominal sensitivity limit for circular polarization experiments with the Atacama Large Millimeter/submillimeter Array. In both systems, high-polarization (≳1.8 per cent) pixels tend to lie at an intermediate distance away from the central star and where the line-centre opacity of the CN emission is moderately optically thin (τLC ∼ 0.1–1). Furthermore, our computed V/I values scale roughly with the density-weighted mean line-of-sight magnetic field strength, indicating that Zeeman observations can effectively diagnose the strength of envelope-scale magnetic fields. We also find that pixels with large V/I are preferentially co-located where the absolute value of the velocity-integrated V is also large, suggesting that locations with favourable percentage polarization are also favourable in terms of raw signal. 

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5. Lagrangian and Eulerian time and length scales of mesoscale ocean chlorophyll from Bio-Argo floats and satellites

   https://doi.org/10.5194/bg-19-5927-2022  

   McKee, Darren C; Doney, Scott C; Della_Penna, Alice; Boss, Emmanuel S; Gaube, Peter; Behrenfeld, Michael J; Glover, David M (January 2022, Biogeosciences)

   Abstract. Phytoplankton form the base of marine food webs and playan important role in carbon cycling, making it important to quantify ratesof biomass accumulation and loss. As phytoplankton drift with oceancurrents, rates should be evaluated in a Lagrangian as opposed to an Eulerianframework. In this study, we quantify the Lagrangian (from Bio-Argo floatsand surface drifters with satellite ocean colour) and Eulerian (fromsatellite ocean colour and altimetry) statistics of mesoscale chlorophylland velocity by computing decorrelation time and length scales and relatethe frames by scaling the material derivative of chlorophyll. Because floatsprofile vertically and are not perfect Lagrangian observers, we quantify themean distance between float and surface geostrophic trajectories over thetime spanned by three consecutive profiles (quasi-planktonic index, QPI) toassess how their sampling is a function of their deviations from surfacemotion. Lagrangian and Eulerian statistics of chlorophyll are sensitive to thefiltering used to compute anomalies. Chlorophyll anomalies about a 31 dtime filter reveal an approximate equivalence of Lagrangian and Euleriantendencies, suggesting they are driven by ocean colour pixel-scale processesand sources or sinks. On the other hand, chlorophyll anomalies about aseasonal cycle have Eulerian scales similar to those of velocity, suggestingmesoscale stirring helps set distributions of biological properties, andratios of Lagrangian to Eulerian timescales depend on the magnitude ofvelocity fluctuations relative to an evolution speed of the chlorophyllfields in a manner similar to earlier theoretical results for velocityscales. The results suggest that stirring by eddies largely sets Lagrangiantime and length scales of chlorophyll anomalies at the mesoscale. 

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