The curious case of large-N expansions on a (pseudo)sphere
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Alexander M. Polyakov↗
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Uneven Inflation Load Share Trends in Clusters
The use of parachute clusters for payload recovery is still seeing widespread use ever since the early days of WWII. By involving the (near) simultaneous deployment of several smaller and identical canopies connected to the payload, cluster systems offer flexibility in tailoring to needed descent rates and load management, as well as providing robustness against individual canopy deployment or opening failure. Their downside, of course, resides in the possibility of differing inflation rates by each cluster member as caused by deployment variability, canopy-to-canopy interference, etc. Such variability leads to the lead-lag phenomenon, which causes uneven loading among the parachutes, often times leaving a single canopy to take up a significant portion of the system’s inflation loads. Herein we investigate how serious such an effect can be in terms of the number N of cluster members, underinflation drag of the lagging canopies, inflation swiftness of the leader in comparison to the laggards’, disreefing cutter activation staggering and pre-disreefing drag area. Two new metrics are used to highlight load share unevenness, namely, the peak and average leader canopy riser load in comparison to the leader’s drag during no-lead-lag; and leader peak load, as compared to total peak load. Results are calculated from data collected in NASA’s Orion/CPAS test program, as well as from simple algebraic expressions informing leader drag as sustained in different cluster systems (i.e., of different N) and varying leader inflation time relative to the laggards. Generally, using large-N cluster systems confers better load sharing among canopies. However, and in deployments where significant lead-lag occur, large-N systems may feature greater leader overload excursions, oftentimes in excess of 50% the no-lead-lag levels. These excursions are particularly made worse when cutter activation among the members are far from simultaneous and the laggards’ pre-disreefing drag area is small in comparison to the leader’s.
parachutes↗
Ballooning stability of axisymmetric plasmas with sheared equilibrium flows
A WKB theory is formulated for large-n ballooning modes in axisymmetric, toroidal plasmas with sheared equilibrium flows. The validity of the standard ballooning respresentation is severely restricted in the presence of sheared toroidal flow, despite the fact that to leading order in (1/n), where n is the azimuthal number, the eigenmode equation contains only derivatives along a field line. Necessary and sufficient conditions for stability are obtained in a high-beta ordering for rigid toroidal rotation as well as field-aligned flows.
Bhattacharjee, A.↗
Ballooning stability of anisotropic, rotating plasmas
The linearized equation of motion is given in a Lagrangian representation for a rotating plasma with anisotropic pressure. A WKB theory is developed for large-n ballooning modes in an axisymmetric configuration with field-aligned and rigid toroidal flows. In the presence of field-aligned flows, it is shown that a resonance occurs which is strongly suggestive of a generalized mirror instability. In the presence of toroidal rotation, a possible stabilizing effect is identified for P(normal) greater than P(parallel). Finally, as a special case of the theory, the necessary and sufficient conditions for stability in a static, anisotropic plasma are obtained.
Wang, X.-H.↗
MeV Gamma Ray Detection Algorithms for Stacked Silicon Detectors
By making use of the signature of a gamma ray event as it appears in N = 5 to 20 lithium-drifted silicon detectors and applying smart selection algorithms, gamma rays in the energy range of 1 to 8 MeV can be detected with good efficiency and selectivity. Examples of the types of algorithms used for different energy regions include the simple sum mode, the sum-coincidence mode used in segmented detectors, unique variations on sum-coincidence for an N-dimensional vector event, and a new and extremely useful mode for double escape peak spectroscopy at pair-production energies. The latter algorithm yields a spectrum similar to that of the pair spectrometer, but without the need of the dual external segments for double escape coincidence, and without the large loss in efficiency of double escape events. Background events due to Compton scattering are largely suppressed. Monte Carlo calculations were used to model the gamma ray interactions in the silicon, in order to enable testing of a wide array of different algorithms on the event N-vectors for a large-N stack.
McMurray, Robert E. Jr.↗