Investigating the cosmic-ray ionization rate in the galactic interstellar medium through observations of H3+

Observations of H3+ in the Galactic diffuse interstellar medium (ISM) have led to various surprising results, including the conclusion that the cosmic-ray ionization rate (zeta_2) is about 1 order of magnitude larger than previously thought. The present survey expands the sample of diffuse cloud sight lines with H3+ observations to 50, with detections in 21 of those. Ionization rates inferred from these detections are in the range (1.7+-1.0)x10^-16 s^-1 < zeta_2 < (10.6+-6.8)x10^-16 s^-1 with a mean value of zeta_2=(3.3+-0.4)x10^-16 s^-1. Upper limits (3sigma) derived from non-detections of H3+ are as low as zeta_2 < 0.4x10^-16 s^-1. These low upper-limits, in combination with the wide range of inferred cosmic-ray ionization rates, indicate variations in zeta_2 between different diffuse cloud sight lines. Calculations of the cosmic-ray ionization rate from theoretical cosmic-ray spectra require a large flux of low-energy (MeV) particles to reproduce values inferred from observations. Given the relatively short range of low-energy cosmic rays --- those most efficient at ionization --- the proximity of a cloud to a site of particle acceleration may set its ionization rate. Variations in zeta_2 are thus likely due to variations in the cosmic-ray spectrum at low energies resulting from the effects of particle propagation. To test this theory, H3+ was observed in sight lines passing through diffuse molecular clouds known to be interacting with the supernova remnant IC 443, a probable site of particle acceleration. Where H3+ is detected, ionization rates of zeta_2=(20+-10)x10^-16 s^-1 are inferred, higher than for any other diffuse cloud. These results support both the concept that supernova remnants act as particle accelerators, and the hypothesis that propagation effects are responsible for causing spatial variations in the cosmic-ray spectrum and ionization rate. Future observations of H3+ near other supernova remnants and in sight lines where complementary ionization tracers (OH+, H2O+, H3O+) have been observed will further our understanding of the subject.

Incorporation of Hysteretic Effects in Model-Order Reduction Analysis of Magnetic Devices

The ability to predict the properties of magnetic materials in a device is essential to ensuring the correct operation and optimization of the design as well as the device behavior over a wide range of input frequencies. Typically, development and simulation of wide-bandwidth models requires detailed, physics-based simulations that utilize significant computational resources. Balancing the trade-offs between model computational overhead and accuracy can be cumbersome, especially when the nonlinear effects of saturation and hysteresis are included in the model. This study focuses on the development of a system for analyzing magnetic devices in cases where model accuracy and computational intensity must be carefully and easily balanced by the engineer. A method for adjusting model complexity and corresponding level of detail while incorporating the nonlinear effects of hysteresis is presented that builds upon recent work in loss analysis and magnetic equivalent circuit (MEC) modeling. The approach utilizes MEC models in conjunction with linearization and model-order reduction techniques to process magnetic devices based on geometry and core type. The validity of steady-state permeability approximations is also discussed.