MHD-PIC simulations find that the non-thermal particle spectral index alpha steepens as alpha proportional to beta to the power 0.5 in the relativistic regime, due to inertial mass density acting as an energy sink that reduces Alfven velocity.
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Numerical modeling of time-dependent cosmic-ray advection and diffusion in spherically symmetric wind bubbles shows escaping spectra harder than E^{-2} during the wind-driven phase, with low-energy suppression depending on the turbulence model.
Hybrid simulations of tearing reconnection show magnetic energy converts to ion bulk flows and heating in the nonlinear phase, with island contraction driving parallel ion temperature anisotropy that firehose instabilities regulate by redistributing energy to the perpendicular direction.
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Time-dependent cosmic-ray escape from wind bubbles: hard spectra formation
Numerical modeling of time-dependent cosmic-ray advection and diffusion in spherically symmetric wind bubbles shows escaping spectra harder than E^{-2} during the wind-driven phase, with low-energy suppression depending on the turbulence model.