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1. A Kinetic Study of the Saturation of the Bell Instability

   https://doi.org/10.22323/1.395.0483  

   Zacharegkas, Georgios; Caprioli, Damiano; Haggerty, Colby; Gupta, Siddhartha (July 2021, 37th International Cosmic Ray Conference (ICRC2021))

   null (Ed.)

   The nonresonant cosmic ray instability, predicted by Bell (2004), is thought to play an important role in the acceleration and confinement of cosmic rays (CR) close to supernova remnants. Despite its importance, the exact mechanism responsible for the saturation of the instability has not been determined, and there is no first-principle prediction for the amplitude of the saturated magnetic field. Using a survey of self-consistent hybrid simulations (with kinetic ions and fluid electrons), we study the non-linear evolution of the Bell instability as a function of the parameters of the CR population. We find that saturation is achieved when the magnetic pressure in the amplified field is comparable to the initial CR momentum flux. 

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2. Modeling the Saturation of the Bell Instability Using Hybrid Simulations

   Zacharegkas, G.; Caprioli, D.; Haggerty, C. (January 2019, ICRC2019)

   The nonresonant cosmic ray instability, predicted by Bell (2004), is thought to play an important role in the acceleration and confinement of cosmic rays (CRs) close to supernova remnants. Despite its importance, the exact mechanism responsible for the saturation of the instability has not been determined, and there is no first-principle prediction for the amplitude of the saturated magnetic field. Using a survey of self-consistent kinetic hybrid simulations (with kinetic ions and fluid electrons), we study the saturation of the non-resonant streaming instability as a function of the parameters of both the thermal background plasma and the CR population. The strength of the saturated magnetic field has important implications for both CR acceleration in supernova remnants and CR diffusion in the Galaxy. 

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3. Understanding Streaming Instabilities in the Limit of High Cosmic-Ray Current Density

   https://doi.org/10.3847/1538-4357/adadf5  

   Lichko, Emily; Caprioli, Damiano; Schroer, Benedikt; Gupta, Siddhartha (February 2025, The Astrophysical Journal)

   Abstract A critical component of particle acceleration in astrophysical shocks is the nonresonant (Bell) instability, where the streaming of cosmic rays (CRs) leads to the amplification of magnetic fields necessary to scatter particles. In this work we use kinetic particle-in-cell simulations to investigate the high-CR-current regime, where the typical assumptions underlying the Bell instability break down. Despite being more strongly driven, significantly less magnetic field amplification is observed than in low-current cases, an effect due to the anisotropic heating that occurs in this regime. We also find that electron-scale modes, despite being the fastest growing, mostly lead to moderate electron heating and do not affect the late evolution or saturation of the instability. 

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4. Hybrid Simulations of the Resonant and Non-Resonant Cosmic Ray Streaming Instability

   Haggerty, C.; Caprioli, D.; Zweibel, E. (July 2019, 36th International Cosmic Ray Conference (ICRC2019))

   Using hybrid simulations (kinetic ions--fluid electrons), we test the linear theory predictions of the cosmic ray (CR) streaming instability. We consider two types of CR distribution functions: a "hot" distribution where CRs are represented by a drifting power law in momentum and an anisotropic "beam" of monochromatic particles. Additionally, for each CR distribution we scan over different CR densities to transition from triggering the resonant to the non-resonant (Bell) streaming instability. We determine the growth rates of these instabilities in simulations by fitting an exponential curve during the linear stage, and we show that they agree well with the theoretical predictions as a function of wave number agree. We also examine the magnetic helicity as a function of time and wave number, finding a general good agreement with the predictions, as well as some unexpected non-linear features to the instability development. 

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5. Turbulent Cosmic Ray–Mediated Shocks in the Hot Ionized Interstellar Medium

   https://doi.org/10.3847/1538-4357/ac6ddc  

   Wang, B.-B.; Zank, G. P.; Zhao, L.-L.; Adhikari, L. (June 2022, The Astrophysical Journal)

   Abstract The structure of shocks and turbulence are strongly modified during the acceleration of cosmic rays (CRs) at a shock wave. The pressure and the collisionless viscous stress decelerate the incoming thermal gas and thus modify the shock structure. A CR streaming instability ahead of the shock generates the turbulence on which CRs scatter. The turbulent magnetic field in turn determines the CR diffusion coefficient and further affects the CR energy spectrum and pressure distribution. The dissipation of turbulence contributes to heating the thermal gas. Within a multicomponent fluid framework, CRs and thermal gas are treated as fluids and are closely coupled to the turbulence. The system equations comprise the gas dynamic equations, the CR pressure evolution equation, and the turbulence transport equations, and we adopt typical parameters for the hot ionized interstellar medium. It is shown that the shock has no discontinuity but possesses a narrow but smooth transition. The self-generated turbulent magnetic field is much stronger than both the large-scale magnetic field and the preexisting turbulent magnetic field. The resulting CR diffusion coefficient is substantially suppressed and is more than three orders smaller near the shock than it is far upstream. The results are qualitatively consistent with certain observations. 

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