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• W795367940 abstract "A central problem in the theory of cosmic ray acceleration at supernova shock fronts is the generation of turbulent magnetic fields needed to scatter particles across a shock front. In this paper we build on previous studies [1], [2] into the effect of streaming cosmic rays produced by the outer shocks of supernova remnants on the stochastic component of the magnetic field. A three dimensional, MHD code has been constructed which demonstrates the nonlinear growth of the turbulent field. Introduction There is clear radio, X-ray and gamma ray observational evidence that electrons, and probably protons, are accelerated to energies in excess of 10 eV in supernova remnants ( [1]). Diffusive shock acceleration provides the most natural explanation for the spectral shape. This process requires the presence of magnetic field turbulence that repeatedly scatters particles across the shock front. The timescale for acceleration is constrained by the level of the turbulence, through the particle’s diffusion coefficient. Bell ( [1]) has recently shown that, in the MHD limit, particle anisotropy upstream of the shock can excite turbulence many orders of magnitude greater than the background interstellar medium value thereby lowering the particle diffusion coefficient and making the process more rapid than previously though. In this paper we confirm Bell’s linear analysis by using kinetic theory ( [3]) and present some intial results from a code using a three dimensional Godunov scheme. Linear Instability in Kinetic Theory The linear dispersion relation for circularly polarised transverse waves propagating parallel to the zeroth order magnetic field is ck ω2 −1 = ∑ s χs(k,ω) (1) where the summation is over species f0s with charge qs and χs = 4πqs ω2 ∫ d p v⊥p⊥ ω ±ωcs − kv‖ [ (ω − kv‖) ∂ f0s ∂ p2⊥ + kv‖ ∂ f0s ∂ p2‖ ] (2) 33rd EPS Conference on Plasma Phys. Rome, 19 23 June 2006 ECA Vol.30I, P-4.056 (2006) is the susceptibility of each plasma component. We assume the plasma has three components; (i) cold background protons of density np, with a small drift velocity up along the mean magnetic field, (ii) cold background electrons with small drift velocity ue, density ne, also drifting along the mean magnetic field and (iii) anisotropic cosmic rays, for simplicity consists only of protons We also require the plasma to have overall charge neutrality, ∑s qsns = 0, and zero net current, ∑s qsnsus = 0. If the background proton and electron distributions are Maxwellian with drifts up and ue respectively, the susceptibility of the background plasma is χbg = Σ ωsω 2 ps ω(ωs ±ωcs) [ (ωs ±ωcs) √ 2kVts Z ( (ωs ±ωcs) √ 2kVts )] (3) where ωs = ω − kus denotes the doppler shifted frequency of each species, ωps the plasma frequency, ωcs the cyclotron and Z(ζ ) is the plasma dispersion function. For a cold plasma (ζ ≫ 1) and waves of short wavelength ωs ≪ ωc, the background susceptibility is ωχbg = c cA [ ω i ∓ kV 2 ti ωci ωi ∓ ωcikJ 1 cr ni ] (4) in agreement with Achterberg [3]. J cr = ncrucr − ωk ncr is related to the cosmic ray flux density. The J cr term results from the background plasma attempting to compensate for the CR current and corresponds to the return current [1, 2, 4]. The CR distribution is expressed as the first two terms in the Chapman-Enskog expansion fcr(p,μ) = f0(p)+ μ f1(p) giving the susceptibility of the CRs as, with λ = eB0/kpc, ωχcr ≈± c cA ωcik ni ( 1− ω 2 k2c2 )1/2[∫ d p4π p 1 3 v f1σp ] w (5) where σp(λ ) = 3 4 λ (1−λ ) [" @default.
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• W795367940 date "2006-01-01" @default.
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• W795367940 title "The Nonlinear Amplification of Magnetic Fields by Cosmic Rays at Supernova Remnant Shocks" @default.
• W795367940 doi "https://doi.org/10.21427/dgzw-f436" @default.
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