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1. Ultra-High-Energy Cosmic Rays Accelerated by Magnetically Dominated Turbulence

   https://doi.org/10.3847/2041-8213/ad955f  

   Comisso, Luca; Farrar, Glennys_R; Muzio, Marco_S (December 2024, The Astrophysical Journal Letters)

   Abstract Ultra-high-energy cosmic rays (UHECRs), particles characterized by energies exceeding 10¹⁸eV, are generally believed to be accelerated electromagnetically in high-energy astrophysical sources. One promising mechanism of UHECR acceleration is magnetized turbulence. We demonstrate from first principles, using fully kinetic particle-in-cell simulations, that magnetically dominated turbulence accelerates particles on a short timescale, producing a power-law energy distribution with a rigidity-dependent, sharply defined cutoff well approximated by the form $f_{\mathrm{cut}}\left(E,E_{\mathrm{cut}}\right)=\mathrm{sech}\left({\left(E/E_{\mathrm{cut}}\right)}^2\right)$. Particle escape from the turbulent accelerating region is energy dependent, witht_esc∝E^−δandδ∼ 1/3. The resulting particle flux from the accelerator follows $\mathit{dN}/\mathit{dEdt}\propto E^{-s}\mathrm{sech}\left({\left(E/E_{\mathrm{cut}}\right)}^2\right)$, withs∼ 2.1. We fit the Pierre Auger Observatory’s spectrum and composition measurements, taking into account particle interactions between acceleration and detection, and show that the turbulence-associated energy cutoff is well supported by the data, with the best-fitting spectral index being $s={2.1}_{-0.13}^{+0.06}$. Our first-principles results indicate that particle acceleration by magnetically dominated turbulence may constitute the physical mechanism responsible for UHECR acceleration. 

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2. Kinetic-scale Current Sheets in the Solar Wind at 1 au: Scale-dependent Properties and Critical Current Density

   https://doi.org/10.3847/2041-8213/ac4fc4  

   Vasko, I. Y.; Alimov, K.; Phan, T.; Bale, S. D.; Mozer, F. S.; Artemyev, A. V. (February 2022, The Astrophysical Journal Letters)

   Abstract We present analysis of 17,043 proton kinetic-scale current sheets (CSs) collected over 124 days of Wind spacecraft measurements in the solar wind at 11 samples s⁻¹magnetic field resolution. The CSs have thickness,λ,from a few tens to one thousand kilometers with typical values around 100 km, or within about 0.1–10λ_pin terms of local proton inertial length,λ_p. We found that the current density is larger for smaller-scale CSs,J₀≈ 6 nAm⁻²· (λ/100 km)^−0.56, but does not statistically exceed a critical value,J_A,corresponding to the drift between ions and electrons of local Alvén speed. The observed trend holds in normalized units: $J_0/J_A\approx 0.17·{\left(\lambda /{\lambda }_p\right)}^{-0.51}$. The CSs are statistically force-free with magnetic shear angle correlated with CS spatial scale: $\mathrm{\Delta }\theta \approx 19°·{\left(\lambda /{\lambda }_p\right)}^{0.5}$. The observed correlations are consistent with local turbulence being the source of proton kinetic-scale CSs in the solar wind, while the mechanisms limiting the current density remain to be understood. 

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3. Bounds on eigenfunctions of quantum cat maps

   https://doi.org/10.1088/1402-4896/ad0331  

   Kim, Elena; Koirala, Robert (October 2023, Physica Scripta)

   Abstract We studyℓ^∞norms ofℓ²-normalized eigenfunctions of quantum cat maps. For maps with short quantum periods (constructed by Bonechi and de Biévre in F Bonechi and S De Bièvre (2000,Communications in Mathematical Physics,211, 659–686)) we show that there exists a sequence of eigenfunctionsuwith $\parallel u{\parallel }_{\infty }\gtrsim {\left(\log N\right)}^{-1/2}$. For general eigenfunctions we show the upper bound $\parallel u{\parallel }_{\infty }\lesssim {\left(\log N\right)}^{-1/2}$. Here the semiclassical parameter is $h={\left(2\pi N\right)}^{-1}$. Our upper bound is analogous to the one proved by Bérard in P Bérard (1977,Mathematische Zeitschrift,155, 249-276) for compact Riemannian manifolds without conjugate points. 

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4. Analytic genericity of diffusing orbits in a priori unstable Hamiltonian systems

   https://doi.org/10.1088/1361-6544/ac50bb  

   Chen, Qinbo; de la Llave, Rafael (March 2022, Nonlinearity)

   Abstract The genericity of Arnold diffusion in the analytic category is an open problem. In this paper, we study this problem in the followinga prioriunstable Hamiltonian system with a time-periodic perturbation ${\mathcal{H}}_{\epsilon }\left(p,q,I,\phi ,t\right)=h\left(I\right)+\sum _{i=1}^n\pm \left(\frac{1}{2}{p}_i^2+V_i\left(q_i\right)\right)+\epsilon H_1\left(p,q,I,\phi ,t\right),$where $\left(p,q\right)\in {\mathbb{R}}^n\times {\mathbb{T}}^n$, $\left(I,\phi \right)\in {\mathbb{R}}^d\times {\mathbb{T}}^d$withn,d⩾ 1,V_iare Morse potentials, andɛis a small non-zero parameter. The unperturbed Hamiltonian is not necessarily convex, and the induced inner dynamics does not need to satisfy a twist condition. Using geometric methods we prove that Arnold diffusion occurs for generic analytic perturbationsH₁. Indeed, the set of admissibleH₁isC^ωdense andC³open (a fortiori,C^ωopen). Our perturbative technique for the genericity is valid in theC^ktopology for allk∈ [3, ∞) ∪ {∞,ω}. 

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5. Compression Acceleration of Protons and Heavier Ions at the Heliospheric Current Sheet

   https://doi.org/10.3847/1538-4357/ad6e80  

   Murtas, Giulia; Li, Xiaocan; Guo, Fan (October 2024, The Astrophysical Journal)

   Abstract Recent observations by the Parker Solar Probe (PSP) suggest that protons and heavier ions are accelerated to high energies by magnetic reconnection at the heliospheric current sheet (HCS). By solving the energetic particle transport equation in large-scale MHD simulations, we study the compression acceleration of protons and heavier ions in the reconnecting HCS. We find that the acceleration of multispecies ions results in nonthermal power-law distributions with a spectral index consistent with the PSP observations. Our study shows that the high-energy cutoff of protons can reach $E_{\max }\sim 0.1$–1 MeV depending on the particle diffusion coefficients. We also study how the high-energy cutoff of different ion species scales with the charge-to-mass ratio $E_{\max }\propto {\left(Q/M\right)}^{\alpha }$. When determining the diffusion coefficients from the quasi-linear theory with a Kolmogorov magnetic power spectrum, we find thatα∼ 0.4, which is somewhat smaller thanα∼ 0.7 observed by PSP. 

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