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Journal articles on the topic 'Nekhoroshev Theorem'

Author: Grafiati

Published: 9 March 2023

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1

Wiggins, S., and A. M. Mancho. "Barriers to transport in aperiodically time-dependent two-dimensional velocity fields: Nekhoroshev's theorem and "Nearly Invariant" tori." Nonlinear Processes in Geophysics 21, no. 1 (February 4, 2014): 165–85. http://dx.doi.org/10.5194/npg-21-165-2014.

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Abstract. In this paper we consider fluid transport in two-dimensional flows from the dynamical systems point of view, with the focus on elliptic behaviour and aperiodic and finite time dependence. We give an overview of previous work on general nonautonomous and finite time vector fields with the purpose of bringing to the attention of those working on fluid transport from the dynamical systems point of view a body of work that is extremely relevant, but appears not to be so well known. We then focus on the Kolmogorov–Arnold–Moser (KAM) theorem and the Nekhoroshev theorem. While there is no finite time or aperiodically time-dependent version of the KAM theorem, the Nekhoroshev theorem, by its very nature, is a finite time result, but for a "very long" (i.e. exponentially long with respect to the size of the perturbation) time interval and provides a rigorous quantification of "nearly invariant tori" over this very long timescale. We discuss an aperiodically time-dependent version of the Nekhoroshev theorem due to Giorgilli and Zehnder (1992) (recently refined by Bounemoura, 2013 and Fortunati and Wiggins, 2013) which is directly relevant to fluid transport problems. We give a detailed discussion of issues associated with the applicability of the KAM and Nekhoroshev theorems in specific flows. Finally, we consider a specific example of an aperiodically time-dependent flow where we show that the results of the Nekhoroshev theorem hold.

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2

Bambusi, Dario, and Beatrice Langella. "A $C^\infty$ Nekhoroshev theorem." Mathematics in Engineering 3, no. 2 (2021): 1–17. http://dx.doi.org/10.3934/mine.2021019.

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3

Gaeta, Giuseppe. "The Poincaré–Lyapounov–Nekhoroshev Theorem." Annals of Physics 297, no. 1 (April 2002): 157–73. http://dx.doi.org/10.1006/aphy.2002.6238.

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4

Guzzo, M. "The nekhoroshev theorem and long-term stabilities in the solar system." Serbian Astronomical Journal, no. 190 (2015): 1–10. http://dx.doi.org/10.2298/saj1590001g.

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The Nekhoroshev theorem has been often indicated in the last decades as the reference theorem for explaining the dynamics of several systems which are stable in the long-term. The Solar System dynamics provides a wide range of possible and useful applications. In fact, despite the complicated models which are used to numerically integrate realistic Solar System dynamics as accurately as possible, when the integrated solutions are chaotic the reliability of the numerical integrations is limited, and a theoretical long-term stability analysis is required. After the first formulation of Nekhoroshev?s theorem in 1977, many theoretical improvements have been achieved. On the one hand, alternative proofs of the theorem itself led to consistent improvements of the stability estimates; on the other hand, the extensions which were necessary to apply the theorem to the systems of interest for Solar System Dynamics, in particular concerning the removal of degeneracies and the implementation of computer assisted proofs, have been developed. In this review paper we discuss some of the motivations and the results which have made Nekhoroshev?s theorem a reference stability result for many applications in the Solar System dynamics.

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5

FIORANI, EMANUELE. "GEOMETRICAL ASPECTS OF INTEGRABLE SYSTEMS." International Journal of Geometric Methods in Modern Physics 05, no. 03 (May 2008): 457–71. http://dx.doi.org/10.1142/s0219887808002886.

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We review some basic theorems on integrability of Hamiltonian systems, namely the Liouville–Arnold theorem on complete integrability, the Nekhoroshev theorem on partial integrability and the Mishchenko–Fomenko theorem on noncommutative integrability, and for each of them we give a version suitable for the noncompact case. We give a possible global version of the previous local results, under certain topological hypotheses on the base space. It turns out that locally affine structures arise naturally in this setting.

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6

Froeschlé, Claude, and Elena Lega. "On the Diffusion Along Resonant Lines in Continuous and Discrete Dynamical Systems." International Journal of Modern Physics B 17, no. 22n24 (September 30, 2003): 3964–76. http://dx.doi.org/10.1142/s0217979203023033.

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We detect and measure diffusion along resonances in a discrete symplectic map for different values of the coupling parameter. Qualitatively and quantitatively the results are very similar to those obtained for a quasi-integrable Hamiltonian system, i.e. in agreement with Nekhoroshev predictions, although the discrete mapping does not fulfill completely, a priori, the conditions of the Nekhoroshev theorem.

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7

Todorovic, N. "The role of a steepness parameter in the exponential stability of a model problem: Numerical aspects." Serbian Astronomical Journal, no. 182 (2011): 25–33. http://dx.doi.org/10.2298/saj1182025t.

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The Nekhoroshev theorem considers quasi integrable Hamiltonians providing stability of actions in exponentially long times. One of the hypothesis required by the theorem is a mathematical condition called steepness. Nekhoroshev conjectured that different steepness properties should imply numerically observable differences in the stability times. After a recent study on this problem (Guzzo et al. 2011, Todorovic et al. 2011) we show some additional numerical results on the change of resonances and the diffusion laws produced by the increasing effect of steepness. The experiments are performed on a 4-dimensional steep symplectic map designed in a way that a parameter smoothly regulates the steepness properties in the model.

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8

Henrici, Andreas. "Nekhoroshev Stability for the Dirichlet Toda Lattice." Symmetry 10, no. 10 (October 16, 2018): 506. http://dx.doi.org/10.3390/sym10100506.

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In this work, we prove a Nekhoroshev-type stability theorem for the Toda lattice with Dirichlet boundary conditions, i.e., with fixed ends. The Toda lattice is a member of the family of Fermi-Pasta-Ulam (FPU) chains, and in view of the unexpected recurrence phenomena numerically observed in these chains, it has been a long-standing research aim to apply the theory of perturbed integrable systems to these chains, in particular to the Toda lattice which has been shown to be a completely integrable system. The Dirichlet Toda lattice can be treated mathematically by using symmetries of the periodic Toda lattice. Precisely, by treating the phase space of the former system as an invariant subset of the latter one, namely as the fixed point set of an important symmetry of the periodic lattice, the results already obtained for the periodic lattice can be used to obtain analogous results for the Dirichlet lattice. In this way, we transfer our stability results for the periodic lattice to the Dirichlet lattice. The Nekhoroshev theorem is a perturbation theory result which does not have the probabilistic character of related theorems, and the lattice with fixed ends is more important for applications than the periodic one.

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9

Xue, Jinxin. "Continuous averaging proof of the Nekhoroshev theorem." Discrete & Continuous Dynamical Systems - A 35, no. 8 (2015): 3827–55. http://dx.doi.org/10.3934/dcds.2015.35.3827.

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10

Moszynski, M. "A quantum version of the Nekhoroshev theorem." Journal of Physics A: Mathematical and General 25, no. 8 (April 21, 1992): L443—L448. http://dx.doi.org/10.1088/0305-4470/25/8/011.

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11

Henrici, Andreas, and Thomas Kappeler. "Nekhoroshev theorem for the periodic Toda lattice." Chaos: An Interdisciplinary Journal of Nonlinear Science 19, no. 3 (September 2009): 033120. http://dx.doi.org/10.1063/1.3196783.

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12

Monti, F., and H. R. Jauslin. "Quantum Nekhoroshev Theorem for Quasi-Periodic Floquet Hamiltonians." Reviews in Mathematical Physics 10, no. 03 (April 1998): 393–428. http://dx.doi.org/10.1142/s0129055x98000124.

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A quantum version of Nekhoroshev estimates for Floquet Hamiltonians associated to quasi-periodic time dependent perturbations is developped. If the unperturbed energy operator has a discrete spectrum and under finite Diophantine conditions, an effective Floquet Hamiltonian with pure point spectrum is constructed. For analytic perturbations, the effective time evolution remains close to the original Floquet evolution up to exponentially long times. We also treat the case of differentiable perturbations.

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13

Perfetti, Paolo. "A Nekhoroshev theorem for some infinite--dimensional systems." Communications on Pure & Applied Analysis 5, no. 1 (2006): 125–46. http://dx.doi.org/10.3934/cpaa.2006.5.125.

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14

Bambusi, Dario, and Alessandra Fusè. "Nekhoroshev theorem for perturbations of the central motion." Regular and Chaotic Dynamics 22, no. 1 (January 2017): 18–26. http://dx.doi.org/10.1134/s1560354717010026.

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15

Morbidelli, Alessandro, and Massimiliano Guzzo. "The nekhoroshev theorem and the asteroid belt dynamical system." Celestial Mechanics and Dynamical Astronomy 65, no. 1-2 (1997): 107–36. http://dx.doi.org/10.1007/bf00048442.

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16

Cong, Hongzi, Chunyong Liu, and Peizhen Wang. "A Nekhoroshev type theorem for the nonlinear wave equation." Journal of Differential Equations 269, no. 4 (August 2020): 3853–89. http://dx.doi.org/10.1016/j.jde.2020.03.015.

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17

Guzzo, Massimiliano. "Nekhoroshev Stability in Quasi-Integrable Degenerate Hamiltonian Systems." International Astronomical Union Colloquium 172 (1999): 443–44. http://dx.doi.org/10.1017/s0252921100073085.

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Many classical problems of Mechanics can be studied regarding them as perturbations of integrable systems; this is the case of the fast rotations of the rigid body in an arbitrary potential, the restricted three body problem with small values of the mass-ratio, and others. However, the application of the classical results of Hamiltonian Perturbation Theory to these systems encounters difficulties due to the presence of the so-called ‘degeneracy’. More precisely, the Hamiltonian of a quasi-integrable degenerate system looks likewhere (I, φ) є U × Tn, U ⊆ Rn, are action-angle type coordinates, while the degeneracy of the system manifests itself with the presence of the ‘degenerate’ variables (p, q) є B ⊆ R2m. The KAM theorem has been applied under quite general assumptions to degenerate Hamiltonians (Arnold, 1963), while the Nekhoroshev theorem (Nekhoroshev, 1977) provides, if h is convex, the following bounds: there exist positive ε0, a0, t0 such that if ε < ε0 then if where Te is the escape time of the solution from the domain of (1). An escape is possible because the motion of the degenerate variables can be bounded in principle only by , and so over the time they can experience large variations. Therefore, there is the problem of individuating which assumptions on the perturbation and on the initial data allow to control the motion of the degenerate variables over long times.

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18

Henrici, Andreas. "Nekhoroshev Theorem for the Toda Lattice with Dirichlet Boundary Conditions." Proceedings 2, no. 1 (January 3, 2018): 18. http://dx.doi.org/10.3390/proceedings2010018.

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19

Zhou, Shidi, and Jiansheng Geng. "A Nekhoroshev Type Theorem of Higher Dimensional Nonlinear Schrödinger Equations." Taiwanese Journal of Mathematics 21, no. 5 (October 2017): 1115–32. http://dx.doi.org/10.11650/tjm/7951.

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20

Efthymiopoulos, Christos. "On the connection between the Nekhoroshev theorem and Arnold diffusion." Celestial Mechanics and Dynamical Astronomy 102, no. 1-3 (August 5, 2008): 49–68. http://dx.doi.org/10.1007/s10569-008-9151-8.

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21

Fiorani, Emanuele, Giovanni Giachetta, and Gennadi Sardanashvily. "The Liouville Arnold Nekhoroshev theorem for non-compact invariant manifolds." Journal of Physics A: Mathematical and General 36, no. 7 (February 5, 2003): L101—L107. http://dx.doi.org/10.1088/0305-4470/36/7/102.

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22

Bambusi, Dario. "Nekhoroshev theorem for small amplitude solutions in nonlinear Schrödinger equations." Mathematische Zeitschrift 230, no. 2 (February 1999): 345–87. http://dx.doi.org/10.1007/pl00004696.

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23

Cong, Hongzi, Lufang Mi, and Peizhen Wang. "A Nekhoroshev type theorem for the derivative nonlinear Schrödinger equation." Journal of Differential Equations 268, no. 9 (April 2020): 5207–56. http://dx.doi.org/10.1016/j.jde.2019.11.005.

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24

Gaeta, Giuseppe. "The Poincaré–Lyapounov–Nekhoroshev theorem for involutory systems of vector fields." Annals of Physics 321, no. 6 (June 2006): 1277–95. http://dx.doi.org/10.1016/j.aop.2006.01.002.

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25

Pavlovic, R. "Third derivatives of the integrable part of an asteroid Hamiltonian." Serbian Astronomical Journal, no. 174 (2007): 53–60. http://dx.doi.org/10.2298/saj0774053p.

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To apply the theorem of Nekhoroshev (1977) to asteroids, one first has to check whether a necessary geometrical condition is fulfilled: either convexity, or quasi-convexity, or only a 3-jet non-degeneracy. This requires computation of the derivatives of the integrable part of the corresponding Hamiltonian up to the third order over actions and a thorough analysis of their properties. In this paper we describe in detail the procedure of derivation and we give explicit expressions for the obtained derivatives. .

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26

Mi, Lufang, Chunyong Liu, Guanghua Shi, and Rong Zhao. "A Nekhoroshev type theorem for the nonlinear wave equation on the torus." Pure and Applied Mathematics Quarterly 16, no. 5 (2020): 1739–65. http://dx.doi.org/10.4310/pamq.2020.v16.n5.a14.

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27

Faou, Erwan, and Benoît Grébert. "A Nekhoroshev-type theorem for the nonlinear Schrödinger equation on the torus." Analysis & PDE 6, no. 6 (November 18, 2013): 1243–62. http://dx.doi.org/10.2140/apde.2013.6.1243.

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28

Pasquali, Stefano. "A Nekhoroshev type theorem for the nonlinear Klein-Gordon equation with potential." Discrete & Continuous Dynamical Systems - B 23, no. 9 (2018): 3573–94. http://dx.doi.org/10.3934/dcdsb.2017215.

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29

Liu, Chunyong, Huayong Liu, and Rong Zhao. "A Nekhoroshev Type Theorem for the Nonlinear Wave Equation in Gevrey Space." Chinese Annals of Mathematics, Series B 40, no. 3 (May 2019): 389–410. http://dx.doi.org/10.1007/s11401-019-0140-x.

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30

Guzzo, Massimiliano. "A Direct Proof of the Nekhoroshev Theorem for Nearly Integrable Symplectic Maps." Annales Henri Poincaré 5, no. 6 (December 2004): 1013–39. http://dx.doi.org/10.1007/s00023-004-0188-2.

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31

Cellett, Alessandra, and Laura Ferrara. "An application of the Nekhoroshev theorem to the restricted three-body problem." Celestial Mechanics & Dynamical Astronomy 64, no. 3 (1996): 261–72. http://dx.doi.org/10.1007/bf00728351.

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32

Guzzo, Massimiliano, and Elena Lega. "The Nekhoroshev theorem and the observation of long-term diffusion in Hamiltonian systems." Regular and Chaotic Dynamics 21, no. 6 (November 2016): 707–19. http://dx.doi.org/10.1134/s1560354716060101.

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33

Pöschel, Jürgen. "On Nekhoroshev estimates for a nonlinear Schrödinger equation and a theorem by Bambusi." Nonlinearity 12, no. 6 (October 6, 1999): 1587–600. http://dx.doi.org/10.1088/0951-7715/12/6/310.

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34

Benettin, Giancarlo, J�rg Fr�hlich, and Antonio Giorgilli. "A Nekhoroshev-type theorem for Hamiltonian systems with infinitely many degrees of freedom." Communications in Mathematical Physics 119, no. 1 (March 1988): 95–108. http://dx.doi.org/10.1007/bf01218262.

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35

Guzzo, Massimiliano, and Giancarlo Benettin. "A spectral formulation of the Nekhoroshev theorem and its relevance for numerical and experimental data analysis." Discrete & Continuous Dynamical Systems - B 1, no. 1 (2001): 1–28. http://dx.doi.org/10.3934/dcdsb.2001.1.1.

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36

Pavlović, R., and M. Guzzo. "Fulfillment of the conditions for the application of the Nekhoroshev theorem to the Koronis and Veritas asteroid families." Monthly Notices of the Royal Astronomical Society 384, no. 4 (March 2008): 1575–82. http://dx.doi.org/10.1111/j.1365-2966.2007.12813.x.

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37

Guzzo, M., L. Chierchia, and G. Benettin. "The Steep Nekhoroshev’s Theorem." Communications in Mathematical Physics 342, no. 2 (January 21, 2016): 569–601. http://dx.doi.org/10.1007/s00220-015-2555-x.

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38

Bates, Larry, and Richard Cushman. "A generalization of Nekhoroshev’s theorem." Regular and Chaotic Dynamics 21, no. 6 (November 2016): 639–42. http://dx.doi.org/10.1134/s1560354716060046.

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39

Bounemoura, Abed, and Stéphane Fischler. "A Diophantine duality applied to the KAM and Nekhoroshev theorems." Mathematische Zeitschrift 275, no. 3-4 (May 22, 2013): 1135–67. http://dx.doi.org/10.1007/s00209-013-1174-5.

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40

Morbidelli, Alessandro, and Antonio Giorgilli. "On a connection between KAM and Nekhoroshev's theorems." Physica D: Nonlinear Phenomena 86, no. 3 (September 1995): 514–16. http://dx.doi.org/10.1016/0167-2789(95)00199-e.

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41

Guzzo, Massimiliano, Luigi Chierchia, and Giancarlo Benettin. "The steep Nekhoroshev’s Theorem and optimal stability exponents (an announcement)." Rendiconti Lincei - Matematica e Applicazioni 25, no. 3 (2014): 293–99. http://dx.doi.org/10.4171/rlm/679.

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42

Moan, Per Christian. "On the KAM and Nekhoroshev theorems for symplectic integrators and implications for error growth." Nonlinearity 17, no. 1 (September 29, 2003): 67–83. http://dx.doi.org/10.1088/0951-7715/17/1/005.

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43

Benettin, Giancarlo, Luigi Galgani, and Antonio Giorgilli. "A proof of Nekhoroshev's theorem for the stability times in nearly integrable Hamiltonian systems." Celestial Mechanics 37, no. 1 (September 1985): 1–25. http://dx.doi.org/10.1007/bf01230338.

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44

De Blasi, Irene, Alessandra Celletti, and Christos Efthymiopoulos. "Satellites’ orbital stability through normal forms." Proceedings of the International Astronomical Union 15, S364 (October 2021): 146–51. http://dx.doi.org/10.1017/s174392132100137x.

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AbstractA powerful tool to investigate the stability of the orbits of natural and artificial bodies is represented by perturbation theory, which allows one to provide normal form estimates for nearly-integrable problems in Celestial Mechanics. In particular, we consider the orbital stability of point-mass satellites moving around the Earth. On the basis of the J2 model, we investigate the stability of the semimajor axis. Using a secular Hamiltonian model including also lunisolar perturbations, the so-called geolunisolar model, we study the stability of the other orbital elements, namely the eccentricity and the inclination. We finally discuss the applicability of Nekhoroshev’s theorem on the exponential stability of the action variables. To this end, we investigate the non-degeneracy properties of the J2 and geolunisolar models. We obtain that the J2 model satisfies a “three-jet” non-degeneracy condition, while the geolunisolar model is quasi-convex non-degenerate.

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45

Desogus, Marco, and Elisa Casu. "A SURVEY ON MACROECONOMIC DATA IN THE EUROZONE AND A CONTROL DASHBOARD MODEL BASED ON THE KAM AND NEKHOROSHEV THEOREMS AND THE HÉNON ATTRACTOR." Journal of Academy of Business and Economics 21, no. 3 (October 1, 2021): 67–85. http://dx.doi.org/10.18374/jabe-21-3.6.

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46

Celletti, Alessandra, Irene De Blasi, and Christos Efthymiopoulos. "Nekhoroshev estimates for the orbital stability of Earth’s satellites." Celestial Mechanics and Dynamical Astronomy 135, no. 2 (February 26, 2023). http://dx.doi.org/10.1007/s10569-023-10124-9.

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AbstractWe provide stability estimates, obtained by implementing the Nekhoroshev theorem, in reference to the orbital motion of a small body (satellite or space debris) around the Earth. We consider a Hamiltonian model, averaged over fast angles, including the $$J_2$$ J 2 geopotential term as well as third-body perturbations due to Sun and Moon. We discuss how to bring the Hamiltonian into a form suitable for the implementation of the Nekhoroshev theorem in the version given by Pöschel, (Math Z 213(1):187–216, 1993) for the ‘non-resonant’ regime. The manipulation of the Hamiltonian includes (i) averaging over fast angles, (ii) a suitable expansion around reference values for the orbit’s eccentricity and inclination, and (iii) a preliminary normalization allowing to eliminate particular terms whose existence is due to the nonzero inclination of the invariant plane of secular motions known as the ‘Laplace plane’. After bringing the Hamiltonian to a suitable form, we examine the domain of applicability of the theorem in the action space, translating the result in the space of physical elements. We find that the necessary conditions for the theorem to hold are fulfilled in some nonzero measure domains in the eccentricity and inclination plane (e, i) for a body’s orbital altitude (semimajor axis) up to about 20 000 km. For altitudes around 11 000 km, we obtain stability times of the order of several thousands of years in domains covering nearly all eccentricities and inclinations of interest in applications of the satellite problem, except for narrow zones around some so-called inclination-dependent resonances. On the other hand, the domains of Nekhoroshev stability recovered by the present method shrink in size as the semimajor axis a increases (and the corresponding Nekhoroshev times reduce to hundreds of years), while the stability domains practically all vanish for $$a>20{\,}000$$ a > 20 000 km. We finally examine the effect on Nekhoroshev stability by adding more geopotential terms ($$J_3$$ J 3 and $$J_4$$ J 4 ) as well as the second-order terms in $$J_2$$ J 2 in the Hamiltonian. We find that these terms have only a minimal effect on the domains of applicability of Nekhoroshev theorem and a moderate effect on the stability times.

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47

Giorgilli, Antonio. "IL FLEBILE SUSSURRO DEL CAOS NELL’ARMONIA DEI PIANETI." Istituto Lombardo - Accademia di Scienze e Lettere - Incontri di Studio, October 5, 2018. http://dx.doi.org/10.4081/incontri.2018.392.

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The hystorical development of the problem of stability of the Solar System is revisited, starting fromthe work of Kepler. The following topics are included: (i) the discovery of the so called ‘‘great inequality’’ of Jupiter and Saturn by Kepler himself; (ii) the dawn of perturbation theory in the work of Lagrange and Laplace and the problem of resonances; (iii) the discovery of chaotic motions in the work of Poincar´e; (iv) the theorem of Kolmogorov on persistence of quasi periodic motions and the theory of Nekhoroshev on stability over exponentially long times. Finally, an account is given concerning some recent work on the actual applicability of the theorems of Kolmogorov and Nekhoroshev to realistic models of the Solar System, thus pointing out their relevance in discussing the problem of stability.

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48

Bambusi, D. "A Reversible Nekhoroshev Theorem for Persistence of Invariant Tori in Systems with Symmetry." Mathematical Physics, Analysis and Geometry 18, no. 1 (July 7, 2015). http://dx.doi.org/10.1007/s11040-015-9190-9.

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49

Bounemoura, Abed, and Jacques Féjoz. "Hamiltonian perturbation theory for ultra-differentiable functions." Memoirs of the American Mathematical Society 270, no. 1319 (March 2021). http://dx.doi.org/10.1090/memo/1319.

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Some scales of spaces of ultra-differentiable functions are introduced, having good stability properties with respect to infinitely many derivatives and compositions. They are well-suited for solving non-linear functional equations by means of hard implicit function theorems. They comprise Gevrey functions and thus, as a limiting case, analytic functions. Using majorizing series, we manage to characterize them in terms of a real sequence M M bounding the growth of derivatives. In this functional setting, we prove two fundamental results of Hamiltonian perturbation theory: the invariant torus theorem, where the invariant torus remains ultra-differentiable under the assumption that its frequency satisfies some arithmetic condition which we call BR M _M , and which generalizes the Bruno-Rüssmann condition; and Nekhoroshev’s theorem, where the stability time depends on the ultra-differentiable class of the pertubation, through the same sequence M M . Our proof uses periodic averaging, while a substitute for the analyticity width allows us to bypass analytic smoothing. We also prove converse statements on the destruction of invariant tori and on the existence of diffusing orbits with ultra-differentiable perturbations, by respectively mimicking a construction of Bessi (in the analytic category) and Marco-Sauzin (in the Gevrey non-analytic category). When the perturbation space satisfies some additional condition (we then call it matching), we manage to narrow the gap between stability hypotheses (e.g. the BR M _M condition) and instability hypotheses, thus circumbscribing the stability threshold. The formulas relating the growth M M of derivatives of the perturbation on the one hand, and the arithmetics of robust frequencies or the stability time on the other hand, bring light to the competition between stability properties of nearly integrable systems and the distance to integrability. Due to our method of proof using width of regularity as a regularizing parameter, these formulas are closer to optimal as the the regularity tends to analyticity.

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50

Montanari, C. E., A. Bazzani, and M. Giovannozzi. "Probing the diffusive behaviour of beam-halo dynamics in circular accelerators." European Physical Journal Plus 137, no. 11 (November 21, 2022). http://dx.doi.org/10.1140/epjp/s13360-022-03478-w.

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AbstractCircular particle accelerators at the energy frontier are based on superconducting magnets that are extremely sensitive to beam losses as these might induce quenches, i.e. transitions to the normal-conducting state. Furthermore, the energy stored in the circulating beam is so large that hardware integrity is put in serious danger, and machine protection becomes essential for reaching the nominal accelerator performance. In this challenging context, the beam halo becomes a potential source of performance limitations and its dynamics needs to be understood in detail to assess whether it could be an issue for the accelerator. In this paper, we discuss in detail a recent framework, based on a diffusive approach, to model beam-halo dynamics. The functional form of the optimal estimate of the perturbative series, as given by Nekhoroshev’s theorem, is used to provide the functional form of the action diffusion coefficient. The goal is to propose an effective model for the beam-halo dynamics and to devise an efficient experimental procedure to obtain an accurate measurement of the diffusion coefficient.

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