Beam Instabilities in Hadron Synchrotrons

Métral, E.; Argyropoulos, Theodoros; Bartosik, Hannes; Biancacci, Nicolò; Buffat, Xavier; Müller, J. F. Esteban; Herr, W.; Iadarola, Giovanni; Lasheen, Alexandre; Li, K.; Oeftiger, Adrian; Pieloni, Tatiana; Quartullo, Danilo; Rumolo, G.; Salvant, Benoît; Schenk, Michael; Shaposhnikova, E.; Tambasco, Claudia; Timkó, Helga; Zannini, Carlo; Burov, A.; Bànfi, D.; Barranco, J.; Mounet, Nicolas; Boine‐Frankenheim, Oliver; Niedermayer, Uwe; Kornilov, V.; White, S.

doi:10.1109/tns.2015.2513752

Cited by 47 publications

(29 citation statements)

References 104 publications

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“…Therefore, we count each application of Boris trick as one evaluation of f, ignoring the cost of computing vector products. Non-staggered Boris (2) requires one evaluation of f per time step. Thus, its total cost when computing N steps many time steps is simply W boris = N steps .…”

Section: Bgsdc For Inhomogeneous Magnetic Fieldsmentioning

confidence: 99%

“…Here, x(t) is a vector containing all particles' position at some time t, v(t) contains all particles' velocities, α is the charge-tomass ratio, E the electric field (both externally applied and internally generated from particle interaction) and B the magnetic field. The Lorentz equations are used in many applications in computational plasma physics, for example laser-plasma interactions [1], particle accelerators [2] or nuclear fusion reactors [3]. The Boris method, introduced by Boris in 1970 [4], is the most popular numerical scheme used for solving (1) although other numerical time stepping methods like Runge-Kutta-4 are used as well.…”

Section: Introductionmentioning

confidence: 99%

“…Algorithm 1: Boris' trick for unstaggered Velocity-Verlet (2). See Birdsall and Langdon [23, for the geometric derivation.…”

Section: Introductionmentioning

confidence: 99%

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An arbitrary order time-stepping algorithm for tracking particles in inhomogeneous magnetic fields

Tretiak

Ruprecht

2019

Journal of Computational Physics: X

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The Lorentz equations describe the motion of electrically charged particles in electric and magnetic fields and are used widely in plasma physics. The most popular numerical algorithm for solving them is the Boris method, a variant of the Störmer-Verlet algorithm. Boris' method is phase space volume conserving and simulated particles typically remain near the correct trajectory. However, it is only second order accurate. Therefore, in scenarios where it is not enough to know that a particle stays on the right trajectory but one needs to know where on the trajectory the particle is at a given time, Boris method requires very small time steps to deliver accurate phase information, making it computationally expensive. We derive an improved version of the high-order Boris spectral deferred correction algorithm (Boris-SDC) by adopting a convergence acceleration strategy for second order problems based on the Generalised Minimum Residual (GMRES) method. Our new algorithm is easy to implement as it still relies on the standard Boris method. Like Boris-SDC it can deliver arbitrary order of accuracy through simple changes of runtime parameter but possesses better long-term energy stability. We demonstrate for two examples, a magnetic mirror trap and the Solev'ev equilibrium, that the new method can deliver better accuracy at lower computational cost compared to the standard Boris method. While our examples are motivated by tracking ions in the magnetic field of a nuclear fusion reactor, the introduced algorithm can potentially deliver similar improvements in efficiency for other applications.

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Section: Bgsdc For Inhomogeneous Magnetic Fieldsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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An arbitrary order time-stepping algorithm for tracking particles in inhomogeneous magnetic fields

Tretiak

Ruprecht

2019

Journal of Computational Physics: X

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“…This paper will present the results of a series of analytic and simulation studies that aim to show how linear coupling can affect the single bunch transverse stability by modification of the amplitude detuning from the LOs. Time domain simulations will be performed using PYHEADTAIL [14][15][16], a self-consistent 6D macroparticle tracker. These will be compared with an analytic approach which consists of several frequency domain calculations.…”

Section: Introductionmentioning

confidence: 99%

Transverse beam instabilities in the presence of linear coupling in the Large Hadron Collider

Carver

Buffat

et al. 2018

Phys. Rev. Accel. Beams

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In the past, transverse coherent instabilities have been observed at the Hadron-Electron Ring Accelerator (HERA) proton ring that were instigated by the presence of linear coupling. Linear coupling can also potentially explain some transverse instabilities that were observed in the Large Hadron Collider (LHC) in both run I and run II, however a detailed description of the destabilizing mechanism of linear coupling was not known at the time. A study into the effect of linear coupling on transverse beam stability was carried out, and a new mechanism that could incite transverse instabilities by causing a loss of Landau damping has been found. The study includes time domain simulations with PYHEADTAIL and frequency domain computations based on analytical approaches, and was then verified by measurements with a single proton bunch in the LHC.

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“…The amplitude detuning introduced by the octupoles will modify the overall tune spread and when the beams are not colliding head-on their contribution, detrimental or not, can become important. Dedicated studies and analysis on the impact and role of the octupoles during the LHC operation cycle can be found in [10]. The contribution of octupoles will therefore not be further discussed but was taken into account when attempting to reproduce experimental data in Sec.…”

Section: Introductionmentioning

confidence: 99%

Transverse mode coupling instability of colliding beams

White

Buffat

Mounet

et al. 2014

Phys. Rev. ST Accel. Beams

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In high brightness circular colliders, coherent and incoherent beam dynamics are dominated by beambeam interactions. It is generally assumed that the incoherent tune spread introduced by the beam-beam interactions is sufficiently large to cure any instabilities originating from impedance. However, as the two counterrotating beams interact they can give rise to coherent dipole modes and therefore modify the coherent beam dynamics and stability conditions. In this case, coherent beam-beam effects and impedance cannot be treated independently and their interplay should be taken into account in any realistic attempt to study the beam stability of colliding beams. Due to the complexity of these physics processes, numerical simulations become an important tool for the analysis of this system. Two approaches are proposed in this paper: a fully self-consistent multiparticle tracking including particle-in-cell Poisson solver for the beambeam interactions and a linearized model taking into account finite bunch length effects. To ensure the validity of the results a detailed benchmarking of these models was performed. It will be shown that under certain conditions coherent beam-beam dipole modes can couple with higher order headtail modes and lead to strong instabilities with characteristics similar to the classical transverse mode coupling instability originating from impedance alone. Possible cures for this instability are explored both for single bunch and multibunch interactions. Simulation results and experimental evidences of the existence of this instability at the LHC will be presented for the specific case of offset collisions.

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Beam Instabilities in Hadron Synchrotrons

Cited by 47 publications

References 104 publications

An arbitrary order time-stepping algorithm for tracking particles in inhomogeneous magnetic fields

An arbitrary order time-stepping algorithm for tracking particles in inhomogeneous magnetic fields

Transverse beam instabilities in the presence of linear coupling in the Large Hadron Collider

Transverse mode coupling instability of colliding beams

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