Vlasov description of the effects of nonlinear chromaticity on transverse coherent beam instabilities

We present a linearized method to study transverse instabilities due to electron clouds. It is based on an accurate and compact characterization of the cloud dipolar and quadrupolar forces, that can be easily obtained from quick single-pass numerical simulations. The long-term stability properties of the bunch are then predicted by solving the linearized Vlasov equation, taking into account the dipolar forces introduced by the e-cloud along the bunch as well as the betatron tune modulation with the longitudinal coordinate due to the e-cloud quadrupolar forces. The method is benchmarked against macroparticle simulations based on the same characterization of the e-cloud and the results are compared against conventional "brute-force" simulations based on the Particle-In-Cell method. The effect of transverse nonlinearities due to the e-cloud, which are neglected by the linearized method, is also analyzed.

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“…[17], with an additional detuning term depending on the longitudinal phase space coordinates ΔQðr; ϕÞ, as done in Ref. [18]:…”

Section: Vlasov Treatmentmentioning

confidence: 99%

“…Schenk et al in Ref. [18] used an approach very similar to the one discussed so far, to handle the detuning introduced by nonlinear chromaticity.…”

Section: A Handling the Detuning Functionmentioning

confidence: 99%

Linearized method for the study of transverse instabilities driven by electron clouds

Iadarola

Mether

Mounet

et al. 2020

Phys. Rev. Accel. Beams

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“…Some work is being done to try and use the nonlinear optics as a path to high intensity, providing "infinite (transverse) Landau damping" [111], or electron lenses [112] or Radio Frequency Quadrupoles (or similarly second order chromaticity) [113][114][115]. The latter two methods are believed to be more efficient than Landau octupoles at high energy due to the adiabatic damping and the associated significant reduction of the transverse beam sizes.…”

Section: Transversementioning

confidence: 99%

Impedance and Collective Effects

Métral

Rumolo

Herr

2020

Particle Physics Reference Library

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As the beam intensity increases, the beam can no longer be considered as a collection of non-interacting single particles: in addition to the "single-particle phenomena", "collective effects" become significant. At low intensity a beam of charged particles moves around an accelerator under the Lorentz force produced by the "external" electromagnetic fields (from the guiding and focusing magnets, RF cavities, etc.). However, the charged particles also interact with themselves (leading to space charge effects) and with their environment, inducing charges and currents in the surrounding structures, which create electromagnetic fields called wake fields. In the ultra-relativistic limit, causality dictates that there can be no electromagnetic field in front of the beam, which explains the term "wake". It is often useful to examine the frequency content of the wake field (a time domain quantity) by performing a Fourier transformation on it. This leads to the concept of impedance (a frequency domain quantity), which is a complex function of frequency. The charged particles can also interact with other charged particles present in the accelerator (leading to two-stream effects, and in particular to electron cloud effects in positron/hadron machines) and with the counter-rotating beam in a collider (leading to beam-beam effects). As the beam intensity increases, all these "perturbations" should be properly quantified and the motion of the charged particles will eventually still be governed by the Lorentz force but using the total electromagnetic fields, which are the sum of the external and perturbation fields. Note that in some cases a perturbative treatment is not sufficient and the problem has to be solved self consistently. These perturbations can lead to both incoherent (i.e. of Coordinated by E. Metral

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“…-beam-beam effects [18,19], -electron-cloud (and more generally two-stream effects) [20,21], -space-charge [22], -combined effect of impedance and space-charge [23][24][25][26], -longitudinal impedance [27,28], -transverse impedance [5,6,17,[29][30][31][32][33][34][35][36][37][38].…”

Section: A Short Review Of Existing Vlasov Solversmentioning

confidence: 99%

Direct Vlasov solvers

Mounet

2020

Preprint

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Vlasov description of the effects of nonlinear chromaticity on transverse coherent beam instabilities

Cited by 7 publications

References 7 publications

Linearized method for the study of transverse instabilities driven by electron clouds

Linearized method for the study of transverse instabilities driven by electron clouds

Impedance and Collective Effects

Direct Vlasov solvers

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