Space charge impedance and electromagnetic fields in elliptical vacuum chambers

Migliorati, M.; Biancacci, Nicolò; Masullo, M.R.; Palumbo, L.; Vaccaro, V. G.

doi:10.1103/physrevaccelbeams.21.124201

Cited by 9 publications

(7 citation statements)

References 12 publications

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“…We study a particular harmonic component with an angular frequency ω=2πf (or wave number k=ω/v). The charge and current densities ( 𝜌, 𝐉 ) and longitudinal component Ez can be written as [1,2,4] 𝜌(𝑥, 𝑦, 𝑧, 𝑡) = 𝜌 ⊥ (𝑥, 𝑦)𝑒 𝑗(𝜔𝑡−𝑘𝑧) , 𝐉 = 𝜌𝐯 (2)…”

Section: A Problem Formulationmentioning

confidence: 99%

“…Such coupling effects are quantified using the concept of the beam coupling impedance [2] in the frequency domain. The following two approaches have been widely used to calculate the impedances of various accelerator vacuum chambers: analytical approaches such as the mode-matching method [3,4], the image charge method [5], and numerical methods such as the finite integration technique (FIT) [6], and finite element method (FEM) [7]. In the FIT and FEM, a computational domain is decomposed into a set of volume meshes.…”

Section: Introductionmentioning

confidence: 99%

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Physics-Informed Neural Network Method for Space Charge Effect in Particle Accelerators

Fujita¹

2021

IEEE Access

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The electromagnetic coupling of a charged particle beam with vacuum chambers is of great interest for beam dynamics studies in the design of a particle accelerator. A deep learning-based method is proposed as a mesh-free numerical approach for solving the field of space charges of a particle beam in a vacuum chamber. Deep neural networks based on the physical model of a relativistic particle beam with transversally nonuniform charge density moving in a vacuum chamber are constructed using this method. A partial differential equation with the Lorentz factor, transverse charge density, and boundary condition is embedded in its loss function. The proposed physics-informed neural network method is applied to round, rectangular, and elliptical vacuum chambers. This is verified in comparison with analytical solutions for coupling impedances of a round Gaussian beam and an elliptical bi-Gaussian beam. The effects of chamber geometries, charge density, beam offset, and energy on the beam coupling impedance are demonstrated.

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Section: A Problem Formulationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Physics-Informed Neural Network Method for Space Charge Effect in Particle Accelerators

Fujita¹

2021

IEEE Access

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“…Moreover, in Ref. [22], we have also derived the longitudinal electric field produced by a small dipole oriented along y and x, and moving with velocity βc as…”

Section: Longitudinal Electric Field In a Perfectly Conducting Elmentioning

confidence: 99%

“…In this paper we expand the formalism of previous works [21][22][23], in which we derived the longitudinal and transverse driving and detuning space charge impedances produced by a point charge and a small dipole traveling on the axis of a perfectly conducting elliptic vacuum chamber, by considering the case of a finite resistivity of the beam pipe walls. The resistive wall term is introduced by using the concept of surface impedance, which can also be extended to the multilayer case, of interest for many particle accelerators (see, e.g., [8]).…”

Section: Introductionmentioning

confidence: 99%

Resistive wall impedance in elliptical multilayer vacuum chambers

Migliorati

Palumbo

Zannini

et al. 2019

Phys. Rev. Accel. Beams

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The resistive wall impedance of a vacuum chamber with elliptic cross section is of particular interest for circular particle accelerators as well as for undulators in free electron lasers. By using the electric field of a point charge and of a small dipole moving at arbitrary speed in an elliptical vacuum chamber, expressed in terms of Mathieu functions, in this paper we take into account the finite conductivity of the beam pipe walls by means of the surface impedance, and evaluate the longitudinal and transverse driving and detuning impedances for any beam velocity. We also extend the definition of the Yokoya form factors, valid in the thick wall regime, at any beam energy, and show that, in the ultra-relativistic limit, they coincide with the ones that are found in literature. The method is also extended to the multilayer vacuum chamber case. Under conditions generally satisfied with particle accelerator beam pipes, the classical transmission line theory can be used to modelling the impedance seen by a bunch in a vacuum chamber with several layers as an equivalent circuit with the same number of load impedances, giving, as result, a surface impedance that can be used in combination with the fields of the elliptic geometry to obtain the resistive wall impedance in an elliptical multilayer vacuum chamber. The results are also compared with a more time consuming 3D electromagnetic code and with solutions for known cases of circular and flat beam pipe.

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“…In Refs. [9,10], the authors looked into the case of chambers with elliptic geometry for which the Mathieu functions can be used to express the electromagnetic fields.…”

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confidence: 99%

Wake fields and impedance of space charge in Cartesian coordinate system

Zhou,

Nie

2021

Preprint

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In Cartesian coordinate system, the fields generated by a point charge moving parallel to the axis of a rectangular vacuum chamber can be formulated in terms of eigenfunctions of the rectangular waveguide using the mode expansion method. In combination with the conventional impedance theory, the Green-function forms of the wake functions and impedance for space-charge effects can be obtained, and are found to be functions of the positions of both the source and test particles.Using the Green's functions calculated for a point charge, the wake fields and impedance of a beam with various distributions can be calculated, and should be useful to model the three-dimensional space-charge effects. This paper summarizes our findings and also show comparisons to the existing theories. I. INTRODUCTIONSpace charge is an important source of collective effects and can exert a strong impact on the machine performance of modern particle accelerators with low-energy but high-intensity beams, or with high-energy but high peak-current beams. To simulate the beam dynamics with space charge, many tracking codes use self-consistent models based on particle-in-cell (PIC) method (for typical examples, see Refs. [1, 2]). On the other hand, many other codes use non-self-consistent models based on space charge impedance with given beam distribution (for an example, see Ref. [3]).The analytic theories of space charge wake functions and impedance have usually been derived in the cylindrical coordinate system with round vacuum chambers [4][5][6]. With the wake potential expanded in terms of cylindrical coordinates, usually the leading terms of longitudinal monopole and the transverse dipole are of important concern for evaluations of space charge effects [7]. In recent years, efforts have been made to extend the theories to cover various cases such as non-round chambers or non-uniform beam distributions. In Ref.[8], the longitudinal space charge impedance of a round uniform beam was studied in details in the presence of parallel-plates or rectangular chambers. In Refs. [9,10], the authors looked into the case of chambers with elliptic geometry for which the Mathieu functions can be used to express the electromagnetic fields.

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Space charge impedance and electromagnetic fields in elliptical vacuum chambers

Cited by 9 publications

References 12 publications

Physics-Informed Neural Network Method for Space Charge Effect in Particle Accelerators

Physics-Informed Neural Network Method for Space Charge Effect in Particle Accelerators

Resistive wall impedance in elliptical multilayer vacuum chambers

Wake fields and impedance of space charge in Cartesian coordinate system

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