Wave dispersion theory in a plasma column bounded by a cylindrical waveguide

Uhm, Han S.; Nguyen, Khanh; Schneider, R. F.; Smith, J. R.

doi:10.1063/1.341869

Cited by 22 publications

(20 citation statements)

References 2 publications

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“…The dispersion relation for the TE mode of an EM wave of wavenumber k and angular frequency ω propagating in a cylindrical pipe of radius R containing a plasma of frequency ω p is given by [16] …”

Section: Microwave Propagation Through the Electron Cloudmentioning

confidence: 99%

HINS R&D Collaboration on Electron Cloud Effects: MidyearReport

Furman¹,

Sonnad²,

Vay³

2006

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We present a report on ongoing activities on electron-cloud R&D for the MI upgrade. These results update and extend those presented in Refs. 1, 2. In this report we have significantly expanded the parameter range explored in bunch intensity N b , RMS bunch length σz and peak secondary emission yield (SEY) δmax, but we have constrained our simulations to a field-free region. We describe the threshold behaviors in all of the above three parameters. For δmax ≥ 1.5 we find that, even for N b = 1 × 10 11 , the electron cloud density, when averaged over the entire chamber, exceeds the beam neutralization level, but remains significantly below the local neutralization level (ie., when the electron density is computed in the neighborhood of the beam). This "excess" of electrons is accounted for by narrow regions of high concentration of electrons very close to the chamber surface, especially at the top and bottom of the chamber, akin to virtual cathodes. These virtual cathodes are kept in equilibrium, on average, by a competition between space-charge forces (including their images) and secondary emission, a mechanism that shares some features with the space-charge saturation of the current in a diode at high fields. For N b = 3 × 10 11 the electron cloud build-up growth rate and saturation density have a strong dependence on σz as σz decreases below ∼ 0.4 m, when the average electron-wall impact energy roughly reaches the energy Emax where δ peaks. We also present improved results on emittance growth simulations of the beam obtained with the code WARP/POSINST in quasi-static mode, in which the beam-(electron cloud) interaction is lumped into Ns "stations" around the ring, where Ns = 1, 2, . . . , 9. The emittance shows a rapid growth of ∼ 20% during the first ∼ 100 turns, followed by a much slower growth rate of ∼ 0.03%/turn. Concerning the electron cloud detection technique using microwave transmission, we present an improved dispersion relation for the TE mode of the microwaves, and a corresponding analytic estimate of the phase shift. I. ELECTRON CLOUD BUILD-UP.A. Remarks on the simulations.We have replaced the Poisson solver of the code POSINST [3][4][5][6], used in the computation of the electron cloud space-charge forces, by a multigrid-type solver that is much faster and more accurate than the old one. We have carefully tested the new solver in stand-alone mode, and we are confident that it gives correct (indeed, quite accurate) results. Owing to its inefficiency, the old solver could realistically be used only for very coarse grids, leading to intermittent problems at high N b and/or high δ max that sometimes crashed the code. For MI simulations, the improved code yields results only a few percent different from the old ones [1] for those cases in which the above-mentioned problem did not materialize. For other cases, notably the simulation of an LHC * Work supported by the FNAL HINS R&D Effort and by the US DOE under contract DE-AC02-05CH11231.† Electronic address: mafurman@lbl.gov; URL: http://mafurman. lbl.go...

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Section: Microwave Propagation Through the Electron Cloudmentioning

confidence: 99%

HINS R&D Collaboration on Electron Cloud Effects: MidyearReport

Furman¹,

Sonnad²,

Vay³

2006

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“…[3]. The derivation involves a perturbation about an equilibrium configuration of the Maxwell and fluid equations and where all higher order perturbation terms are neglected.…”

Section: Discussion Of the Dispersion Relation And The Resulting Phasmentioning

confidence: 99%

Simulation and analysis of microwave transmission through an electron cloud, a comparison of results

Sonnad

Furman

Veitzer

et al. 2007

2007 IEEE Particle Accelerator Conference (PAC)

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Simulation studies for transmission of microwaves through electron cloudes show good agreement with analytic results. The elctron cloud produces a shift in phase of the microwave. Experimental observation of this phenomena would lead to a useful diagnostic tool for acessing the local density of electron clouds in an accelerator. These experiments are being carried out at the CERN SPS and the PEP-II LER at SLAC and is proposed to be done at the Fermilab maininjector. In this study, a brief analysis of the phase shift is provided and the results are compared with that obtained from simulations.

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“…In the laboratory experiment, dispersion properties of whistler waves can be studied in great detail, but the plasma boundaries must be taken into account. The influence of boundaries on the dispersion of electromagnetic waves was already theoretically investigated [20,21]. Most experiments circumvented the effect by going to very small wavelengths [22,23] and large-size experiments [24,25].…”

Section: Whistler Wavesmentioning

confidence: 99%

“…Plasma dimensions much larger than λ are usually found in ionospheric plasmas [18], some large sized laboratory experiments [24,25] or if plasma density or wave frequency are high enough to ensure sufficiently small wavelengths [1,22]. A rigorous theoretical treatment of electromagnetic waves in a plasma filled waveguide with axial magnetic field was developed by Uhm and co-workers [21]. An analytic expression is found only for the low-frequency approximation (ω ω ce , ω kc) [21].…”

Section: Whistler Wave Dispersion In Bounded Plasmasmentioning

confidence: 99%