Analytical study of higher order modes of elliptical cavities using oblate spheroidal eigenvalue solution

Jain, Vikas; Bhandarkar, Upendra; Joshi, S.C.; Krishnagopal, S.

doi:10.1103/physrevstab.14.042002

Cited by 3 publications

(2 citation statements)

References 18 publications

(31 reference statements)

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“…In general, the frequency of the RF cavity and particle energy determine the shape of the cavity. Elliptically shaped π-mode cavity with accelerating gap of βλ/2 is the general choice for accelerator [12], where λ is the wavelength of cavity resonance frequency used for acceleration. An elliptical cavity profile is presented in figure 1 and table 1 for single-cell 650 MHz β g =0.92 SCRF cavity.…”

Section: Single Cell 650 Mhz β=092 Scrf Cavitymentioning

confidence: 99%

Estimation of Lorentz force detuning and its compensation on 650 MHz βg = 0.92 single cell SCRF cavity

Rathore¹,

Jain

Singh

et al. 2021

Eng. Res. Express

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Superconducting technologies are widely used in modern radiofrequency (RF) cavities for particle accelerators in various fields of applications. The Superconducting radiofrequency (SCRF) cavities are highly sensitive to small perturbation on cavity dimensions. The operation of the superconducting cavity becomes challenging due to narrow resonance bandwidth on account of a very high-quality factor. The main perturbing source is Lorentz Force acting on the cavity wall, which detunes the cavity from resonance. Finite element (FE) analysis has an important role in Lorentz force detuning (LFD) estimation, which requires coupled-field FE analysis between the structural and RF domains of the cavity. The LFD effect can be mitigated up to a certain extent by using a proper fast tuning methodology. This paper represents the methodology for structural-high frequency electromagnetic coupled field simulation for LFD calculation of 650MHz, βg = 0.92 single-cell SCRF cavity. First, the static LFD is calculated for various voltage gradients of SCRF cavity structure and then dynamic behavior of cavity due to LFD pressure pulse is studied at different pulse widths (PW) and pulse repetition rates (PRR). A comparison of transient FE analysis of the single-cell cavity with one end fixed and another end free and cantilever beam for similar loading is done for benchmarking. To counter the detuning effect, the SCRF cavity employs a piezo tuning device. The dynamic behavior of piezo pulse response on the cavity is also studied. An experimental test of the piezo tuner system has been performed at room temperature to validate the FE coupled simulation. Further, dynamic analysis has been carried for the combined effect of LFD pressure and piezo load pulse to compensate for the LFD effect. Optimizing the piezo load for compensating the frequency shift is also discussed and based on optimum load, LFD has been mitigated for different acceleration gradients.

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Section: Single Cell 650 Mhz β=092 Scrf Cavitymentioning

confidence: 99%

Estimation of Lorentz force detuning and its compensation on 650 MHz βg = 0.92 single cell SCRF cavity

Rathore¹,

Jain

Singh

et al. 2021

Eng. Res. Express

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show abstract

“…To overcome the shortcomings, we first apply the variational method [7] to find the wave functions of the nondegenerate modes in the spheroid and then use the wave functions in the perturbation theory to estimate the resonance shifts due to adsorption and the RI change. It is also possible to solve the spheroidal wave equation [8], but computation of spheroidal wave functions is more demanding. Furthermore, expressing the wave functions with familiar spherical Bessel functions and Legendre functions will help us visualize the effect of shape distortion.…”

Section: Introductionmentioning

confidence: 99%

Resonance shifts of transverse-electric whispering gallery modes in a spheroidal resonator

Teraoka¹

2012

Appl. Opt.

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A variational method was applied to find the wave function of a transverse-electric whispering gallery mode (WGM) in a spheroidal resonator of a uniform refractive index (RI). It was found that the electric field is tangential to the resonator surface as in the sphere, up to the linear order of the ellipticity. Using the wave function, the resonance shift due to adsorption of a thin, uniform dielectric layer onto the surface and the shift by a uniform RI change in the surroundings were evaluated in the perturbation theory. The shift by the RI change is not affected by the ellipticity, but the shift by the layer adsorption now depends on the meridional order. However, the correction is not large unless the ellipticity is large and the meridional order is away from the one for the equatorial mode of WGM.

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Note: Matching index technique for avoiding higher order mode resonance in accelerators: INDUS-2 accelerator as a case study

Jain

Bhandarkar

Joshi

et al. 2013

Review of Scientific Instruments

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Resonance between circulating beam frequencies and RF cavity Higher Order Modes (HOMs) of accelerators can lead to coupled-bunch instabilities. Shifting these HOMs to avoid the resonance is a topic of active interest. A study has been carried out for the accelerating cavities of the INDUS-2. For quantitative measure of deciding which modes have to be moved and by how much, we introduce a new index called the matching index (IM), as a measure of how close a HOM is to the nearest beam mode. Depending on the value of IM, the operating scenarios are classified as safe and unsafe.

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Analytical study of higher order modes of elliptical cavities using oblate spheroidal eigenvalue solution

Cited by 3 publications

References 18 publications

Estimation of Lorentz force detuning and its compensation on 650 MHz βg = 0.92 single cell SCRF cavity

Estimation of Lorentz force detuning and its compensation on 650 MHz βg = 0.92 single cell SCRF cavity

Resonance shifts of transverse-electric whispering gallery modes in a spheroidal resonator

Note: Matching index technique for avoiding higher order mode resonance in accelerators: INDUS-2 accelerator as a case study

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