Transverse Impedance and Transverse Instabilities in Fermilab Booster
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N/An attempt was made to improve earlier measurements of transverse impedance in RHIC. Measurement with protons at injection were made on March 7, 2012. Data were taken in the yellow ring with the current as a function of time shown in Figure 1. We used the RHICBTF application with varying numbers of bunches. The measured beam transfer functions are shown in Figures 2 and 3. The two indicies parameterizing each curve are the peak current and the number of bunches in the symmetric fill. For the horizontal data in Fig 1 the two blue curves for 8A peak current with 28 bunches have a larger measured tune difference than the green cure with 5A peak current and 6 bunches or the magenta curve with 4A peak current and 28 bunches. The expected tune shift for a transverse impedance of 4MΩ/m and 4 amps is 0.0012. This is comparable to the measured vertical tune shift when changing from 8 to 28 bunches. The RHIC impedance is broadband so any change in tune with bunch number is an instrumental effect. We conclude that another measurement technique is needed to obtain reliable results.
An attempt was made to improve earlier measurements of transverse impedance in RHIC. Measurement with protons at injection were made on March 7, 2012. Data were taken in the yellow ring with the current as a function of time shown in Figure 1. We used the RHICBTF application with varying numbers of bunches. The measured beam transfer functions are shown in Figures 2 and 3. The two indices parameterizing each curve are the peak current and the number of bunches in the symmetric fill. For the horizontal data in Fig 1 the two blue curves for 8A peak current with 28 bunches have a larger measured tune difference than the green cure with 5A peak current and 6 bunches or the magenta curve with 4A peak current and 28 bunches. The expected tune shift for a transverse impedance of 4MΩ/m and 4 amps is 0.0012. This is comparable to the measured vertical tune shift when changing from 8 to 28 bunches. The RHIC impedance is broadband so any change in tune with bunch number is an instrumental effect. We conclude that another measurement technique is needed to obtain reliable results.
The RHIC luminosity upgrade program aims for an increase of the polarized proton luminosity by a factor 2. To achieve this goal a significant increase in the beam intensity is foreseen. The beam coupling impedance could therefore represent a source of detrimental effects for beam quality and stability at high bunch intensities. For this reason it is essential to quantify the accelerator impedance budget and the major impedance sources, and possibly cure them. In this MD note we summarize the results of the 2013 transverse impedance measurements in the AGS and RHIC. The studies have been performed measuring the tune shift as a function of bunch intensity and deriving the total accelerator machine transverse impedance. For RHIC, we could obtain first promising results of impedance localization measurements as well.
The goal of this task was to provide reliable means, either via direct RF measurements and/or 3D simulations, of assessing the transverse impedance of an accelerating gap in a linear accelerator cell.
Impedance could represent a limitation of running high intensity bunches in the Fermilab recycler. With high intensity upgrades foreseen, it is important to quantify the impedance. To do this, studies have been performed measuring the tune shift as a function of bunch intensity allowing the transverse impedance to be derived.
In this paper results of the transverse and longitudinal impedance calculations by means of GdfidL code are presented in axially symmetric and rectangular structures. Wakepotentials are calculated up to 10 m with a bunch length of 1.4 mm. Three types of transitions are considered for each geometry; “narrowing” step, “widening” step and ridge transition. Investigation of the longitudinal impedances in rectangular and in axially symmetric geometries were done earlier by H. G. Hereward and S. A. Kheifets. They considered the coupling impedance of the “widening” and the “narrowing” steps.
The strength of the dangerous beam breakup (BBU) instability in linear induction accelerators (LIAs) is characterized by the transverse coupling impedance Z ⊥ . This note addresses the dimensional scaling of Z ⊥ , which is important when comparing new LIA designs to existing accelerators with known i BBU growth. Moreover, it is shown that the scaling of Z ⊥ with the accelerating gap size relates BBU growth directly to high-voltage engineering considerations. It is proposed to firmly establish this scaling though a series of AMOS calculations.
Transverse instability of a bunch in a ring accelerator is considered with space charge and wakefield taken into account. It is assumed that space charge tune shift significantly exceeds the synchrotron tune. Bunch spectrum, instability growth rate, and effects of chromaticity are studied with different bunch and wake forms. Fast instability caused by coupling of transverse modes is studied in detail. It is shown that, for monotonic wakes, the transverse mode coupling instability is possible only with a certain sign of the wake. Its threshold and growth rate are calculated precisely over a wide range of parameters.
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To estimate the vertical impedance of more complex geometry as an In-Vacuum Undulator we crosschecked first the results for simplified geometries. Axially symmetric tapered structures and rectangular structures are under discussion. Comparisons of analytical results with numerical results obtained with the electromagnetic field solver GdfidL are presented. Intensive studies were carried out to determine the dependence of the wake potential and kick factor on the collimator’s geometric parameters. We discuss the relationship of our results to the earlier work of G. Stupakov.
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The Electron Ion Collider (EIC) requires crab cavities to correct for crossing angle effects. These cavities produce a time varying horizontal kick that makes the collision head on in the center of mass frame of the bunches. This results in a luminosity that is very close to the the luminosity obtained without a crossing angle. Producing the kick requires a transverse RF field. This field requires a superconducting resonator and reasonable power levels require loaded quality factors of order a million. This results is a very large transverse impedance for the crabbing mode. The horizontal beta function is large and this, coupled with the large transverse impedance of the resonator can lead to strong instabilities. In the first section of the paper a simple model is used to describe the situation without feedback. There are large ranges of tune leading to strong instabilities in both the electron and hadron storage rings of the EIC. These estimates are confirmed with simulations. In the second section, RF feedback is used to reduce the apparent impedance of the crabbing mode. Simulating the actual feedback would require both a significant rewrite of the tracking code and a significant reduction in computational speed. Instead, the apparent impedance is fitted using one pole filters, which allows use of the existing simulation code. In the third section a transverse damping system is outlined.
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When a beam bunch traverses a transverse impedance, the bunch head generates a transverse wakefield that kicks the bunch tail, generating a betatron motion of the tail relative to the head. In a storage ring, in a steady state, this kick to the bunch tail produces a transverse closed orbit (e.g. in the y-direction) of the bunch tail relative to the bunch head, which means the beam now has a y-z tilt. Such beam tilt due to transverse wakefields may cause a loss of luminosity in storage ring colliders or loss of brightness in light sources. In this paper, we present a preliminary study of the beam tilt effect for the colliders DAFNE, SuperB, KEKB and SuperKEKB.
The paper describes a method for calculating the longitudinal and transverse impedances of the laminated round pipe with many layers of different materials. The charge is moving along the pipe axis with arbitrary constant velocity. The study is based on the field-matching technique applied for the arbitrary harmonic of the electromagnetic field. The matrix formalism has been developed to describe the field transitions through the subsequent layers that allow coupling the electromagnetic fields inside and outside the pipe. The number of equations to be solved is then reduced to four algebraic equations. The solutions and ultrarelativistic limits for the field harmonics in the inner and outer regions of the pipe are derived.
It has been proposed to use solid-state pulsed-power modules to power the new Scorpius accelerator. Since this highcurrent accelerator would have 360 gaps (more than five times the number of cells as present radiography LIAs), it is natural to be concerned about the beam-breakup (BBU) instability. Earlier calculations of this effect used a half-scale model of the accelerator to avoid the limitation to 200 gaps in the code. We have now updated the code to accommodate the extraordinary number of gaps in this proposed LIA. The results of these early simulations are presented here. They indicate that BBU can only be suppressed to the same level as in designs powered by conventional pulsed power, if the calculated cell impedance can truly be achieved in practice. The magnetic focusing field required for this is of the same order as the field required for a conventionally powered LIA only if the transverse impedance can indeed be constrained to the values obtained in some simulations of the cell.