Coupling impedances of a resistive insert in a vacuum chamber

Abstract

We have developed a theory to calculate both longitudinal and transverse impedances of a resistive short (typically shorter than the chamber radius) insert with cylindrical symmetry, sandwiched by perfectly conductive chambers on both sides. It is found that unless the insert becomes extremely thin (typically a few nm for a metallic insert) the entire image current runs on the thin insert, even in the frequency range where the skin depth exceeds the insert thickness, and therefore the impedance increases drastically from the conventional resistive-wall impedance. In other words, the wakefields do not leak out of the insert unless it is extremely thin. Formulas of the impedance valid for various cases of the insert are categorized in summary.

Impedance of a ceramic break and its resonance structures

“…The green lines show the result for the g ¼ 10 mm case calculated using the previous short insert theory [11], where only a short thin resistive insert is sandwiched by two thin metals. While the agreement between the present and previous theories for the real parts of the impedance is good, the imaginary parts of the impedance reveal discrepancy at high frequency.…”

“…In order to obtain formal solutions of the fields, the field matching technique is applied to this system [12]. Unlike the previous studies [10,11], the ceramic ring can be thick, and the length g of the ring can be arbitrary.…”

“…(7). With the help of the discussion of the previous study [11], let us categorize the impedances of the ceramic break with the TiN coating for various TiN thickness. The frequency parameter f δ is introduced as…”

“…The first paper is for a pure short gap (the gap is left empty in vacuum) [10]. The second case assumes that a short gap is filled with a thin resistive ring [11]. In both cases, the gap is sandwiched with thin metal chambers on both sides.…”

Beam Instabilities in Hadron Synchrotrons

“…Due to the large number of beam pipe transitions in circular accelerator machines, the contribution to the total machine impedance of these discontinuities can be important. The structure discussed before can model a thin insert when L << t. The mode matching model to the calculation of the longitudinal impedance of thin inserts as well as comparisons with the SCT theory [52] are shown in Fig. 5.…”