BBLR impedance

Calculations with GdfidL and HFSS for the new device in LSS5 were performed  by A. Grudiev in May 2004. Gdfidl results are available for the longitudinal impedance (open circuit), horizontal impedance (open circuit) and vertical impedance (open circuit) and for the longitudinal impedance (short circuit), horizontal impedance (short circuit) and vertical impedance (short circuit).

The asymmetric structure generates a current-dependent kick even when the beam is on axis. The effective single-bunch impedance is -9 Ohm vertically and -18 Ohm horizontally with an open circuit and -49.1 Ohm and -9.2 Ohm with a short-circuited wire (units are Ohm and not Ohm/meter, since this kick occurs for zero offset). The resulting closed-orbit deflection has been estimated.

Mode field patterns were computed with HFSS with an open geometry. The horizontal field is largest and changes sign at the center of the chamber.

Typical Q values are of the order of 1000 at 1 GHz indicating that the wake could couple over half of a batch.

The change in impedance per transverse offset, which is the impedance driving instabilities and tune shifts is obtained by subtracting impedances computed with a transverse offset and on axis. Open circuit on axis: ImZx0=-18.1 Ohm and ImZy0 = -9.1 Ohm. With a vertical offset dy = -2mm:  ImZx2 = -16.7 Ohm and ImZy2 = -19.0 Ohm. vertical impedance is increased by factor of 2, what one could expect taking into account the field structure of the relevant modes.  A. Grudiev estimates that dZy = -(-19.0+9.1)/0.002 ~ 5 kOhm/m is the impedance change related to the offset for an open circuit. Taking this number we can estimate the tune shift. Short circuit results on axis: ImZx = -9.2 Ohm and ImZy = -49.1 Ohm. and with shift  dy=-2mm: ImZx = -3.7 Ohm and ImZy = -72.4 Ohm so that dZy = -(-72.4+49.1)/0.002 ~ 12 kOhm/m.

Summary talk at LCE Meeting 28.05.04.

Related literature: T. Guenzel, "Single Bunch Tune Shifts and their Link to the Vacuum Chamber Geometry".