Longitudinal Misalignment Error

Here we talk about the longitudinal misalignments occurred due to the temperature variation around the ring tunnel. The misalignment errors of the magnets due to installation are discussed in general misalignment errors. In the existing PETRA II tunnel it is measured that there is a sinusoidal variation of displacement over which the random displacement variations due to ground or what so ever is super imposed.

In this figure the longitudinal displacement error Ds(mm) is estimated by fitting a sinusoidal displacement due temperature increase with a wavelength of half of the circumference and maximum amplitude of 5mm. the old octants are coarsely aligned with respect to the new octant. Here the random misalignments are assumed 1mm in old octant and 0.5mm in new octant. The displacements so calculated at quadrupole locations are submitted as errors and the corresponding closed orbits are calculated and corrected using the available correctors.

Below the beta beat and the tune shifts are calculated for different combination of misalignment errors in PETRA III tunnel.

Case 1: In old octants the misalignment is 1mm and in new octant it is 0.5mm.

Case 2: In old octants the misalignment is 5mm and in new octant it is 0.5mm.

Case 3: In old octants the misalignment is 10mm and in new octant it is 0.5mm.

Now combining all the above results together and observing the beta betas for old octants the misalignment for 1 to 10 mm and in new octant with 0.5mm.

From these studies it is evident that a longitudinal misalignment of 5mm is allowed while a beta beat below 3% is admissible.

Long Term Stability

The following steps are taken to ensure long term stability of the beam.

• Alignment of the machine every half a year

• Temperature stability (new octant ± 0.1 °C old octant ± 1°C)

• Cooling water temperature ± 0.2°C)

• Establishing a new golden orbit ≥ 24 h

Form the ATL law Dx² = A.T.L

With, A=4*10-6 µm²/m/s ; L = 65 m and Δx = 15 µm, one can find out that the stability of the golden orbit is

è T = 10 days.

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