Closed Orbit

One of the useful expressions to come out of the derivation of the algorithm gives the magnitude of the momentum-dependent closed orbit:

x0+ D¯δ =

(¯x++ ¯x−)

2 . (5.32)

To test the accuracy of this algorithm, two sets of simulations were run using the Python script, with the pessimistic βx/Dx ratio C2, and bi-Gaussian distribu-

tions with the usual σδ and ninc. Firstly, the average momentum offset, ¯δ, was held

at zero whilst the closed orbit, x0, was increased incrementally. For each value of

x0, 10 simulations of 10,000 particles were run. The quantity on the right-hand

value and the input value were calculated and averaged over all simulations. The results are shown in Fig. 5.27 and confirm that the algorithm will estimate the closed orbit offset with very high accuracy.

Figure 5.27: Accuracy of the algorithm when estimating the closed orbit offset.

Secondly, the closed orbit offset was held at zero whilst adjusting the mean momentum offset of the beams. The offset was adjusted such that it would give a transverse shift of the same order as the range for the closed orbit offset trials. The quantity returned by Eq. 5.32 was divided by Dx at the scraper, and the difference

from the input ¯δ was found and averaged over the simulations. The results are shown in Fig. 5.28 and again show that the accuracy reconstructs the transverse offset extremely well.

Further testing was performed to ensure that the algorithm correctly calculates the transverse offset when a combination of both imperfections is present. As expected, the returned quantities were around the same level of high accuracy as with the individual tests.

5.8

Summary

In this chapter, simulations have been performed to test the effectiveness of the scraping algorithms. First, an investigation into errors arising from transmission

Figure 5.28: Difference in values of input and calculated momentum offset values.

through the scraper blade using FLUKA was performed and found the 1 mm thick aluminium blades to be suitable. The methods for tracking and scraping the beam in MAD-X were presented including a description of beam generation for bi-Gaussian beams. Similar simulation methods using a custom Python script were also presented.

The code currently used for the AD scraper was tested on results from MAD- X scraper simulations in ELENA for beams of varying degrees of a bi-Gaussian nature and momentum spread. The tests were performed for two different βx/Dx

ratios and found that in both cases the AD algorithm is not suitable for use within ELENA.

The Gaussian only fitting algorithm was shown to work for Gaussian beams with various momentum spreads. When considering its use for bi-Gaussian beams it was found that the algorithm could reconstruct the emittance to within a 10% error for values of around ninc = 1.7. This means the algorithm could provide

a rough estimate for the emittance in the case only one direction measurement is available and beams appear to the operators to be approximately Gaussian. Similarly, the algorithm was used to estimate the momentum spread of a beam at various values of ninc showing larger errors for a higher βx/Dx ratio. Again this

does not appear to be strongly non-Gaussian.

For the two scan arbitrary beam profile method, a comparison of spline fitting and Reimann sums for treating data was performed and showed that computa- tionally less expensive Reimann sums were just as suitable for differentiating the data. The algorithm was shown to work to well within the desired error tolerance of 10% in all cases in the absence of errors i.e. for a non-Gaussian beam with momentum spread in a dispersive region, and an emittance-momentum offset cor- relation. Error tolerances for the algorithm were determined for a range of errors and none were found to cause any significant problems. Finally, the algorithm was shown to accurately reconstruct an emittance-momentum offset correlation for a range of values and to accurately estimate the closed orbit of the beam.

This chapter has shown through the use of simulations that both algorithms work well under the conditions they were developed for and has investigated error tolerances. In the next chapter, the algorithms are put to use on data taken from ELENA at the end of the commissioning run in 2018.

Measurements

6.1

Introduction

Numerous scraper measurement campaigns were made during ELENA commis- sioning in 2018, which were then analysed using a combination of the two new scraping algorithms. A total of 18 individual scraper measurements are used for analysis here. These were taken in all four scraper directions at three differ- ent times during the ELENA cycle, along the intermediate and ejection cooling plateaus.

In this chapter, the details of the data acquisition process are presented, fol- lowed by an explanation of how the collected data is treated and then analysis of the measurements. The chapter concludes with a discussion of all results, including summary tables containing all measured and reconstructed quantities.