F ILTROS DE S EGURIDAD S ANITARIA PARA EL A CCESO AL CENTRO DE EXPOSICIONES Y CONGRESOS DE LA

5.5.1

Scraping Results Analysis

Figure 5.12: Intensity data for beams of varying parameters overlaid with the Gaussian algorithm fit.

To check the simulations were working properly, the single scrape Gaussian algorithm was applied first. Since the algorithm incorporates well established scraping techniques it is a better candidate for benchmarking and testing the simulations.

The first simulations were performed for the most simple input. Gaussian beams with emittances of 1 µm and 1.6 µm, with no momentum spread, σδ =

0, were scraped. The scraper blade moved from positive x and the resultant distribution was saved as F+(xs). The top two plots in Fig. 5.12 show the resultant

cumulative probability curves obtained, overlaid by the fit from the algorithm, Eq. 4.19, using MATLAB’s custom equation fitting tool and taking both x and

σδ as free parameters. The numerical results from the algorithm are also included

and it can be seen for both emittances, there is good agreement with the input values, well within the target accuracy of 10%. The estimations for momentum spread are small enough that they could be considered negligible and are a good estimation for an input value of zero. The error on the results could be attributed to statistical fluctuations and/or the discreet scraper steps of 0.1 mm.

The Gaussian beam was run again, with non-zero values of momentum spread. The results may also be seen in Fig. 5.12, where again the algorithm agrees with the input values to a satisfactory level. The estimations for longitudinal momentum spread are within 10% of the respective input values. This is more accurate than the expected accuracy of the Schottky diagnostic device (≈ 20%) and hence this method could be used to determine the momentum spread in combination with such a device, in the circumstances that the beam may appear Gaussian enough. An investigation into the accuracy of this method for momentum spread estimation of non-Gaussian beams can be found later in this section. In addition to the potential sources of error mentioned above, taking the momentum spread as a free parameter as opposed to knowing its exact value also contributes to the small inaccuracy in reconstructed emittance value.

5.5.2

Momentum Spread Estimation

The Python analysis code was used to generate beam scraping profiles with ninc

starting at 1, a Gaussian beam, up to ninc ≈ 3, around the expected value after

electron cooling in ELENA. The output scraping data was then analysed by the Gaussian reconstruction algorithm taking emittance and momentum spread as free parameters. To minimise statistical fluctuations, this was done 4 times for each value of ninc and the mean and standard deviation in the results were calculated.

The process was carried out using the same values of βxand Dx as for the previous

It was also then repeated for values which are closer to the expected values in the scraper’s current position in ELENA, C4, which minimise the impact of Dx.

In Fig. 5.13, it can be seen that as nincincreases, the error in the reconstructed

emittance value also increases as expected. Using the gradient from a very simpli- fied linear fit to compare the results it can be seen that the larger βx/Dx ratio has

little to no impact on the effectiveness of the algorithm. The error quickly grows above 10% for values of ninc around 1.7 in both cases. It would not be recom-

mended that the algorithm be used for emittance reconstruction in the presence of electron cooling. However, if the beam is injected and operators can ascertain how Gaussian it is, based on for example profiles measured by the BTV screen along the injection line, the algorithm could still be used for emittance reconstruction in ELENA.

Figure 5.13: Error on reconstructed emittance values from the Gaussian fit algorithm based on increasingly bi-Gaussian beams. The plot on the left shows the results for the simulation standard values of βx = 0.688 m and Dx= 1.29 m.

The plot on the right has βx= 3.21 m and Dx = 1.38 m, closer to the expected

values at the new scraper position.

The same analysis for the reconstructed momentum spread values can be seen in Fig. 5.14. Here the difference between the two cases of differing Twiss parame- ters can be seen much more clearly, the gradient of the approximate line fit is more than 2.5 times greater for the higher βx/Dx ratio case, C4. This result could be

expected since a higher βx/Dx ratio gives the scraper profile less of a momentum

spread related tail at the core of the beam, and hence this momentum spread re- lated characteristic of the distribution does not influence the fitting algorithm as

much. It would be recommended that a local adjustment of Twiss parameters to reduce the βx/Dx ratio should be applied if using this algorithm for the purpose of

acquiring the momentum spread of the beam. Additionally, the algorithm should not be used for this purpose if the profile shows strong bi-Gaussian effects after electron cooling.

A second set of simulations were performed with the same conditions, but only taking the momentum spread as an unknown value. The emittance could be accurately calculated from the two scan method instead. The results showed that even inputting the exactly correct emittance into the algorithm does not improve the momentum spread estimation performance with respect to increasing ninc for

either case.

Figure 5.14: Reconstructed momentum spread values based on increasingly bi-Gaussian beams. Left plot: βx = 0.688 m and Dx = 1.29 m. Right plot:

βx= 3.21 m and Dx= 1.38 m.