Ejecución de los sistemas de control de la presión 1 Montaje del grupo de sobreelevación

The ALICE tomography section, with its three screens and four quadrupoles, was mod- elled in detail using GPT, with the addition of quadrupole QUAD-07 which is at the end of the preceding ‘matching section’. QUAD-07 forms part of the configuration proposed for experiments on space-charge, to be used for horizontal phase-space to- mography scans in conjunction with screen YAG-02. As a further development, the defocussing quadrupole QUAD-06 was added to model tomography-scan experiments for vertical phase-space, which would also use YAG-02. The arrangement is shown in Fig. 4.5.

Figure 4.5: A schematic of the ALICE tomography section shows quadrupole magnets and 3 screens, identified by shorter versions of their ALICE project names. Conven- tional symbols distinguish focussing quadrupoles (e.g. Q-07) from defocussing (e.g. Q-09).

Space-Charge Effect: Beam-Size Difference Analysis

The horizontal RMS beam-sizeσx (andσy vertically) was selected as a suitable metric

for observing space-charge effects, as it was anticipated that beam-size would be suit- able as a parameter for the sensitivity of tomography reconstructions to space-charge. ‘Screens’, which in GPT are defined as virtual planes for tallying particles when they

cross, and can optionally correspond to physical devices such as YAGs, are specified ap- propriately along the beam-line. It is at screens that particle positions (and momenta) are computed by GPT; from these, the beam-size may be readily derived either within GPT, or by calculation.

A bunch-length of 4 ps in time - equivalent to 1.2 mm at light-speed - was taken as representative, based on typical measurements made after the LINAC. Preliminary data taken with a 9 mm bunch - a typical value at the ALICE gun - predictably gave effects two to ten times smaller; however, it is quite realistic to expect significant compression of bunches both in the buncher cavity and in the LINAC itself, which follow the gun.

Input parameters were specified in a separate ‘.mr’ file (see Fig. 4.4); this method supports nested loops for scanning multiple parameters, such as ‘quad current’ and ‘bunch charge’. Quadrupole currents used corresponded to the same range of values as in the original tomography experiments to produce appropriate projection angles.

After running the GPT simulation itself, the analysis program GDFA was used to extract σx and σy from the raw (x, y)z data in the GDF output file. This data could

be plotted within GPT, and also exported in text format. As effects on beam-size were small in absolute terms, the σx and σy data was processed outside GPT in ‘text’

form, to determine the fractional differences ∆σx/σx between the 0 pC case with no

space-charge, and 80 pC which was the maximum charge obtainable experimentally. Combining realistic initial phase-space parameters, as measured by tomography experiments, with the established GPT model, a series of runs was made at both 0 pC and 80 pC bunch charge, with quadrupole currents for QUAD-07 and QUAD-10 scanned over the range of tomography settings as before.

Figure 4.6: As the current in quadrupole QUAD-07 and then in QUAD-10 is scanned, the fractional horizontal beam-size difference, related to space-charge effects, is plotted at three screen positions, recorded in m., in the line.

Beam sizes were extracted to find the percentage differences between 0 and 80 pC, ∆σx/σx, which are plotted against current for each screen position in Fig. 4.6. At the

first screen position after the scanned quadrupole (i.e. at YAG-02 after QUAD-07, or at YAG-04 after QUAD-10), ∆σx/σx was found to be a strong function of magnet current,

and a significant but less marked trend was seen at the screen further downstream. A very small but positive effect was even observed at a position almost immediately after the bunch was started, i.e. just before QUAD-07 or QUAD-10.

The peaked structure of the beam-size difference plots, seen at YAG-02 for a QUAD- 07 scan, and at YAG-04 for a QUAD-10 scan, has been correlated with the absolute beam-size σx, which in Fig. 4.7 is plotted in red for the ‘zero charge’ (0 pC) case

and in broken green for the ‘high charge’ (80 pC) case. As the absolute difference ∆σx between 0 pC and 80 pC is small, the red and green plots almost coincide. In

the same figure, there is a rapid change of sign in the fractional beam-size difference ∆σx/σx, plotted in blue, which occurs exactly at the point where the strength of the

quadrupole focussing causes a minimum in σx. It is here that the largest effect from

space-charge would be expected in the plane of focus, which in this case is horizontal, due to the closer proximity of the particles in the bunch. It has been postulated [1] that the rapid beamwidth increase over a small range of quadrupole strength occurs

when the focussing is such that the horizontal beam waist coincides with a vertical waist, suddenly forcing the electrons much closer together. Confirmation of the exact mechanism would however require further work.

Figure 4.7: Details of the simulated effect of quadrupole current on horizontal beam- size difference due to space-charge, for QUAD-07 observed at the YAG-02 position and for QUAD-10 at YAG-04. Absolute beam-size at 0 pC and at 80 pC is plotted on the primary axes (red/green), with fractional beam-size difference on the secondary (blue).

Convergence Check of Beam-Size against Number of Particles Simulated When a macroscopic parameter is calculated from the results of a simulation code such as GPT, there is a possibility of statistical effects due to the finite sample of particles modelled. For the ‘beam-size-difference with bunch-charge’ metric, its dependence on Number of Particles (nps) in the bunch was estimated by making a series of GPT runs with ‘nps’ as an additional multi-valued parameter.

Selected setting for the check (shown at left of Fig. 4.8, taken from Fig. 4.6) was:- QUAD-07 current = 1.149 A

σx calculated at screen YAG-02, at Position = 0.342 m

Figure 4.8: Choosing appropriate quadrupole current/screen position settings, the de- pendence of fractional beam-size difference on number of particles simulated nps is plotted, to confirm convergence and establish a working minimum fornps (arrowed).

These representative results indicate that the minimum number of macro-particles for convergence is about 1000. To provide a suitable margin, an appropriate choice is therefore 2000, unless time constraints indicate running a reduced number.