Design of new vacuum chambers for the CMBL dipole magnets

After the 2015 test beam much eort was spent on the renement of the simulation and the source of losses. Modications to both dipole magnets ASL & ASK were found to be necessary:

ˆ Pole-gap widening vertically for both magnets

ˆ Corresponding new vacuum chambers for both

ˆ Change of the current 60° bending angle of the ASK magnet to 65° to allow sucient space for the Mu3e solenoid

ˆ Optimal vacuum chamber design to allow the beam to pass through the most homo-geneous part of the dipole eld

The solution for the ASL magnet came in form of a large 330 mm pole-gap spare ASL magnet in storage. Although the corresponding vacuum chamber had the wrong deection angle it could be relatively easily modied to a 90° bend due to its exible design - split into the chamber body and the two dismountable end-plates with the coupling anges.

Hence only new end anges had to be made. In the case of the ASK magnet the pole-gap had to be widened and a new complete vacuum chamber made, modelled on the ASL design. Figure 2.80 shows the original ASL magnet together with the nal end-plates for the ASK magnet. For the construction of the end-plate anges of both chambers

(a) The picture shows the 330 mm gap ASL in storage (b) End-plates that need to be mounted to the body of the ASK vacuum chamber Figure 2.80.: The spare ASL magnet shown on the left was acquired for the CMBL setup, although the end-plate anges needed to be replaced. The ASK vacuum chamber uses a similar but shorter vacuum chamber design that also consists of a central body and attached end-plate anges.

the intersection point of both in- and outgoing centrelines with the ange plane had to be determined. Therefore TOSCA models of both magnets (with 330 mm gap) were generated and the corresponding eldmaps for both magnets were implemented into a small G4BL tracking simulation. In the following iterative process a 28 MeV/c reference particle is tracked through the eldmap of each magnet, which is initially positioned according to

the previous setup, with the strength of the eldmap adjusted to provide the desired 90°

/ 65° bending angle. The initial trajectory in the magnetic midplane of e.g. the ASK is illustrated in gure 2.81. It can be seen that the reference trajectory does not pass

Figure 2.81.: Shown is the eld of the calculated 330 mm gap ASK dipole in the magnetic midplane together with a 28 MeV/c reference trajectory. As can be seen the trajectory does not pass the most homogeneous inner region of the magnetic eld and traverses a curved fringe eld at the injection/extraction.

the innermost eld region with the highest homogenouity optimally. The eld that acts on the particle, plotted against the distance covered during its propagation through the eldmap is shown in gure 2.82. From this the eective length can be determined to be lef f,ASK,rst try=792.2 mm, leading to the corresponding radius:

ref f,ASK,rst try= l_{ef f,ASK,rst try}

65^◦ = 698.3mm (2.34)

In a next step, the eldmap in the simulation has to be shifted in order use the most homogeneous part of the dipole eld for the central trajectory. The amount by which the eldmap has to be shifted is extracted from the dierence between the magnet centre and the centre of the rectangle enclosing the lower left and right sides of the arc trajectory and its sagitta.

Once determined, the simulation is restarted and the new eective length is extracted. The whole procedure is then repeated until the desired convergence found. The nal positioning of the ASK and the ASL is shown in gure 2.83. The eective lengths arel_{ef f,ASK}= 802.3 mm and lef f,ASL= 1373.7 mm. To check the horizontal alignment gure 2.84 shows the horizontal displacements from the centrelines in front of and behind the magnet. The spikes (ASL: z∼0,700,1400 & ASK z∼0,400,800) near the vertex in G4BL are due to the

Figure 2.82.: Shown is the By eld that is "seen" by the reference particle in gure 2.81. From this the eective length is extracted aslef f,ASK,rst try=792.2 mm.

(a) Field and central trajectory in the midplane of

the ASL (b) Field and central trajectory in the midplane of

the ASK

Figure 2.83.: The central trajectories (red lines) are overlayed on a heatplot of the magnetic eld in the midplane of the ASL and ASK. The orange arc trajectories indicate the ideal orbit according to the extracted eective lengths. The centres of the dipoles match the centres of the cyan rectangles that are given by the orange ideal trajectories for the shown alignment. The centred vacuum chambers are inidacted with black lines.

position output near vertices, however the displacement of the optimum trajectory from the ideal orbit given by arcs can be seen in gure 2.83.

(a) x¯ of reference particle injected on-axis to the

ASL eld (b) x¯ of reference particle injected on-axis to the

ASK eld

Figure 2.84.: To check the alignment for the positioning that was shown in gure 2.83 the ho-rizontal deviation from the centreline is checked for both magnets. The plots show the hoho-rizontal osetx¯ of a reference particle that is injected on-axis after being deected by 90°/65°. The spikes at the magnets' central positions are due to an artefact in the G4BL position reconstruction near a vertex.