The ultra-lightweight support structure and gaseous helium cooling for the Mu3e silicon pixel tracker

The Mu3e experiment searches for charged lepton flavor violation in the rare decay μ→eee. In order to reach a sensitivity of better than 10−16, more than 109 muon decays per second have to be observed over a running time of one year. Precise determination of particle momentum, vertex position and time are necessary for background suppression. These requirements can be met by combining an ultra-lightweight tracker based on High-Voltage Monolithic Active Pixel Sensors (HV-MAPS) with a timing system which consists of a scintillating fiber detector and a tile hodoscope. As the momentum of particles from muon decay at rest is below 53 MeV/c, the silicon pixel tracker resolution is dominated by multiple Coulomb scattering. This leads to extreme requirements for the material budget of the tracking detector of below 0.1% of a radiation length per layer. Even though the target power consumption of the HV-MAPS detector is as low as 150 mW/cm2, the detector cooling must be very efficient and at the same time avoid adding material inside the active tracking volume.

2 Ultra-light support structure for the pixel tracker In order to achieve a material budget of as little as 0.1% of a radiation length X 0 per tracking layer, the Mu3e pixel detector is built in a sandwich design from thinned HV-MAPS sensors, Kapton TM flex prints and Kapton TM frame Modules, see figure 2.

High Voltage Active Pixel Sensors
The pixel detector is based on High Voltage Monolithic Active Pixel Sensors (HV-MAPS). These novel chips contain the pixel sensor matrix, preamplifiers, discriminators and digital electronics which generate a fast (0.8 Gbit/s) zero suppressed serial data stream. As a consequence, no further readout electronics are required in the active tracking volume. In addition, they can be thinned to -2 - 50 µm, since the depletion zone used for charge collection is only around 10 µm thick. Thus, the pixel chips add as little as 5.34 × 10 −4 of X 0 to the material budget. The size of the sensor chips will be around 1 times 2 cm 2 for the vertex layers and 2 times 2 cm 2 for all outer pixel layers. Six to eighteen sensors share one Kapton TM flex print, the electrical connection between chips and flex print is established with wire bonds. The characterization of recent HV-MAPS prototypes [11][12][13][14], including chips which have been thinned to 80 µm, confirm good performance and very little sensitivity to thinning.

Flex print
Kapton TM flex prints support the HV-MAPS chips, supply power, high voltage (60 V) and signal lines for controls and readout. It is foreseen to use flex prints which are based on a laminate of 25 µm Kapton TM and 12.5 µm aluminum. The traces are cut into the aluminum layer with the help of a laser. If needed, two layers of laminated foil can be used for the flex print which would provide better grounding and shielding and relieve the very tight space constraints. A flex print with two layers, one with 25 µm Kapton TM and 12.5 µm aluminum for grounding and one layer with 25 µm Kapton TM and half coverage of 12.5 µm aluminum for the signal traces adds 3.86 × 10 −4 of X 0 to the material budget.

Frame modules
In order to support the flex prints inside the tracking volume, support structures made from Kapton TM foil have been developed. To increase the stability of the 25 µm thick foil it is folded along the beam axis. In the case of the 12 cm long vertex layers, two half-modules form the prismatic shaped detector frame which, together with the flex print and sensors, is fully self-supporting. For the 36 cm long outer layers of the tracking detector frame, modules supporting four flex prints each have been designed. A v-shaped fold underneath each flex print adds stability to the three times longer outer layer frames. The 25 µm thick Kapton TM frame modules add around 0.9 × 10 −4 of X 0 to the material budget. The material budget is summarized in table 1. Prototypes of frame modules have been built for all four detector layers, showing that they are fully self-supporting, see figure 3. Plastic end-pieces outside the acceptance and aluminum mounting wheels add further stability to the detector mechanics.

Cooling
The cooling of the Mu3e detector is based on liquid cooling for most of the readout electronics and gaseous helium cooling for silicon tracker sensors.

Liquid cooling
The beam pipes inside the Mu3e detector are realized as a pair of massive stainless steel tubes with u-shaped grooves for the cooling liquid. It is foreseen to mount the FPGAs for the detector readout and the power regulators directly onto the stainless steel covers of these groves. The estimated combined power consumption of the over 100 front-end FPGAs is in the order of a few kW. As there is a separate beam pipe upstream and downstream of the target with seven cooling grooves each, the flow rate per grove can be moderate, i.e. 2.5 ml/s assuming 26.25 W per FPGA and ∆T of 20 • C.

Gaseous helium cooling
In order to precisely measure the particle momentum it is important to minimize multiple Coulomb scattering and thus the material inside the tracking volume. This constrains the cooling options for the silicon pixel detector. Gaseous helium has been chosen because of its low nuclear charge number and good thermal transport capabilities. The estimated power dissipation of the pixel sensors is 150 mW/cm 2 which leads to a total power of 2.86 kW for all Mu3e pixel sensors. The target temperature range for the HV-MAPS operation is between 5 • C and 70 • C. It has been shown that the performance of recent prototypes is sufficiently constant up to at least 70 • C. In order to cool the silicon pixel sensors the helium is inserted in multiple ways. There is a slow flow of cool helium inside the entire magnet volume of 3 m length and 1 m diameter, referred to as global helium flow.
Since the global flow can only reach part of the HV-MAPS chips directly, an additional local flow of cool helium gas is foreseen. The helium for the local flow is distributed either to the v-shaped folds of the detector support structure or to its outer surface, see figure 4 left. In both cases, helium flows underneath the HV-MAPS chips along the beam axis. The local helium flow distribution is realized by means of the module end-pieces, see figure 4.

Simulation of gaseous cooling
The effectiveness of the gaseous helium cooling concept has been tested with the help of a simulation [15]. This simulation has been performed for a station of the two outer layers of the silicon pixel tracker. The simulated power dissipation is 150 mW/cm 2 , the gas speed is between 0.5 and 4 m/s and the simulation has been carried out for both, air and helium, see figure 5. The simulation indicates that in order to establish sensor temperatures between 20 • C and 70 • C gaseous helium of below 20 • C must be inserted at velocities above 2 m/s. For otherwise identical conditions the maximum ∆T for the sensors is twice as large if air is used as coolant instead of helium.

Laboratory tests for gaseous cooling
Gaseous cooling for the silicon pixel tracker has been tested with a scale model of one outer pixel station [15,16]. In the model the silicon pixel modules of layers 3 and 4 of one station are replaced by sheets of aluminum Kapton TM laminate foil which is ohmically heated. The laminated foil is -5 -

Summary and outlook
The Mu3e experiment searches for the lepton flavor violating decay µ → eee with the help of a novel pixel detector based on high voltage monolithic active pixel sensors (HV-MAPS). In order to minimize multiple Coulomb scattering in the active tracking volume the HV-MAPS sensors, the support structure and the cooling system must be built from very thin and, if possible, low Z material. An ultra-lightweight detector module sandwich structure composed of thinned HV-MAPS chips, aluminum Kapton TM laminate flex prints and an aluminum Kapton TM support frame has been designed. These detector modules have a thickness of approximately 0.1 % of a radiation length per tracking layer. First mechanical prototypes have been assembled successfully and turn out to be self-supporting. The cooling concept of the Mu3e detector foresees liquid cooling for most of the read out electronics and gaseous helium cooling for the silicon pixel detector. Both simulation and measurements carried out with at full scale model of one station of the outer tracking layers indicate that for the expected power dissipation of 150 mW/cm 2 and an operating temperature range between 5 • C and 70 • C sufficient cooling can be achieved with a moderate gas flow of around 4.0 m/s. Simulation results and preliminary measurements show that the maximum ∆T is a factor two lower for helium than for air.
In the upcoming months the gaseous helium distribution integrated in the ultra-lightweight detector module design will be tested.