FEA calculations

To confirm the expected properties of the employed titanium alloy and thus minimize any risk, a verification of both the chemical composition and the me-chanical properties of the raw material has been required from the supplier. Test results for the latter are summarized in Table 3.2. They are within requirements and have been the basis of a simple finite element analysis (FEA) on the me-chanical deformation of the support structure by the tremendous coil repulsion.

While the ANSYS-based software did not allow a realistic implementation of all possible degrees of freedom, the simulations should still be useful to get a feeling for the resulting stresses when operating the magnet at full current.

Core and plates Pegs Tensile strength, ultimate 795.214 MPa 964.845 MPa Tensile strength, yield 726.404 MPa 884.894 MPa

Elongation, break 14.4 % 17.4 %

Modulus of elasticity 118.004 GPa 117.942 GPa Compressive yield strength 774.150 MPa 914.279 MPa Poisson’s ratio (typical) 0.31

Density (typical) 4.48 g/cm³

Table 3.2: Measured mechanical properties of the Ti-5Al-2.5Sn alloy. The mandrel and the plates have been machined from 260 mm diameter cylindrical material, and the pegs from a 22 mm diameter round bar. The lower values from “Core and plates”

have been used in the FEA calculations to study a worst case scenario.

48 EXPERIMENTAL REALIZATION

0 8 16 24 32 40 48 56 64 72 MPa

Figure 3.9: Finite element analysis results. Colors reflect the estimated von-Mises equivalent stress for a magnet current ofI= 75A.

FEA results forI = 75 A and a corresponding coil repulsion of 193.3 kN are visualized in Figure 3.9. The scale for deformations and von-Mises equivalent stress has been exaggerated to emphasize local differences. As the cut indicates, the highest stresses occur on the 4 mm thick inner wall of the mandrel, causing the whole magnet to slightly bend outwards. An overall stretch of 63.3m is predicted for the complete structure. This behavior is anticipated and the conse-quence of a compromise between the mandrel wall thickness and the remaining radially accessible trap depth, as already outlined in Section 3.2.2. Nonetheless, all values are still well within safety margins. The simulations yield an approx-imate security factor of 5 before mechanical failure, which should leave enough room for possible effects not included in the model.

3.2.4 Performance

The performance of any superconducting magnet is limited by the point at which resistance is restored to the coil wire. This will ultimately happen when the magnet current or the external field exceed the critical values of the wire material. More commonly, however, frictional heating from imperceptible

move-SUPERCONDUCTING MAGNET 49

0 5 10 15 20 25 30 35 40

0 10 20 30 40

-5 0 5 10 15 20

Magnetcurrent[A]

Time [s]

Excitationvoltage[V]

voltage current

Figure 3.10:Typical magnetic field ramp.

ments of the conductor due to the Lorentz force cause a breakdown of super-conductivity much earlier. Since the heat capacity of all materials is quite low at 4.2 K, a small amount of heat dissipated inside one of the solenoids can easily raise the temperature of the conductor above its critical temperature at the am-bient field and current density. The resulting local resistive heating will spread to adjacent areas and drive more of the conductor out of the superconduct-ing state, until the magnet is completely discharged. Such an event is called a quench.

In the case of a quench, the enormous energy stored in the magnetic field has to be safely extracted from the magnet again. A lot of it will be converted into heat and cause excessive evaporation of large amounts of liquid helium.

A quench therefore is an exceptional event making high demands on the cryo-genic system, the magnet, and its power supply. A special quench-protected 4-quadrant power supply (Oxford IPS120-20) is used here. It provides a maxi-mum of±120 A at±20 V and allows automated sweeping of the magnet current.

55 cm long vapor-cooled current leads (AMI L-75-S) and 1.5 m long supercon-ducting bus bars (AMI BB-75-S) carry it through the cryostat to and from the solenoids.

The limiting quench current can sometimes be successively improved upon reenergizing the magnet several times, causing the wires to gradually move to more optimal positions. Such training might have to be repeated once the magnet has been brought to room-temperature again. The quench current also depends on the ramping speed, which limits sweeping times.

Extensive testing of the magnet has been performed in a special heavy duty LHe dewar (PVS-10/58) both by AMI and again after delivery. The average quench current observed in all tests has been 44.2±1.8 A, and merely negligible

50 EXPERIMENTAL REALIZATION

-200 -100 0 100 200

-80 -60 -40 -20 0 20 40 60

Magneticfield[mT]

Axial coordinate [mm]

radial field

axial field

Figure 3.11:Experimental field values. The lines have been obtained from equations (2.12)without any free fit parameters.

training effects were seen. To date, it can only be speculated why this value is so far below the design current of 75 A.

While major material problems are ruled out by the experimental test val-ues of Table 3.2, microscopic imperfections leading to a larger motion of the core cannot be excluded. They are expected to be a very unlikely explanation, though, since the repulsive force at 44 A is only 34 % of that at 75 A. It was thus speculated that the tolerance on the pegs connecting the core and the 8 outer plates could be too large. They have therefore been glued in place with Stycast 2850 FT epoxy, which however did not lead to a noticeable improve-ment. Another source causing a more than anticipated movement of the coils might be an insufficient matching of the G-10 flanges to the curvatures in the mandrel structure. This suspicion cannot be experimentally verified, though.

One possibility also defying control is that the small elongation of the support structure due to the high forces is already too much when compared with the wire diameter. It is expected to be 18m at 40 A. The estimated security factor at this current is 15.

Since any further improvements of the magnet performance seem impossible at this point, its operating current should stay below 40 A, especially since a quench is better avoided in the dilution refrigerator. Still, a more than sufficient trap depth is obtained for all species under study in this thesis. As shown in Figure 3.10, the 40 A limit can be reached in 24 s with a maximum ramping speed of 100 A/min. The same values apply for de-energizing the magnet, so that it should allow for an efficient implementation of evaporative cooling in fu-ture experiments. If either the maximum ramping speed or current is exceeded, unpredictable quenching is observed.

To confirm the quadrupole nature of the magnet, the field characteristics

EXPERIMENTAL CELL 51 have been qualitatively verified outside the test dewar at I = 41 A with a Hall probe. Quantitative values were taken at the extrema. They are plotted in Figure 3.11 together with a calculated curve for ρ = 184.8 mm. This radius is exactly 7 mm away from the circumference of the test dewar and thus nicely agrees with the actual position of the center of the Hall probe, that was guided along its outer wall. The results demonstrate the accuracy of magnetic field predictions obtained from equation (2.12).