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CST – Computer Simulation Technology

Heat Load Investigation of a PETRA III Toroid

DESY is one of the world's leading accelerator centers that develops, builds and operates large particle accelerators. These accelerators produce photon beams which are used to investigate the structure of matter. The ring accelerator PETRA III is a storage-ring based X-ray radiation source that produces X-rays of an exceptionally high brilliance.

Toroids are used in accelerators to measure beam charge. They are basically a kind of transformer where the beam can be considered as a primary circuit inducing a current in the secondary winding. Figure 1 shows a model of such a non-destructive beam current monitor. It consists of beam tube, ceramic, bellow, core and holders. The bellow is shielded with an elongated tube, and a spring separates the volume of the tube from the volume between the tube and the bellow....

Courtesy of DESY, Hamburg, Germany



Figure 1: Structure of the toroid

CST PARTICLE STUDIO® (CST PS), together with the thermal solver of CST MPHYSICS® STUDIO (CST MPS), can be used to investigate the thermal environment of this setup. The energy loss of the beam is simulated with CST PS wake field solver (WAK) to calculate the induced heat load in the toroid. The stationary thermal solver is then used to simulate the maximum temperature in the device.

The induced power in the toroid is calculated as follows:

Pmax = Imax Q kloss = Imax2 t kloss / Nmin (1)

where Imax = 100 mA is the beam current, t = 7.685µ s the accelerator revolution time, Nmin = 40 the number of bunches in the accelerator, and Q and k are beam charge and wake loss factor respectively.

For a simulation with the WAK solver, only vacuum, ceramic and air part around the core are considered. The particle beam has a bunch length of 13.2 mm and charge of 1 nC. Figure 2 shows the cross section of the model used for the WAK Solver. The blue and orange lines are the beam path and wake field integration path. Since the beam is assumed to be ultrarelativistic an indirect integration method can be used to improve the results.



Figure 2: Wake field simulation model

To ensure an appropriate accuracy a mesh convergence study has been performed. The mesh has to be fine enough to resolve the structure properly, especially at the bellow and the spring (see Figure 3). The loss factor converges to kloss = 7.9 V/nC (see Figure 4), resulting in a deposited Power of Pmax = 15.17 W according to (1).



Figure 3: Final mesh after convergence study


Figure 4: Convergence of loss factor vs. mesh refinement

For the thermal simulation, a tube with 20 cm length is added on both sides. Each end of the tube terminates at a thermal boundary with constant temperature of 20°C. No cooling is applied in the transverse direction, which implies that no air cooling is being assumed in the setup. Thermal conductivity of the materials is needed for the stationary thermal solver and can be loaded from the material library. Radiation properties are applied as surface conditions (see Figure 5). This setup, considering the cooling due to the longer tube as well as heat radiation, represents the actual cooling process in the monitor.



Figure 5: Thermal boundary conditions (left) and radiation surfaces showing emissivity values between 0.015 and 0.28 (right)

The induced power is distributed uniformly on the inner surface of the ceramic and on both ends of the tube near the ceramic. This setup is valid, since an a priori simulation revealed no influence of eigenmodes in the structure. With Imax = 100 mA and 40 bunches (resulting in 15.17 W), the temperature rises to Tmax = 79.2°C (see Figure 6). This means an increase of 59.2°C. Measurements on a slightly different model showed comparable values.



Figure 6: Temperature distribution on the surface

Performing a parameter sweep of the beam current, we can see that the temperature shows quadratic behavior as also predicted by equation (1). The beam setting with 100 mA and 40 bunches is chosen for thermal analysis because it is assumed to be the case with highest induced power. The maximum temperature of 80°C is not expected to influence the properties of the toroid.



Figure 7: Temperature vs. beam current

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