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Transcript
FCC Beam Screen cooling – First estimations Claudio Kotnig Content 1. Conditions & Presumptions 2. Calculations • Cryogen (without heat conduction resistivity in the BS) • Beam Screen (wrt the heat conduction in the BS) 3. Interconnections 4. Perspectives 2 Presumptions & Conditions Goal: Estimation of the possible cooled length of the BS in the FCC • Calculations only for the arc • Heat load only due to the synchrotron radiation • No cryogen delivery issues PSR in W/m LHC FCC (100 km) FCC (83 km) 0.33 28.4 44.3 →”bad case” - scenario 3 Presumptions & Conditions ”bad case” - scenario • PSR = 44.3 W/m (FCC 83 km) • Total heat load absorbed by the outer half of the BS • Bundling of the SR on a small area 4 Presumptions & Conditions Beam Screen Conditions • Temperature 40 K – 60 K • Material: steel or titanium (with copper layer) • Size constrained by beam and cold bore Cryogens • Helium 20 bar • Helium 50 bar • Neon 20 bar (Tsat = 42.2 K → two phase area) • Neon 50 bar 5 Calculations Calculation scheme Set up supply temperature and pressure → fluid properties from tables Calculation of cooled length for a given mass flow limited by • Max. temperature of Beam Screen (60 K) • Max. pressure drop (10 % of the supply pressure) • Max. velocity (10 % of the sound velocity) 6 Calculations Cryogen heat absorption ability Total Power of Synchrotron Radiation is absorbed by the cryogen w.n.r.t. the heat conduction resistance (e.g. temperature differences in the BS) Goals of the calculation: • compare the cryogens • establish the limits set by the cryogens Parameter in the following diagrams is the diameter of a capillary 7 Calculations 8 Calculations Doubling the allowed pressure drop increases cooled length by 50 % (→ disproportional increase of exergetic costs) 9 Calculations Amendments Calculation were made for 2 capillaries → unused space on the center-side Possible solutions: • Use the two inside capillaries to distribute unheated cryogen → mixing → alternating cooling Problem: Different pressure drops in heated and unheated capillaries • Helically wrapped capillaries around the BS (Production?) 10 Calculations Summary • The cooled length increases linearly with the mass flow • With Neon the cooled length can be doubled • Enlarging the diameter of the capillaries is an easy and effective way to increase the cooled length • Instabilities due to high velocities can be avoided • The available space should be used 11 Calculations Temperature Differences in the Beam Screen Total Power of Synchrotron Radiation is absorbed by the cryogen w.r.t. the heat conduction processes in the Beam Screen Goals of the calculation: • Estimation of the temperature differences in the BS • establish the limits set by the BS geometry and material Changing parameter in the following diagrams are the beam screen material and the breadth of the Capillary–BS-contact 12 Calculations Heat conduction resistance The whole heat flux has to pass the small contact between the capillary and the Beam Screen → high temperature difference By doubling the breadth, the temperature difference can be halved The largest heat conduction resistance is decisive for total heat conduction resistance 13 Calculations Increase of the Cooled length Mass flow 25% - ratio of about 15% 14 Calculations Summary • Using e.g. titanium instead of steel, the cooled length can be increased due to the higher heat conductivity • Assimilation of the heat conduction resistances in series to avoid large temperature differences 15 Interconnections Estimation of BS temperature between the dipoles • In the LHC the Beam Screen between the dipoles aren’t cooled • BUT: the PSR of the FCC is two magnitudes higher • Due to the low heat conductivity of steel in the given temperature range, the temperature differences in the interconnections with necessary distances are to high • To keep the temperature of the BS between the dipoles below 60 K (with an minimal cooling temperature of 40K), the gap distance must have an magnitude of 10-2 m 16 Interconnections Assumptions • Half of the heat load of the interconnection shall be absorbed by each adjacent dipole • The synchrotron radiation heats the whole BS consistently (no hot spots!) • The heat conduction coefficients are constant (l = l (T=50 K)) • Max. temperature of the BS = 60 K dT q x l A dx 60 l IC 2 dT Tmax 0 q x dx Al 2 q lIC 60 Tmax 8 A l 17 Interconnections Summary • The Beam Screen temperature between the dipoles can’t be kept under the necessary limit without any additional actions • Some Possibilities to decrease the temperature difference: o Increase cross section area of BS between the dipoles o Different material or composition of materials o Separate cooling 18 Perspectives Perspectives • The possibility to cool at least one dipole seems to be very probable • Neon seems to be the more interesting cryogen, but availability, costs and properties have to be assessed • Titanium seems to be the more interesting BS material, but availability, costs and properties have to be assessed • The interconnection cooling issue has to be solved 19 Perspectives Thank you very much for your attention 20