Download Temperature Differences in the Beam Screen

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
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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
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Calculations
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Calculations
Doubling the allowed pressure drop increases cooled length by
50 % (→ disproportional increase of exergetic costs)
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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?)
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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
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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
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Calculations
Increase of the
Cooled length
Mass flow
25%
- ratio of about 15%
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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
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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
Al

2
q lIC
60 
 Tmax
8 A l
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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
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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
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Perspectives
Thank you very much for your attention
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