Heat load in Cavity beam pipe due to Thermal Radiation coming - - PowerPoint PPT Presentation

• Heat load in Cavity beam pipe due to Thermal Radiation coming

through cryomodule warm end .

Arun Saini, N. Solyak Tuesday 650 MHz cavity Meeting, 13 Aug. 2013

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Thermal Radiation

• Radiation emitted by a surface: = 𝐵𝜗𝜏𝑈4

– 𝜗 =1; for a black body.

• Net radiation exchange between two surfaces:

12 1 4 2 4 1 12 12 1 2 2 2 1 1 1 4 2 4 1 12

). .( bodies Black For 1 . ) 1 ( . ) 1 ( ) .( F A T T Q F A A A T T Q                

Q 

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Case 1 : Maximum heat transfer from 300K to 2 K

• Assumptions:

– Both boundaries are next to each other.

• No interception from 80 K and 5 K

– Both are black bodies.

• Net Radiation transfer

W Q m R R F A L R for F A T T Q 5 059 . ; . 1 ). .(

12 2 12 1 12 1 4 2 4 1 12

         

300 K 2 K {1}

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Case 2 : Minimum heat transfer from 300K to 2 K

• Assumptions:

– 2K boundary is grey and opaque surface.

• No transmission for opaque surface.

300 K 2K

• For L =0.2 m; Radiation reaching to

cavity beam pipe ~ 0.16 W.

• Conclusion : Radiation heat load lays

in interval of [ 0.16 5]

L 11 20.05

View Factor from bottom to curved surface

{2} {3}

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Case 3 : Simplified Realistic model

• ANSYS simulation is performed for simplified model.

– Steady state surface to surface radiation boundary condition is applied. – – No Convection effect. – Emissivity of 80 K and 5 K Stainless steel pipe is varied.

300 K 2 K 80 K 5 K 0.25 m 0.1 0.1 0.175  1  0.05

inci inci emit net

Q Q Q Q     ) 1 (     

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Power deposited in Cavity Beam Pipe (BP)

Cavity BP S.Steel BP

Ptotal = 0.05 W Ptotal = 0.1355 W Ptotal = 0.2358 W

• Conclusion:
• High emissivity of 80 K

and 5K pipes can reduce energy deposition in Cavity BP.

• Reducing the radius of

Steel BP might also help.

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How to increase emissivity

• Rough surface is better attenuator than smooth surface.

– Sandblasting and chemical etching

• High emissivity also leads to high conduction heating load which can

be easily intercepted by 80 K and 5 K cold sheild.

• SNS data suggests that 70 % of total static heat load comes from

thermal radiation.

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Black Surface Rough Black Surface

Temperature Distribution in Cavity Beam Pipe

0.16m 0.m T1 =5K T2 =2K

Q 

pipe beam

• f

e unit volum per generated heat

• f

Rate

2 2

     q K q z T

For 1D steady state equation. K = Thermal conductivity.

1 2 1).

( ) (

2 1

T T dT T K i K

T T i avg

  



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Thermal conductivity data :D. Reschke/DESY, Dec. 2003

Termal Conductivity vs. Temp

1 10 100 1000 1 10 Temperatur [K] Wärmeleitfähigkeit [W/mK]

RRR=760 RRR=525 RRR=400 RRR=270 RRR=120 RRR=40

L270T ( ) exp 4.57848  31.01ln T ( )   54.77795ln T ( )2   46.41167ln T ( )3   17.89282ln T ( )4   2.56625ln T ( )5  

 



L400T ( ) exp 4.38  31.0ln T ( )   54.69ln T ( )2   46.40ln T ( )3   17.917 ln T ( ) ( )4   2.5741ln T ( )5  

   



Fit:

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Thermal conductivity

Kaverage with no. of iteration

Thermal conductivity along beam pipe

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Temperature Distribution in beam pipe for different emittances

• Input power is 2 W

0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 1 2 3 4 5 6 7 8 9 10 Temperature distribution for different emissivity, Power Input 2 W

z (m) Temperature (K)

e =1.0 e =0.75 e =0.5 e =0.25 e =0.1 e=0.05 no power deposit

T1 =5K T2 =2K 2W

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Maximum Temperature in Cavity Beam Pipe

Variation in Max. Temperature with emissivity Variation in Max. Temperature with input thermal radiation

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Calculation of additional RF losses in cavity beam pipe.

• Rise of temperature in beam pipe results increase in BCS surface

resistance.

• Surface resistance is calculated for given temperature distribution in beam

pipe. – Assumption

• Rs = 10 n W @ 2 K.
• Surface magnetic fields in beam pipe is calculated using SLANS for

1 J stored energy.

• For Max. Voltage gain of 17.5 MeV in 650 MHz cavity, stored energy is ~

122.5 J.

d d c c c c c B

P U Q ds H Rs P T T f Rs T T T T T T T k T T K Rs T Rs . . . . 2 1 . . ) . . exp( * * ) 2 ( ) (

2 2 2

                     



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Surface resistance & RF power dissipation in beam pipe.

0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 10 10

1

10

2

10

3

10

4

Surface Resistance along beam pipe for different emissivity, Power Input 2 W

z (m) Rs (n Ohm)

e =1.0 e =0.75 e =0.5 e =0.25 e =0.1 e=0.05

• Input power is 2 W

Surface Resistance along beam pipe RF Power dissipation in beam pipe for operating gradient

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0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 10

• 3

10

• 2

10

• 1

10 10

z (m) Power Dissipation in Beam Pipe (mW)

e =1.0

Q0 ~ 2.9E+13

Heat load in Cavity beam pipe due to Thermal Radiation coming through Power coupler

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Power coupler for 650 MHz cavity Dimensions of cold part of power coupler

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Radiation Surfaces.

Ceramic Window @ 300 K Antenna tip @ 300 K Antenna @ 300 K

• Emissivity of Ceramic Window =1.
• Emissivity of Antenna tip and Antenna = 0.1
• Emissivity of Niobium pipe = 0.05

Cavity Beam pipe @ 2K  ANSYS simulation shows power deposition in cavity beam pipe is ~ 0.15 W

Summary

• Analysis is performed to analyze heat load in beam pipe due to

cryomodule warm end and power coupler. – Estimation for simplified configuration shows no problem in beam pipe.

• Next Steps

– Improving the model and perform the more precise studies.

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1. http://webserver.dmt.upm.es/~isidoro/tc3/Radiation%20View%20factors.pdf 2. http://www.dtic.mil/dtic/tr/fulltext/u2/a284447.pdf 3. http://ieeexplore.ieee.org/stamp/stamp.jsp?arnumber=05643103

References

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Back-up slides

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