β’ 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 8/13/2013 1
Thermal Radiation β’ Radiation emitted by a surface: = π΅πππ 4 ο¦ Q β π =1; for a black body. β’ Net radiation exchange between two surfaces: ο³ 4 ο 4 .( T T ) ο¦ ο½ 1 2 Q ο ο₯ ο ο₯ 12 ( 1 ) ( 1 ) 1 ο« ο« 1 2 ο₯ ο₯ A . A . A F 1 1 2 2 1 12 For Black bodies ο¦ ο½ ο³ 4 ο 4 Q .( T T ). A F 12 1 2 1 12 8/13/2013 2
Case 1 : Maximum heat transfer from 300K to 2 K 300 K 2 K β’ Assumptions: β Both boundaries are next to each other. β’ No interception from 80 K and 5 K β Both are black bodies. β’ Net Radiation transfer {1} ο¦ ο½ ο³ ο 4 4 Q .( T T ). A F 12 1 2 1 12 R οΎοΎ ο½ ο° ο½ 2 for 1 A F . R ; R 0 . 059 m 1 12 L ο¦ ο½ Q 5 W 12 8/13/2013 3
Case 2 : Minimum heat transfer from 300K to 2 K β’ Assumptions: β 2K boundary is grey and opaque surface. β’ No transmission for opaque surface. 300 K 2K ο₯ 1 ο½1 ο₯ 2 ο½0.05 {3} L β’ For L =0.2 m; Radiation reaching to cavity beam pipe ~ 0.16 W. β’ Conclusion : Radiation heat load lays in interval of [ 0.16 5] View Factor from bottom to curved surface {2} 8/13/2013 4
Case 3 : Simplified Realistic model 300 K 2 K 5 K 80 K 0.1 0.1 0.25 m 0.175 ο₯ ο½0.05 ο₯ ο½1 β’ ANSYS simulation is performed for simplified model. β Steady state surface to surface radiation boundary condition is applied. ο¦ ο¦ ο¦ ο¦ β ο½ ο ο« ο ο₯ Q Q Q ( 1 ) Q net emit inci inci β No Convection effect. β Emissivity of 80 K and 5 K Stainless steel pipe is varied. 8/13/2013 5
Power deposited in Cavity Beam Pipe (BP) S.Steel BP Cavity BP β’ Conclusion: β’ High emissivity of 80 K and 5K pipes can reduce energy deposition in P total = 0.2358 W Cavity BP. β’ Reducing the radius of P total = 0.1355 W Steel BP might also help. P total = 0.05 W 8/13/2013 6
How to increase emissivity Black Surface Rough Black Surface β’ Rough surface is better attenuator than smooth surface. β Sandblasting and chemical etching β’ High emissivity also leads to high conduction heating load which can be easily intercepted by 80 K and 5 K cold sheild. β’ SNS data suggests that 70 % of total static heat load comes from thermal radiation. 8/13/2013 7
Temperature Distribution in Cavity Beam Pipe For 1D steady state equation. οΆ 2 T q ο½ ο οΆ 2 z K ο½ q Rate of heat generated per unit volum e of beam pipe K = Thermal conductivity. T 2 ο½ ο² K ( T 1 ). dT ο i T K ( i ) 1 ο avg T T ο¦ 2 1 Q 0.16m T2 =2K 8/13/2013 0.m 8 T1 =5K
Thermal conductivity data :D. Reschke/DESY, Dec. 2003 Termal Conductivity vs. Temp 1000 WΓ€rmeleitfΓ€higkeit [W/mK] 100 10 RRR=760 RRR=525 RRR=400 RRR=270 RRR=120 RRR=40 1 1 10 Temperatur [K] ο¨ ο© ( ) 2 ( ) 3 ( ) 4 ( ) 5 οΊο½ ο ο« ο ο ο ο« ο ο ο ο« ο L270T ( ) exp 4.57848 31.01ln T ( ) 54.77795ln T 46.41167ln T 17.89282ln T 2.56625ln T Fit: ο© οΉ ( ) 2 ( ) 3 ) 4 ( ) 5 ο« ο» οΊο½ ο ο« ο ο ο ο« ο ο ο ο« ο L400T ( ) exp 4.38 31.0ln T ( ) 54.69ln T 46.40ln T 17.917 ln T ( ( ) 2.5741ln T 8/13/2013 9
Thermal conductivity K average with no. of iteration Thermal conductivity along beam pipe 8/13/2013 10
Temperature Distribution in beam pipe for different emittances Input power is 2 W β’ 2W Temperature distribution for different emissivity, Power Input 2 W 10 e =1.0 e =0.75 9 e =0.5 e =0.25 8 e =0.1 T2 =2K e=0.05 T1 =5K no power deposit 7 Temperature (K) 6 5 4 3 2 1 0 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 z (m) 8/13/2013 11
Maximum Temperature in Cavity Beam Pipe Variation in Max. Temperature with Variation in Max. Temperature input thermal radiation with emissivity 8/13/2013 12
Calculation of additional RF losses in cavity beam pipe. β’ Rise of temperature in beam pipe results increase in BCS surface resistance. β’ Surface resistance is calculated for given temperature distribution in beam pipe. ο© οΉ ο β Assumption T T T ο½ ο ο’ οΌ οͺ οΊ 2 c c Rs ( T ) Rs ( 2 K ) * * exp( . ) T T c οͺ οΊ T k . T T T ο« ο» β’ Rs = 10 n W @ 2 K. B c 2 ο ο° . . f ο½ ο’ οΎ Rs T T ο³ c 1 ο² ο½ 2 . . . P Rs H ds d 2 ο· . U ο½ Q P d β’ Surface magnetic fields in beam pipe is calculated using SLANS for 1 J stored energy. β’ For Max. Voltage gain of 17.5 MeV in 650 MHz cavity, stored energy is ~ 122.5 J. 8/13/2013 13
Surface resistance & RF power dissipation in beam pipe. Input power is 2 W β’ Surface Resistance along beam pipe RF Power dissipation in beam pipe for operating gradient Surface Resistance along beam pipe for different emissivity, Power Input 2 W 4 10 1 e =1.0 10 e =0.75 e =1.0 e =0.5 Power Dissipation in Beam Pipe (mW) e =0.25 e =0.1 3 e=0.05 10 0 10 Rs (n Ohm) 2 -1 10 10 Q 0 ~ 2.9E+13 -2 10 1 10 -3 10 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0 10 z (m) 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 z (m) 8/13/2013 14
Heat load in Cavity beam pipe due to Thermal Radiation coming through Power coupler Power coupler for 650 MHz cavity Dimensions of cold part of power coupler 8/13/2013 15
Radiation Surfaces. Antenna @ 300 K Ceramic Window @ 300 K Antenna tip @ 300 K Cavity Beam pipe @ 2K β’ Emissivity of Ceramic Window =1. β’ Emissivity of Antenna tip and Antenna = 0.1 β’ Emissivity of Niobium pipe = 0.05 οΌ ANSYS simulation shows power deposition in cavity beam pipe is ~ 0.15 W 8/13/2013 16
Summary β’ Analysis is performed to analyze heat load in beam pipe due to cryomodule warm end and power coupler. β Estimation for simplified configuration shows no problem in beam pipe. β’ Next Steps β Improving the model and perform the more precise studies. 8/13/2013 17
References 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 8/13/2013 18
Back-up slides 8/13/2013 19
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