Synchrotron Radiation Thermal Effect on the 12 GeV CEBAF
M. Wiseman, S. Slachtouski, K. Wilson, and B. Yunn
June 20, 2006
Introduction
This note will study the effects from Synchrotron Radiation and the 12 GeV upgraded CEBAF. First it defines the problem in terms of the radiation generated from each dipole in the higher energy passes of CEBAF. It will then look at the thermal effects on the machine with general hand calculations and Finite Element Analysis. Temperatures predicted in this note are in general less than 50 C with peak temperature on the outside of the chambers limited to less than 65 C. Peak temperatures formed bellows may be as high as 140 C but are limited to a small area on the inner convolutions of the bellows. The elevated temperatures may create personnel safety concerns immediately following beam operations, but are not a concern for machine protection and no active cooling of elements are currently planned for the upgrade.
Synchrotron Radiation Power at 12 GeV CEBAF Upgrade
Synchrotron radiation power generated by various dipole magnets in Arcs 6 through10 (radiation in lower arcs is less important) and also in the 12 GeV beam line is estimated for the 12 GeV Upgrade. The result is summarized in the following Table 1 and 2. The current will be limited to 90 μA in Arcs 1 through 9 and 5 μA in Arc 10 and the Hall D transport.
Table 1. Total synchrotron radiation power in Arcs 6 to 10 and in the 12 GeV beam line of the CEBAF 12 GeV Upgrade.
Beam line / Beam Current(uA) / Total radiation power (W)
Arc 6 / 90 / 509
Arc 7 / 90 / 587
Arc 8 / 90 / 1029
Arc 9 / 90 / 1502
Arc 10 / 5 / 109
Hall D / 5 / 9
How to use Table 2:
- For a beam line element of concern identify a dipole immediately upstream of the element and locate the row for the dipole from the Table 2.
- Get the radiation power loading value for that dipole and then multiply the value by the length of the element. Synchrotron radiation shines only on a narrow strip whose width is roughly determined by the vertical (or horizontal for spreader and recombiner magnets) size of beam at the bend. For an estimate of the peak power density, divide the total power from the step 2 by 2.5σy × the length of the element (~the area of the strip). Obviously, for spreader and recombiner magnets σx should be used, where σx and σy are the rms transverse beam sizes.
- Find out whether the power density in 3 is acceptable.
Example:
For a 2 inch bellows located near MBA9A01, the total synchrotron radiation power the bellows will receive is 0.67 W. If the σy is 0.5 mm, the power density is 1.1 W/cm2.
Table 2. Synchrotron radiation power loading at or near major dipole magnets for 12 GeV Upgraded CEBAF accelerator. Dipoles with no specified length are all 1 meter long. Note that average power loading for the entire arc vacuum chamber is less than the values listed in the Table 2 by about a factor of 2 to 3.
Dipole / B (kG) / Bend radius (m) / Radiation Power Loading (W/m)Arc 6 (beam energy = 6.6625 GeV)
MAW6S01 / 14.3945 / 15.439 / 10.479
MAX6S02 / 11.8202 / 18.802 / 7.066
MAU6S03(2m) / -13.1303 / 16.926 / 8.718
MAB6S04 / 13.3208 / 16.684 / 8.973
MAB6S06 / -13.3208 / 16.684 / 8.973
MBY6E01 / -9.33064 / 23.818 / 4.403
MBZ6E02(2m) / 9.33064 / 23.818 / 4.403
MBY6E03 / -9.33064 / 23.818 / 4.403
MBB6A01-32(2m) / 10.9055 / 20.378 / 6.015
MAB6R01 / -13.3208 / 16.684 / 8.973
MAB6R03 / 13.3208 / 16.684 / 8.973
MAU6R04(2m) / -13.1303 / 16.926 / 8.718
MAX6R05 / 11.8202 / 18.802 / 7.066
MAW6R06 / 14.3945 / 15.439 / 10.479
Arc 7 (beam energy = 7.7525 GeV)
MAQ1S01 / 12.8911 / 20.06 / 11.380
MAS3S02 / 11.9001 / 21.731 / 9.697
MYR7S03(3m) / -8.26371 / 31.293 / 4.676
MAC7S04 / 7.0686 / 36.584 / 3.421
MAC7S06 / -7.0686 / 36.584 / 3.421
MBY7E01 / -10.857 / 23.818 / 8.072
MBZ7E02(2m) / 10.857 / 23.818 / 8.072
MBY7E03 / -10.857 / 23.818 / 8.072
MBA7A01-32(3m) / 8.45967 / 30.568 / 4.901
MAC7R06 / -7.0686 / 36.584 / 3.421
MAC7R04 / 7.0686 / 36.584 / 3.421
MYR7R03(3m) / -8.26371 / 31.293 / 4.676
MAS3R02 / 11.9001 / 21.731 / 9.697
MAQ1R01 / 12.8911 / 20.06 / 11.380
Arc 8 (beam energy = 8.8425 GeV)
MAW8S01 / 14.3943 / 20.491 / 18.458
MAX8S02 / 11.82 / 24.954 / 12.446
MYR8S03(2m) / -13.1072 / 22.503 / 15.305
MAE8S04 / 12.4133 / 23.761 / 13.727
MAE8S06 / -12.4133 / 23.761 / 13.727
MBY8E01 / -12.3834 / 23.818 / 13.661
MBZ8E02(2m) / 12.3834 / 23.818 / 13.661
MBY8E03 / -12.3834 / 23.818 / 13.661
MBA8A01-32(3m) / 9.64902 / 30.568 / 8.294
MAE8R01 / -12.4133 / 23.761 / 13.727
MAE8R03 / 12.4133 / 23.761 / 13.727
MYR8R04(2m) / -13.1072 / 22.503 / 15.305
MAX8R05 / 11.82 / 24.954 / 12.446
MAW8R06 / 14.3943 / 20.491 / 18.458
Arc 9 (beam energy = 9.9325 GeV)
MAQ1S01 / 12.8911 / 25.701 / 18.679
MAS3S02 / 11.9001 / 27.841 / 15.917
MYR7S03(3m) / -8.26371 / 40.092 / 7.676
MYR9S04(2m) / -4.9191 / 67.351 / 2.720
MAR9S06 / 9.83929 / 33.694 / 10.868
MBY9E01 / -13.9098 / 23.818 / 21.749
MBZ9E02(2m) / 13.9098 / 23.818 / 21.749
MBY9E03 / -13.9098 / 23.818 / 21.749
MBA9A01-32(3m) / 10.8384 / 30.568 / 13.204
MAR9R06 / 9.83929 / 33.694 / 10.868
MYR9R04(2m) / -4.9191 / 67.351 / 2.720
MYR7R03(3m) / -8.26371 / 40.092 / 7.676
MAS3R02 / 11.9001 / 27.841 / 15.917
MAQ1R01 / 12.8911 / 25.701 / 18.679
Arc 10 (beam energy = 11.0225 GeV)
MAW2S01 / 14.3963 / 25.539 / 1.594
MAX4S02 / 11.8303 / 31.079 / 1.076
MYR8S03(2m) / -13.1133 / 28.038 / 1.322
MYRAS04(2m) / -13.1133 / 28.038 / 1.322
MAYAS05 / 11.8303 / 31.079 / 1.076
MAHAS06 / 14.3963 / 25.539 / 1.594
MBAAA01-32(4m) / 9.02079 / 40.758 / 0.626
MAHAR06 / 14.3963 / 25.539 / 1.594
MAYAR05 / 11.8303 / 31.079 / 1.076
MYRAR04(2m) / -13.1133 / 28.038 / 1.322
MYR8R03(2m) / -13.1133 / 28.038 / 1.322
MAX4R02 / 11.8303 / 31.079 / 1.076
MAW2R01 / 14.3963 / 25.539 / 1.594
12 GeV beam line (beam energy = 12.1125 GeV)
MAQ1S01 / 12.8911 / 31.342 / 1.543
MAS3S02 / 11.9001 / 33.952 / 1.315
MYR7S03(3m) / -8.26371 / 48.892 / 0.634
MYR7S04(2m) / -4.9191 / 82.136 / 0.225
MYRBS05(2m) / -5.63625 / 72.685 / 0.287
MARBS06(2m) / 10.5548 / 38.28 / 1.035
The beam spot sizes at each magnet were then obtained at the inlet and exit of the magnet. The power loading and heat fluxes using a 2.5 sigma spot size is attained and listed in Table 3. The maximum, minimum and average values are listed at the top of the table.
Table 3. Spot sizes and power loading. The fluxes are calculated for the bend plan only. Maximum values are highlighted.
Arc 10 and Hall D / 5.000 / uA current
Flux in bend plane
Beam spot size 1 sigma / based on 2.5 sigma beam width
Dipole / x entry / x exit / y entry / y exit / Power Loading / x entry / x exit / y entry / y exit
mm / mm / mm / mm / W/cm / w/cm^2 / w/cm^2 / w/cm^2 / w/cm^2
Maximum / 0.217 / 5.97 / 6.72 / 6.60 / 5.48
Minimum / 0.006 / 0.02 / 0.02 / 0.24 / 0.16
Average / 0.083 / 0.95 / 0.95 / 3.01 / 2.77
Arc 6 (beam energy = 6.6625 GeV)
MAW6S01 / 0.221 / 0.211 / 0.134 / 0.139 / 0.105 / 1.90 / 1.98
MAX6S02 / 0.189 / 0.180 / 0.150 / 0.156 / 0.071 / 1.49 / 1.57
MAU6S03(2m) / 0.152 / 0.135 / 0.178 / 0.191 / 0.087 / 2.30 / 2.58
MAB6S04 / 0.101 / 0.101 / 0.054 / 0.060 / 0.090 / 3.55 / 3.57
MAB6S06 / 0.117 / 0.125 / 0.107 / 0.121 / 0.090 / 3.07 / 2.88
MBY6E01 / 0.123 / 0.135 / 0.147 / 0.142 / 0.044 / 1.19 / 1.24
MBZ6E02(2m) / 0.204 / 0.233 / 0.114 / 0.105 / 0.044 / 1.54 / 1.69
MBY6E03 / 0.308 / 0.324 / 0.087 / 0.085 / 0.044 / 2.03 / 2.08
MBB6A01-32(2m) / 0.217 / 0.170 / 0.066 / 0.088 / 0.060 / 3.62 / 2.72
MAB6R01 / 0.060 / 0.053 / 0.184 / 0.171 / 0.090 / 5.97 / 6.72
MAB6R03 / 0.117 / 0.141 / 0.122 / 0.111 / 0.090 / 3.06 / 2.54
MAU6R04(2m) / 0.286 / 0.331 / 0.340 / 0.330 / 0.087 / 1.22 / 1.05
MAX6R05 / 0.395 / 0.416 / 0.310 / 0.305 / 0.071 / 0.72 / 0.68
MAW6R06 / 0.462 / 0.480 / 0.292 / 0.288 / 0.105 / 0.91 / 0.87
Arc 7 (beam energy = 7.7525 GeV)
MAQ1S01 / 0.608 / 0.595 / 0.310 / 0.313 / 0.114 / 0.75 / 0.77
MAS3S02 / 0.581 / 0.568 / 0.316 / 0.318 / 0.097 / 0.67 / 0.68
MYR7S03(3m) / 0.555 / 0.505 / 0.322 / 0.334 / 0.047 / 0.34 / 0.37
MAC7S04 / 0.298 / 0.301 / 0.095 / 0.104 / 0.034 / 0.46 / 0.45
MAC7S06 / 0.313 / 0.316 / 0.138 / 0.149 / 0.034 / 0.44 / 0.43
MBY7E01 / 0.198 / 0.203 / 0.277 / 0.270 / 0.081 / 1.16 / 1.19
MBZ7E02(2m) / 0.241 / 0.258 / 0.232 / 0.216 / 0.081 / 1.39 / 1.49
MBY7E03 / 0.304 / 0.315 / 0.176 / 0.168 / 0.081 / 1.83 / 1.92
MBA7A01-32(3m) / 0.327 / 0.232 / 0.064 / 0.099 / 0.049 / 3.06 / 1.99
MAC7R06 / 0.072 / 0.080 / 0.119 / 0.107 / 0.034 / 1.91 / 1.72
MAC7R04 / 0.160 / 0.188 / 0.071 / 0.064 / 0.034 / 0.85 / 0.73
MYR7R03(3m) / 0.363 / 0.380 / 0.243 / 0.230 / 0.047 / 0.51 / 0.49
MAS3R02 / 0.385 / 0.388 / 0.227 / 0.224 / 0.097 / 1.01 / 1.00
MAQ1R01 / 0.392 / 0.396 / 0.221 / 0.218 / 0.114 / 1.16 / 1.15
Arc 8 (beam energy = 8.8425 GeV)
MAW8S01 / 0.403 / 0.393 / 0.205 / 0.210 / 0.185 / 1.83 / 1.88
MAX8S02 / 0.370 / 0.361 / 0.221 / 0.226 / 0.124 / 1.34 / 1.38
MYR8S03(2m) / 0.359 / 0.327 / 0.228 / 0.247 / 0.153 / 1.71 / 1.87
MAE8S04 / 0.230 / 0.232 / 0.083 / 0.092 / 0.137 / 2.38 / 2.36
MAE8S06 / 0.246 / 0.254 / 0.121 / 0.133 / 0.137 / 2.23 / 2.16
MBY8E01 / 0.129 / 0.141 / 0.196 / 0.188 / 0.137 / 2.78 / 2.90
MBZ8E02(2m) / 0.251 / 0.304 / 0.150 / 0.136 / 0.137 / 3.65 / 4.03
MBY8E03 / 0.441 / 0.470 / 0.108 / 0.105 / 0.137 / 5.05 / 5.21
MBA8A01-32(3m) / 0.351 / 0.230 / 0.085 / 0.129 / 0.083 / 3.89 / 2.56
MAE8R01 / 0.368 / 0.372 / 0.237 / 0.227 / 0.137 / 1.49 / 1.48
MAE8R03 / 0.389 / 0.398 / 0.195 / 0.182 / 0.137 / 1.41 / 1.38
MYR8R04(2m) / 0.619 / 0.678 / 0.480 / 0.461 / 0.153 / 0.99 / 0.90
MAX8R05 / 0.682 / 0.698 / 0.460 / 0.455 / 0.124 / 0.73 / 0.71
MAW8R06 / 0.736 / 0.753 / 0.442 / 0.436 / 0.185 / 1.00 / 0.98
Arc 9 (beam energy = 9.9325 GeV)
MAQ1S01 / 1.323 / 1.308 / 0.416 / 0.420 / 0.187 / 0.56 / 0.57
MAS3S02 / 1.290 / 1.275 / 0.424 / 0.428 / 0.159 / 0.49 / 0.50
MYR7S03(3m) / 1.258 / 1.195 / 0.432 / 0.448 / 0.077 / 0.24 / 0.26
MYR9S04(2m) / 1.183 / 1.141 / 0.450 / 0.458 / 0.027 / 0.09 / 0.10
MAR9S06 / 0.962 / 0.941 / 0.491 / 0.496 / 0.109 / 0.45 / 0.46
MBY9E01 / 0.390 / 0.417 / 0.245 / 0.239 / 0.217 / 3.55 / 3.64
MBZ9E02(2m) / 0.559 / 0.617 / 0.207 / 0.194 / 0.217 / 4.20 / 4.48
MBY9E03 / 0.764 / 0.795 / 0.164 / 0.159 / 0.217 / 5.29 / 5.48
MBA9A01-32(3m) / 0.571 / 0.405 / 0.080 / 0.123 / 0.132 / 6.60 / 4.28
MAR9R06 / 0.620 / 0.629 / 0.357 / 0.353 / 0.109 / 0.70 / 0.69
MYR9R04(2m) / 0.710 / 0.729 / 0.327 / 0.321 / 0.027 / 0.15 / 0.15
MYR7R03(3m) / 0.735 / 0.766 / 0.319 / 0.306 / 0.077 / 0.42 / 0.40
MAS3R02 / 0.774 / 0.781 / 0.303 / 0.300 / 0.159 / 0.82 / 0.82
MAQ1R01 / 0.790 / 0.798 / 0.296 / 0.293 / 0.187 / 0.95 / 0.94
Arc 10 (beam energy = 11.0225 GeV)
MAW2S01 / 0.804 / 0.787 / 0.295 / 0.301 / 0.016 / 0.08 / 0.08
MAX4S02 / 0.751 / 0.729 / 0.313 / 0.322 / 0.011 / 0.06 / 0.06
MYR8S03(2m) / 0.724 / 0.660 / 0.324 / 0.350 / 0.013 / 0.07 / 0.08
MYRAS04(2m) / 0.648 / 0.588 / 0.354 / 0.373 / 0.013 / 0.08 / 0.09
MAYAS05 / 0.011
MAHAS06 / 0.563 / 0.517 / 0.380 / 0.400 / 0.016 / 0.11 / 0.12
MBAAA01-32(4m) / 0.587 / 0.409 / 0.106 / 0.159 / 0.006 / 0.24 / 0.16
MAHAR06 / 0.906 / 0.981 / 0.744 / 0.717 / 0.016 / 0.07 / 0.06
MAYAR05 / 0.011
MYRAR04(2m) / 1.020 / 1.111 / 0.708 / 0.682 / 0.013 / 0.05 / 0.05
MYR8R03(2m) / 1.129 / 1.221 / 0.676 / 0.644 / 0.013 / 0.05 / 0.04
MAX4R02 / 1.228 / 1.258 / 0.641 / 0.630 / 0.011 / 0.04 / 0.03
MAW2R01 / 1.305 / 1.327 / 0.614 / 0.606 / 0.016 / 0.05 / 0.05
12 GeV beam line (beam energy = 12.1125 GeV)
MAQ1S01 / 1.585 / 1.571 / 0.599 / 0.604 / 0.015 / 0.04 / 0.04
MAS3S02 / 1.557 / 1.543 / 0.610 / 0.615 / 0.013 / 0.03 / 0.03
MYR7S03(3m) / 1.529 / 1.476 / 0.620 / 0.640 / 0.006 / 0.02 / 0.02
MYR7S04(2m) / 1.465 / 1.429 / 0.643 / 0.654 / 0.040 / 0.11 / 0.11
MYRBS05(2m) / 1.418 / 1.382 / 0.657 / 0.668 / 0.052 / 0.15 / 0.15
MARBS06(2m) / 1.223 / 1.219 / 0.712 / 0.706 / 0.010 / 0.03 / 0.03
x entry / x exit / y entry / y exit / Power Loading / x entry / x exit / y entry / y exit
mm / mm / mm / mm / W/cm / w/cm^2 / w/cm^2 / w/cm^2 / w/cm^2
Note that in the spreader and recombiners there are magnets were multiple beams are bent through one magnet. Combining the power loads from Table 3 one obtains the worst case power loads in Table 4. Lower pass beams were included. Note that the worst case line load is less that a factor of two above the single beam case and the power per square cm is lower than the worst case single beam because of the spot sizes in these locations. A detailed study of the actual geometry in these areas will be needed once the geometry is fixed to see if the synchrotron light from these dipoles indeed add together in spots and will be of concern.
Table 4. Multi-beam affects in common dipoles in Spreader and Recombiners.
Multiple beam loadingBend Radius / Energy / x entry / x exit
m / GeV / W/cm / w/cm^2 / w/cm^2
Arc 2 / MAW2S01 / 5.34 / 2.30 / 0.013
Arc 4 / 10.39 / 4.48 / 0.047
Arc 6 / 15.44 / 6.66 / 0.105 / 1.90 / 1.98
Arc 8 / 20.49 / 8.84 / 0.185 / 1.83 / 1.88
Arc 10 / 25.54 / 11.02 / 0.016 / 0.08 / 0.08
Total / 0.365 / 3.81 / 3.94
Arc 4 / MAX4S02 / 12.65 / 4.48 / 0.032
Arc 6 / 18.80 / 6.66 / 0.071 / 1.49 / 1.57
Arc 8 / 24.95 / 8.84 / 0.124 / 1.34 / 1.38
Arc 10 / 31.08 / 11.02 / 0.011 / 0.06 / 0.06
Total / 0.238 / 2.89 / 3.01
Arc 4 / MAX4R05 / 12.65 / 4.48 / 0.032