HIMARC Simulations Divergent Thinking, Convergent Engineering 8117 W. Manchester Avenue, Suite 504 Los Angeles, CA 90293 Ph: (310) 657-7992 Horizontal Superconducting Magnet, ID 1.6m 1
1 Design definition 1.1 Specifications Dimensions The internal diameter shall be MIN 1.6 meters The outside diameter shall be MAX 2.4 meters The height may range from 1.2 meters to 1.4 meters. The maximum weight of any separable component shall not exceed 7.5 tons. Internal Field The magnet assembly shall have minimum field strength of 0.4 Tesla. External Field. The magnet shall be restricted to the following spec: ACGIH Threshold Limit Values Static Magnetic Fields. Specifically: The resultant magnet field shall be less than 6000 gauss when measured 1 cm from the shield surface. The resultant magnetic field shall be less than 600 gauss when measured 10 cm from the shield surface. The resultant magnetic field shall be less than 60 gauss when measured 4 meters from the center of the magnet. 1.2 Design Challenges Generate a high magnetic field over a very large gap with low electrical power Large AT, large current density Shielding required Large forces Coil must be thermally insulated from outside Coil must be supported Circuit protection against quenching 2
1.3 Design Analyses Magneto-static analyses to define required AT and proper shield thickness. TOSCA Stored Energy TOSCA Selection of SC wire to determine A and turns (peak field in conductive regions) TOSCA Coupled Thermal Structural - Magnetics analyses to study nominal operation: ELEKTRA TEMPO STRESS Circuit protection (Discharge of energy into an external resistor bank) QUENCH o o o o Functional physical properties Anisotropic Physical properties Functional BC Table for Cold head representation (heat Flux) 3
2 - ANALYSIS ELEMENTS 2.1.1 Device: Shield 4
2.1.2 Device: Coil and Cryogenic unit Coil is in red 4K copper band is shown in dark blue SS coil holder is shown in light blue. SS coil holder cover is shown in translucent blue. G-10 radial and vertical structural tie-rods are displayed in purple and fushia. G-10 Bumpers are shown in purple Brass nuts are shown in green 5
2.2 Material Properties The following materials have been used in the analysis. Shield: A36 Vacuum Chamber and coil support SS304 50K vessel and 4K band: Copper Brass nuts Brass Support Tie-rods: G10 Mylar (reflectivity of 98%) (Single layers of relatively heavy gauge aluminized Mylar) Nonlinear thermal analyses as the material properties vary with temperature. Thermal conductivity functions have been defined to reflect the change in thermal conductivity with temperature. G-10 material is anisotropic 6
2.2.1 Material Properties versus temperature Copper: Wcu=7.5E7/K 3 +393 Wcu=576 at 4K Wcu=1565 at 40K Note: Particularly in copper, but in other metals as well, the thermal conductivity is a strong function of the purity and the condition of the metal. As a result, there is a considerable spread in the values of thermal conductivity reported in the literature, even for a specific alloy. To provide for better predictability, these metals are sometimes characterized by the residual resistance or RRR (residual resistivity ratio) value. The RRR value is the ratio of the electrical resistivity at 4.2K to the electrical resistivity at 273K. This allows the thermal conductivity to be characterized, because there is a close correspondence between electrical and thermal conductivity in metals. 7
SS304: Wss304=2T.4-3.18 Brass: The thermal conductivity functions have been defined to reflect the change in thermal conductivity with temperature: for the brass material the original data is a linear variation from 59 W/(m K) at 100K up to 113 W/(m K) at 273K: Wbrass= 0.3121T+27.786 G10: This is the largest uncertainty of all material properties. The conductivity is strongly depended on the treatment of the glass mica tape. Experiments have shown that it can vary by a factor of 4 at 4 K from treatment processes alone. G10 s thermal conductivity is directional in the cable, thus typically two values are given. The normal direction is of most interested for modeling of superconducting magnets. Reference: G-10 CR (Normal) tabulated data was fitted to the following equations (Valid for 4<T<150 K, R² = 9.999974932079730E-01) k = -3.622999163833060E-14x6 + 2.996579202182310E-11x5-9.687545615732300E-09x4 + 1.599284085411630E-06x3-1.452811767382280E-04x2 + 8.279441504868440E- 03x + 4.082144325604080E-02 Reference: G-10 CR Norm [13] (Valid for 10<T<300 K) k=10^(-4.1236+13.788*log(t)-26.068*log(t)^2+26.272*log(t)^3-14.663*log(t)^4+4.4954*log(t)^5-0.6905*log^6+0.0397*log(t)^7) 8
2.3 Conductance Thermal contact between materials is a topic of considerable importance in cryogenics and yet it is only qualitatively understood. Whenever two materials are joined together for the purpose of transporting heat a localized resistance occurs at the boundary. The magnitude of this resistance depends on a number of factors, including the properties of the bulk materials, the preparation of the interface between the two materials, whether there are bonding or interface agents present, and external factors such as the applied pressure. Thermal contact conductance as a function of temperature for a variety of contact preparations and conditions. The contact assumes a 1 cm2 area. Data compiled by Radebaugh 9
2.4 Induced Environment Cold head behavior has been represented by a table linking cold head capacity to the temperature. Functional Heat Flux 10
2.5 Thermal boundary conditions Components are subjected to all types of thermal environments, and typical thermal boundary conditions that may be applied include: Natural or forced convection from inner and outer surfaces, Radiation from inner and outer surfaces, Conduction from the structural rods and sleeves to walls of vacuum chamber or shield, Conduction through rigid components, Conduction from coil to mounting frame, etc. 11
3 MODEL 3.1 Model Identification The FEM analysis was performed by means of ANSYS and OPERA. The same model was used for thermal, structural and magnetic analyses. For the thermal solutions nonlinear analyses are required as the material properties have been set to vary with temperature to reflect the change in thermal conductivity with temperature. 3.2 Model Description 1,028,394 nodes 812341 elements - Quadratic elements are used for Coil, G10 rods, and copper parts. 430,000 amp-turns per coil Core OD is 94 (2.4 meters) The coil cross-section is 2 x 2.4 Height is 54.32 (1.38 meters) ID is 34.75, OD 36.75, Height 38 Steel Thickness is 7 behind coil. Angle 60 degrees Top and bottom plates are 4 thick Coil Volume (total): 1,760 in 3, Weight 260 Kg Steel volume: 110,975 in 3, Weight: 15.75 tons 12
4 ANALYSIS RESULTS 4.1 Magnetic Analysis: internal field Magnetic field density (T) over the shield and conductors Magnetic field density (T) over a 31.496 (.8m) area in the center of the device (4110 Gauss in center) 13
4.2 Magnetic Analysis: external field Field at 4m from the center of the device (<20 gauss) Stray Magnetic field distribution from center 600 gauss field surface is contained within the shield 14
4.3 Magnetic Analysis: Force acting on coils Force density (N/m 2 ) acting on coil during nominal operation. Total force on one conductor is: Fz= 841,120 N 15
4.4 Magnetic Analysis: Local Field on Conductors B on coil Current B center [tesla] [A] [Gauss] 5.5 165 3950 3.27 98 2567 2.57 77 2095 1.6 48 1314 2.7 80 no steel 1135 Critical current density is a function of local magnetic field and of temperature Critical Current Density of NbTi Jc(T,B) in Amperes B_Field 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6 6.5 7 7.5 8 Temp [K] [T] [T] [T] [T] [T] [T] [T] [T] [T] [T] [T] [T] [T] [T] [T] 4.2 735 658 580 525 470 435 400 358 315 288 260 224 187 157 126 5 541 484 427 387 346 321 295 264 232 212 192 165 138 115 93 6 322 289 255 231 206 191 176 157 138 126 114 98 82 69 55 6.2 284 254 224 203 182 168 155 138 122 111 101 86 72 61 49 6.5 230 205 181 164 147 136 125 112 98 90 81 65 48 44 39 7 150 135 119 108 96 89 82 73 65 59 53 46 38 32 26 7.2 123 110 97 88 79 73 67 60 53 48 44 37 31 26 21 7.4 98 88 78 70 63 58 54 48 42 38 35 30 25 21 17 7.8 57 51 45 41 37 34 31 28 25 22 20 18 15 12 10 8 41 36 32 29 26 24 22 20 17 16 14 12 10 9 7 4.5 Magnetic Analysis: Stored Energy 1,000,000 joules 16
5.1.a Cool-Down: Temperature (SS) 5 MULTIPHYSICS ANALYSIS RESULTS: COOLDOWN SS Bobbin 4K line (T <5.1K) Coil T <5.1K 50K line (T<39.7K) 17
5.1.b Cool-Down: Temperature (Transient) Ruthenium oxide (TC) location layout Temperature versus time (minutes) during the cool down process Coil resistance versus time (minutes) is monitored during the cool down process SC state was reached in 5 days. 18
5.2 Cool-Down: Displacement Radial disp. (inch) of the bobbin: Max.1755 Vertical disp. (inch) of the bobbin: Max.201 5.3 Cooling down: Stress Von Mises stress < 350 MPa 19
6 MULTIPHYSICS ANALYSIS RESULTS: OPERATION 6.1 Displacement: Operation (395,000 AT,.4 Tesla) Bobbin Display of the bobbin radial and vertical displacement during operation Maximum radial displacement reaches.325 from the ambient position Relative maximum displacement from the cooled (4.2K) position is.175 20
6.2 Displacement: Operation (395,000 AT,.4 Tesla) - 50K Intercept Display of the 50K copper chamber radial displacement during operation Display of the 50K copper chamber radial and vertical displacement during operation 21
6.3 Displacement: Operation (395,000 AT,.4 Tesla) - SC Coil Display of the SC coil radial and vertical displacement during operation Maximum radial displacement reaches.25 from the ambient position Maximum radial displacement reaches.05 from the cooled position 6.4 Displacement: Operation (395,000 AT,.4 Tesla) 4K and 50 Lines 22
6.5 Operation (395,000 AT,.4 Tesla) Stress Display of the Von Misses stress on the bobbin and coil during operation Von Mises stress < 240 MPa Max VM stress on coil is < 60 MPa Von Mises stress < 200 MPa 23
7 MULTIPHYSICS ANALYSIS RESULTS: FULL POWER 7.1 Displacement: Full power (464,800 AT,.45 Tesla) Bobbin Display of the bobbin radial and vertical displacement during operation Maximum radial displacement reaches.37 from the ambient position Relative maximum displacement from the cooled (4.2K) position is.2 24
7.2 Displacement: Full power (464,800 AT,.45 Tesla) - 50K Intercept Display of the 50K copper chamber radial displacement during operation Display of the 50K copper chamber radial and vertical displacement during operation Maximum radial displacement reaches.34 from the ambient position Maximum radial disp. at 50K bus attachment is.2 from the ambient position 25
7.3 Full power (464,800 AT,.45 Tesla) - SC Coil Display of the SC coil radial displacement during operation Display of the SC coil vertical displacement during operation Maximum radial displacement reaches.275 from the ambient position Maximum radial displacement reaches.1 from the cooled position 26
7.4 Full power (464,800 AT,.45 Tesla) Stress Display of the Von Misses stress on the bobbin and coils during operation Von Mises stress < 300 MPa Max VM stress on coil is 70 MPa Von Mises stress < 300 MPa 27
Thank You 28