c100 cryomodule end can pipeline design per asme b31tnweb.jlab.org/tn/2008/08-015.doc · web...

JLAB-TN-08-015 C100 Cryomodule Magnetic Shielding Finite Element Analysis

C100 Cryomodule Magnetic Shielding Finite Element AnalysisGary G. Cheng, Edward F. Daly, and William R. Hicks

Introduction

The magnetic shield design for the C100 cryomodule (CM) is based on the shield design for the 1998 LINAC cryomodule at CEBAF. The design is a variation of the traditional double-shell type in that each of the eight cavities has its own individual inner shield. Transverse shielding factor was the primary consideration in the original design. For the ongoing 12GeV upgrade project, the cryomodule’s shielding performance along longitudinal beam axis, or simply axial shielding factor, is also important. This opens the window for a design notion of adopting high permeability shielding material at cryogenic temperature. The Amumetal material that was used to construct 1998 LINAC CM magnetic shields has a relative permeability r(300K) = 60,000. However, when temperature drops to 4K, the permeability reduces largely, i.e. r(4K) = 3,775. It is thus a question whether the superconducting niobium cavities are sufficiently shielded from axial and transverse external fields. Finite element analysis of the 1998 LINAC CM shields is conducted to investigate the shielding factors that can be attained by use of Amumetal inner shields and to explore other options that may improve the shielding factors.

Magnetostatic analyses of the CM shields are carried out by use of 2-D and 3-D elements provided in ANSYS Multiphysics. ANSYS offers various formulations for low frequency electromagnetic analysis. This report will compare and contrast pertinent methods. A 2-D model with nonlinear B-H curves for shield materials is employed to evaluate axial shielding factors. A 3-D linear model using constant permeabilities is then developed to estimate transverse shielding factors for asymmetric geometries. The 3-D linear model, when subjected to axial external field, encounters saturation in the outer shield. B-H curves are applied to the 3-D model and axial shielding factors are obtained for 0.5 Gauss axial field.

Magnetic Shield Design and Applicable Materials

The purpose of passive magnetic shields in cryomodules is to attenuate the external field that may induce trapped magnetic fluxes on the surfaces of superconducting cavities, that can degrade the quality factor of such cavities [1-2]. Double-shell magnetic shields [3-5] are commonly adopted in advanced CM designs. This shield configuration really attenuates the transverse magnetic fields. There are analytical formulas that can be used to approximate the transverse shielding factors. Such formulas are often used by engineers for first-hand estimation of the shielding effects while designing shields. However, axial shielding factors [4-5] are more difficult to calculate by analytical means. Numerical simulation like finite element analysis (FEA) is therefore relied on to evaluate the axial shielding factors of cylindrical multiple-shell shields. FEA also has the advantage of modeling the actual openings on the shields. Nonlinear shield material properties can be conveniently included in a FEA model within currently available commercial codes such as ANSYS.

High permeability materials are usually used to form the so-called passive magnetic shields. Such high metals and alloys normally saturate at 0.7~0.8 Tesla or even lower. Superconducting

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materials, such as niobium, can also be used as shielding material due to the perfect diamagnetism of the Meissner effect [6-7]. Not many high permeability shield materials maintain their properties at cryogenic temperatures. For example, the Amumetal used to construct CEBAF 1998 Upgrade CM magnetic shield has a dramatically reduced permeability at cryogenic temperature, according to the manufacturer’s measured data sheet [8]. Amuneal, the supplier of Amumetal, has developed a high permeability alloy, named Cryoperm™, that is targeted at cryogenic applications [9]. It is reported in literature [10] that AD-MU-78, akin to AD-MU-80, used in constructing the end can shields in CEBAF 1998 Upgrade CM, has yielded relatively constant shielding factor at low temperature when the applied magnetic field frequency varies lower than 100 Hz. However, going from room temperature to liquid nitrogen temperature, the permeability of AD-MU-80 will decrease [11] by as much a factor as 10. B-H curve data from Amuneal are primarily used in the magnetic shield analyses contained in this report.

Discussions on ANSYS Magnetostatic Analysis Formulations

For conducting static magnetic analysis, ANSYS provides three types of formulations: the magnetic scalar potential (MSP), magnetic vector potential (MVP), and the edge-based formulation. There are a few 2-D and 3-D elements that can be used in modeling. ANSYS Help has extensive introductions of all formulations and applicable elements.

In principle, any of the three formulations can be employed in a magnetostatic analysis. The magnetic shields in this application are immersed in a uniform magnetic field. It is important to find ways to establish such a field in the solution domain. There are at least two methods to achieve this: one approach is to set appropriate boundary conditions and the other approach [12] involves a giant solenoid that creates uniform field in its center. A few sample input files illustrating how to create uniform magnetic field of specified flux density are attached. The codes generating uniform field by setting boundary conditions on nodal degree of freedoms are originated from samples downloaded from ANSYS Customer Portal. The original sample codes had drawbacks. They have been revised and tested by the authors.

A few notes on using ANSYS for magnetic shield analysis:

1. The 3-D MVP formulation element, solid97, is not recommended in a magnetic shield analysis where high permeability gradient exists in the so-called iron-air model. When solid97 is used, according to ANSYS help on this element, “The solution has been found to be inaccurate when the normal component of the vector potential is significant at the interface between elements of different permeability.”

2. The 3-D edge-based formulation element, solid117, is found inconvenient to use in a magnetic shield analysis. Although the sample code 5 (see appendices) provides a way to generate uniform field, one must be cautious of the fact that if both hexahedral and tetrahedral elements exist in the model, the resultant field cannot be uniform both in magnitude and orientation. The undocumented DREC command is flawed and not recommended.

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3. The 3-D infinite element, INFIN111, cannot be used in a 3-D model to create the cuboid boundary that is needed for generating uniform magnetic field. It is mainly due to the peculiar requirement of “only one face of an infinite element may be exposed to infinity”.

4. The magnetic shields are usually thin. It is suggested to control the number of elements, 3 or 4 for example, across the thickness of the shield by mapped meshing so that the field solution inside the high permeability shield is more accurate.

5. Air/vacuum space must be modeled. Since the infinite elements cannot be conveniently applied, the size of the air/vacuum space can be quite large. A convergence study on air/vacuum size versus field results is recommended.

6. A linear model with constant permeability may be used when magnetic flux density is noticeably below the shield material saturation point. Otherwise, nonlinear B-H curve must be used.

Verification of an 2-D Axisymmetric Double-Shell Model

To verify the analysis procedure, a 2-D axisymmetric model of a double-shell magnetic shield layout is analyzed. The model is the same as used by E. Paperno [5]. The axial shielding factors calculated by ANSYS model are compared to those in literature (based on analyses done in Maxwell® 2D) for various scenarios. Figure 1 shows one example comparison. In general, the ANSYS results are in good agreement with literature data.

Fig. 1: Comparison of the axial shielding factors with data in literature

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Axial Shielding Factors from 2-D Axisymmetric Models

Figure 2 shows a simplified magnetic shield configuration for cryomodules. The real shields have more openings on both the inner and outer shields. For shielding factor FEA, a model (Fig. 3) that includes the surrounding air/vacuum space, as well as the space inside the inner shields and between the inner and outer shields, should be used.

Fig. 2: A schematic of cryomodule magnetic shields

To comprehensively investigate the effects of openings on shielding factors, a 3-D model will be necessary. However, a simplified 2-D model, which runs much more efficiently than a 3-D model does, could reveal some facts about the shield design concept. In fact, nonlinear analysis involving B-H curves is more practicable in a 2-D model of the shields.

A 2-D axisymmetric model of the magnetic shields is created and both linear and nonlinear analyses are performed. Figure 4 shows a schematic diagram of the 2-D model. Model size convergence studies are carried out by nonlinear analysis using B-H curves for Amumetal at 300K and constant permeability r = 3,775 for Amumetal at 4K. The purpose is to determine how big should the outskirt air/vacuum space be to reach convergence on shielding factors. Note that for 2-D models, it is possible to use ANSYS’ infinite elements at the outer boundary of the model so that the entire model will not be very big. However, there is great difficulty in using infinite elements in a 3-D model. And 3-D model size study is very costly in the sense of computational resources. Therefore, the 2-D model size study will provide reference information for 3-D model sizes. Figure 5 shows the model sizes versus axial shielding factors. The Do and Lo

dimensions are the outer diameter and length of the outer shield. The D_air and L_air are the outer diameter and overall length of the surrounding air/vacuum space. All shields are assumed to be made of Amumetal.

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Fig. 3: Cryomodule magnetic shields enclosed by/filled with vacuum volumes

Fig. 4: A schematic diagram of the 2-D magnetic shield model

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Fig. 5: Air/vacuum model size convergence study (0.5 Gauss axial field, Amumetal inner and outer shield, B-H curve for outer shield & constant µr for inner shield)

From Fig. 5, it is seen that the convergence of shielding factor commences at case 4. It is also seen that with the 1998 design of using Amumetal for both inner and outer shields, when the axial field is 0.5 Gauss, the axial shielding factors that can be achieved are ranging from 24 to 48. Please note that 2-D model does not account for influence from openings on shields, so actual values will be smaller.

Another finding from the model size analyses is that the magnetic flux density in the inner shields is below 3,000 Gauss. This indicates that constant permeability can be assigned to inner shields without noticeable loss of accuracy. In the outer shield, the linear model presents high magnetic flux density zones that exceed the material’s saturation limit. Nonlinear B-H curves from the manufacturer [13] are used in nonlinear 2-D analyses. Figures 6 and 7 show the B-H curve for Amumetal and Cryoperm 10, respectively. There is no B-H curve for Amumetal at 4K available. It is possibly because that Amumetal is not targeted to be used at cryogenic temperature, instead, Cryoperm 10 [9] shall be used if a high shielding factor at cryogenic temperature is favored.

Compared with Amumetal, Cryoperm has much higher permeabilities at cryogenic temperature. For comparison purpose, the axial shielding factors for Amumetal outer shields and Cryoperm/Amumetal inner shields are listed in Table 1. Please refer to Fig. 4 for the locations of the sampling points. Clearly, Cryoperm can provide much higher shielding factors than Amumetal.

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Fig. 6: B-H curve for Amumetal at room temperature

Fig. 7: B-H curve for Cryoperm 10 at 4.2 K

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Table 1: Axial shielding factors from 2-D nonlinear analyses (0.5 Gauss applied field)Cases Sa_1 Sa_2 Sa_3 Sa_4 Sa_5 Sa_6 Sa_7 Sa_8 Sa_9

Cryoperm Inner Shields 6.8 816 4 529 3 440 2.7 407 2.6

Amumetal Inner Shields 7.4 47.5 5 31 3.8 26 3.4 24 3

There is a concern that the ferromagnetic material existing in some sections of CEBAF tunnel walls may enhance the magnetic field applied on the CM shields. A reasonable estimation of the enhanced axial field intensity is 2 Gauss. To attenuate such a “high” field, Cryoperm 10 is used for inner shields. Figure 8 shows the axial shielding factors inside inner shields from a 2-D model with nonlinear B-H curves assigned to both the inner and outer shields.

Fig. 8: Axial shielding factors inside inner shields by 2-D model (2 Gauss axial field, nonlinear B-H curves for Amumetal outer shield and Cryoperm inner shield)

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The desirable range of cavity surface magnetic field is 5~10 mG. For the 2 Gauss axial field case, this indicates that shielding factor above 200 is needed. Means to further improve the axial shielding factors are investigated. One thought is to increase the shield thicknesses. Some example calculations were conducted and the results are summarized in Table 2. Please refer to Fig. 4 for shield factor sampling position numbering.

Table 2: Axial shielding factors improved by thicker shields (2 Gauss axial field, nonlinear B-H curves for Amumetal outer shield and Cryoperm inner shield)

Outer shield thickness, inch

Inner shield thickness, inch

End can shield thickness, inch Sa_2 Sa_4 Sa_6 Sa_8

0.04 0.02 0.04 387 132 111 1070.04 0.025 0.04 454 145 122 1170.062 0.04 0.062 17,783 298 165 1490.125 0.059 0.125 18,459 3,623 1,353 293

The beam pipe openings’ influence on axial shielding factors can be reduced by bridging cavities with shielding tubes. To simulate this condition, such openings are blocked and the axial shielding factors are calculated. Table 3 lists some sample calculation results for a few optional thicknesses of inner/outer/end can shields.

Table 3: Axial shielding factors improved by bridging cavities (2 Gauss axial field, nonlinear B-H curves for Amumetal outer shield and Cryoperm inner shield)

Outer shield thickness, inch

Inner shield thickness, inch

End can shield thickness, inch Sa_2 Sa_4 Sa_6 Sa_8

0.04 0.02 0.04 407 147 128 1240.04 0.04 0.04 709 207 176 1700.04 0.04 0.059 1001 255 215 2080.062 0.062 0.059 41206 394 235 217

A 2-D axisymmetric model cannot be applied to calculate transverse shielding factors because the field is not axisymmetric. Therefore, a 3-D model needs to be developed to evaluate the transverse shielding factors.

Transverse Shielding Factors from 3-D Models

The 3-D magnetic shield model is based on the 1998 CEBAF upgrade LINAC cryomodule design. Major openings on the shields are maintained in the model. Figure 9 shows the shield model without air/vacuum volumes. For the calculations followed, the shield thicknesses for the outer and end can shields are 0.04". The inner shield thickness is 0.02".

The main purpose of the 3-D model is to evaluate the shielding factors from transverse magnetic field. This is done through a linear analysis with applied transverse field of 2 Gauss. Two cases are studied: 1) assign constant permeability of µr = 70,000 (Cryoperm at 4K) to inner shield and 2) assign permeability of µr = 3,775 (Amumetal at 4K) to the inner shield. The outer shield is assigned a permeability of µr = 60,000 (Amumetal at 300K). Table 4 summarizes the

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transverse shielding factors as calculated. Please refer to Fig. 4 for the numbering of the sampling points.

To verify if the linear analysis is valid for the transverse shielding factor calculations, the flux density in the shields is examined. Figure 10 shows the flux density profile in all shields (case 1, Cryoperm for inner shield). The peak flux density is found to be nearly 0.4 Tesla or 4,000 Gauss. Based on the B-H curves given in Figs. 6 and 7, linear analysis is valid. Therefore, transverse shielding factors in Table 4 are valid.

Fig. 9: 3-D model of the shields excluding air/vacuum volumes

Table 4: Transverse shielding factors from linear analyses (2 Gauss applied field)Cases St_1 St_2 St_3 St_4 St_5 St_6 St_7 St_8 St_9

1: Cryoperm Inner Shields 96 3,971 112 2,673 119 3,806 118 2,694 1032: Amumetal Inner Shields 96 548 108 419 113 526 112 424 99

In the 3-D linear model, when an axial external field of 2 Gauss is applied, it is found that the flux density in the outer shield exceeds the saturation limit of 8,000 Gauss. This indicates that a nonlinear analysis is necessary. In fact, axial shielding factors have been estimated by 2-D

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axisymmetric models. It would be helpful to verify results from the 2-D model by those from 3-D model. However, great difficulty has been encountered while solving the 3-D nonlinear model for axial shielding factors. The program diverges frequently despite the efforts in refining meshes. Among a number of trials, converged solution is attained for the case of Amumetal outer shields and Cryoperm inner shields subjected to 0.5 Gauss axial field. For convenience of comparison, the axial shielding factors from 2-D and 3-D nonlinear models, at 0.5 Guass external field level, are listed in Table 5. It is seen that the 2-D model overestimates the axial shielding factor in the two centering inner shields by a factor of 2.3. The magnetic flux density in shields from 3-D nonlinear model subject to 0.5 Gauss is shown in Fig. 11. It is found that the peak field magnitude did not exceed the saturation limit of Amumetal.

Fig. 10: Magnetic flux density in shields subjected to 2 Gauss transverse magnetic field

Table 5: Axial shielding factors from 2-D & 3-D nonlinear models (0.5 Gauss axial field, Cryoperm inner shields)

Cases Sa_1 Sa_2 Sa_3 Sa_4 Sa_5 Sa_6 Sa_7 Sa_8 Sa_9

2-D Model 6.8 816 4 529 3 440 2.7 407 2.6

3-D Model 9 2458 16 785 6.9 428 2.9 175 2.2

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Fig. 11: Magnetic flux density in shields subjected to 0.5 Gauss axial magnetic field

Concluding Remarks on Shield Analysis

Analytical formulas are good at first-hand estimations of transverse shielding factors for very simple magnetic shield configuration such as an ideal double-shell shield design.

Shielding factors for complex shield layout can be analyzed by finite element modeling. Caution must be taken while choosing the appropriate formulation and element type in ANSYS for magnetic shield analysis.

Axial shielding factors are mainly calculated through a 2-D model applying nonlinear B-H curves for both the inner and outer shields. If the inner shield is made out of Amumetal, which has low permeability at 4K, the lowest axial shielding factor inside the inner shields is around 24 (Fig. 5 and Table 1) when the external field is 0.5 Gauss. If Cryoperm or other shield material that has high permeability at 4K is used to construct the inner shields, the lowest axial shielding factor in inner shields can be above 400 (see Tables 1). However, the 3-D model yielded a much lower minimum axial shielding factor of 175, if Cryoperm is used to construct inner shields. It is thus logical to infer that if Amumetal is used to make all shields, at 0.5 Gauss axial field, the lowest axial shielding factor is less than 10.

Transverse shielding factors are evaluated from a 3-D model with constant permeabilities

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assigned to the inner and outer shields. The 3-D linear model is valid since the peak flux density in shields does not exceed 4,000 Gauss. The transverse shielding factors inside the inner shields are found to be much higher than axial shielding factors (Table 4) no matter the inner shields are made of high permeability (r = 70,000) or low permeability (r = 3,775) material.

Increasing shield thickness and bridging cavities with shield material will enhance the shielding factors. Cost versus performance trade-off shall be the determining factor in design decision making process.

Cavity Surface Magnetic Field on Quality Factor and Design Options

The ultimate goal of the magnetic shield analysis is to provide guidance for the C100 CM shield design. An important performance index of a CM is its quality factor, Qo. The Qo can be conveniently calculated as [1]: Qo = G/Rs. G is the geometry constant. For the low loss cavity [14], G = 281. The Rs, cavity surface resistance, can be divided into contributions from surface magnetic field, termed as RH, and other factors, termed as Rother. The RH can be estimated from the following formula [15]:

Observing these relationships, the influence of cavity surface magnetic field intensity on the CM quality factor can be quantified. The results are plotted as a family of curves corresponding to various levels of Rother, i.e. 5 nΩ, 10 nΩ, 15 nΩ, 20 nΩ, 23.5 nΩ, and 30 nΩ. See Fig. 12 for details. The fundamental frequency used in the calculation is f = 1497 MHz. It is believed that Rother = 23.5 nΩ, the blue curve in Fig. 12, is close to real CM performance. The Qo specification value is 8×109, which is the red line in Fig. 12. The most important conclusion that can be drawn from the curves in Fig. 12 is that the lower the surface magnetic field, the larger the margin above the Qo spec. When Rother = 23.5 nΩ, the maximum allowable Rmag is slightly above 30 mG to meet the Qo specification of 8×109

.

Fabrication cost quotations are collected from Amuneal Manufacturing Corp. and Advance Magnetics Inc. for a few shield design options. The baseline design is to inherit the 1998 Linac CM shield design of using Amumetal for both inner and outer shields. Amuneal is developing a new alloy that has a potential of providing shielding performance similar to Cryoperm’s, but, has lower material cost.

Field surveys [16] of earth magnetic field are conducted in CEBAF tunnel section 1L04 and 1L24. Axial (Z direction) and transverse (X and Y directions) field are measured. It is found that in section 1L04, the peak axial magnetic flux density is 0.4 Gauss (see Fig. 13) and the peak transverse magnetic flux density is 1.1 Gauss (see Fig. 14). These magnetic field data are used to estimate their effects on Qo. A summary of the options is listed in Table 6. The quality factors in Table 6 are calculated by assuming Rother = 23.5 nΩ. The RH used is the resultant of the axial and transverse components of the cavity surface magnetic field. The information provided in Table 6 is for reference in design decision making process. The fabrication cost data may change over time. The quality factors are based on the cavities having the lowest shielding factors.

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Fig. 12 Influence of cavity surface magnetic field on quality factor

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Fig. 13 CEBAF 1L04 cryomodule axial environment magnetic field data

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Fig. 14 CEBAF 1L04 cryomodule transverse environment magnetic field data

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Table 6: Design options for C100 CM magnetic shield

Options Descriptions Vendor

Percentage cost

increase to baseline design

Estimated quality

factor, Qo

Percentage quality factor

increase to baseline design

Axial Shielding

Factor Spec. (Sa)

Cavity 4 axial shielding

factor estimation

(0.5 Guass)

Transverse Shielding

Factor Spec. (St)

Cavity 4 transverse shielding

factor estimation (2 Gauss)

1Baseline design (0.04" outer, 0.02" thk inner, all Amumetal)

Amuneal - 7.35×109 -

100

<10

400

419

2 0.02" thk Cryoperm 10 for inner shield Amuneal 23% 1.15×1010 56% 175 2,673

3 0.02" thk "X" metal for inner shield Amuneal 6% 1.15×1010 56% 175 2,673

4AD-MU-80 outer (0.04") and inner shields (0.02")

Advance Magnetics -27% 7.35×109 0% <10 419

5AD-MU-80 outer (0.04") and "X" metal inner shields (0.02")

Amuneal &

Advance-6% 1.14×1010 56% 175 2,673

Summary and Conclusions:

1. C100 cryomodule magnetic shields transverse and axial shielding factors are analyzed by conducting linear/nonlinear FEA based on 2-D and 3-D models. The transverse shielding factors are generally big and considered sufficient to attenuate fields perpendicular to beam axis. However, the axial shielding factors are much lower than transverse shielding factors because of the beam pipe penetration and other substantial openings on the shields.

2. If Amumetal is used to make the inner shields, the axial shielding factors are found to be insufficient for meeting the quality factor specification of 8×109, especially inside the two centered inner shields.

3. Cryoperm 10 is suggested to be the material for inner shields. There are cost issues associated with Cryoperm 10. If the “X” metal proves to have equivalent permeability to Cryoperm 10, this new material could then be a cost-effective alternative choice to Cryoperm 10.

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4. Due to the convergence difficulties encountered while solving the nonlinear model with Amumetal as inner shield material, the axial shielding factors in Amumetal-for-all shield design are inferred from other calculated shielding factors. Error cannot be eliminated but the inferred shielding factors are informative and conservative.

REFERENCES

[1]. H. Padamsee, J. Knobloch, and T. Hays, “RF Superconductivity for Accelerators,” John Wiley & Sons, Inc., 1998. [2]. S. An, “SNS Cavity Intrinsic Quality Factor Requirements Based on a Cryomodule Magnetic Shielding Calculation”, JLAB-ACC-04-217 & SNS-NOTE-CRYO-120, April 1, 2004.[3]. E. Baum and J. Bork, “Systematic design of magnetic shields,” Journal of Magnetism and Magnetic Materials, 101, 1991, pp. 69-74.[4]. E. Paperno, H. Kiode, and I. Sasada, “A new estimation of the axial shielding factors for multishell cylindrical shields,” Journal of Applied Physics, Vol. 87, No. 9, 2000, pp. 5959-5961.[5]. E. Paperno, S. Peliwal, M. V. Romalis, and A. Plotkin, “Optimum shell separation for closed axial cylindrical magnetic shells,” Jourmal of Applied Physics, 97, 10Q104, 2005.[6]. K. Kamiya, B. A. Warner, M. J. DiPirro, “Magnetic shielding for sensitive detectors,” Cryogenics, 41, 2001, pp. 401-405.[7]. M. Johnson, J. Bierwagen, S. Bricker, C. Compton, P. Glennon, T. L. Grimm, W. Hartung, D. Harvell, A. Moblo, J. Popielarski, L. Saxton, R. C. York, A. Zeller, “Cryomodule Design for a Superconducting LINAC with Quarter-wave, Half-wave and Focusing Elements,” in Proceedings of 2005 Particle Accelerator Conference, Knoxville, TN, 2005, pp. 4317-4319. [8]. http://www.amuneal.com/pages/pdf/AmunealDataSheet2.pdf[9]. L. Maltin, “Amuneal’s Cryoperm™ Magnetic Shielding,” Cold Facts, Vol. 20, No. 5, December 2004, pp. 50-56. [10]. R. F. Arentz, M. H. Johnson, and L. Dant, “Magnetic Shielding in a Cryogenic Environment,” Evaluation Engineering, 25(1986), pp. 80.[11]. G. H. Luo, L. H. Chang, C. T. Chen, F. Z. Hsiao, C. C. Kuo, M. C. Lin, Ch. Wang, T. T. Yang, M. S. Yeh, and M. Pekeler, “Testing Results of Major Components and Progress Report of TLS Superconducting Cavity Project,” in Proceedings of EPAC 2002, Paris, France, pp. 2262-2264.[12]. Private communications with M. Yaksh, NAC International Inc.

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http://www.amuneal.com/pages/pdf/AmunealDataSheet2.pdf


[13]. Data provided by L. Maltin, Amuneal Manufacturing Corporation, Philadelphia, PA.[14]. C. Reece, “SRF Cavity Cell Geometry Options for the 12GeV Upgrade,” JLAB-TN-05-009.[15]. Private communication with Jacek Sekutowicz, DESY, German. [16]. Field surveys performed by Michael Drury et al. at CEBAF tunnel.

APPENDICES

Sample Code 1: Create Uniform Magnetic Field in a 2-D Model by Restraining DOFs

fini/cle

/title,UNIFORM B FIELD USING THE 2-D MVP

C*** DIMENSIONSxmin=0.0 !do not changexmax=0.59ymin=0.14ymax=0.94esz=0.1

C*** DESIRED VALUE OF B FIELDB_uniform=2

C*** GEOMETRY/prep7rect,xmin,xmax,ymin,ymax

C*** ATTRIBUTESet,1,53,,,1 !axisymmetry onmp,murx,1,1

C*** MESHesize,eszames,all

C*** BC's => UNIFORM B

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!Apply field along Y+lsel,s,loc,x,xmindl,all,,az,0lsel,s,loc,x,xmaxdl,all,,az,B_uniform*(xmax-xmin)/2fini

/soluallssolvfini

/post1plve,b,,,,vect,,on

Sample code 2: Create Uniform Magnetic Field in a 2-D Model by Coil with Current Density

fini/cle

/title,UNIFORM B FIELD USING THE 2-D MVP

pi = acos(-1)

C*** DIMENSIONSxmin = 0.0 !do not changexmax=0.838ymin=-0.42ymax=0.98t_coil = 0.034 !thickness of coilesz=0.0573

C*** DESIRED VALUE OF B FIELDB_uniform=2e-3 !Tesla

C*** GEOMETRY

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/prep7rect,xmin,xmax,ymin,ymaxlgen,2,2,,,t_coilA,2,3,6,5lgen,2,5,,,t_coilA,5,6,8,7

C*** ATTRIBUTESet,1,53,,,1mp,murx,1,1iamp = B_uniform*1e7/(4*pi)/t_coil

C*** MESHmshk,2 $msha,0esize,eszames,1mshk,0 $msha,1esize,esz/2ames,2,3fini

/soluasel,s,,,3eslabfe,all,js,,,,iamp,0allssolvfini

/post1set,lastasel,s,,,1,2eslansleplvect,b,,,,vect,node,on

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Sample code 3: Create Uniform Magnetic Field in a 3-D Model by MSP Formulation and Restraining DOFs

fini/cle/vie,1,1,2,3/esha,1

/title,UNIFORM B FIELD USING THE 3-D MSP

C*** DIMENSIONSlen = 0.83xmin=-lenxmax=lenymin=-lenymax=lenzmin=-lenzmax=lenesz=0.1

C*** DESIRED VALUE OF B FIELDB_uniform=2pi=acos(-1)mu0=pi*4e-7MSP=-B_uniform*(ymax-ymin)/mu0

C*** GEOMETRY/prep7bloc,xmin,xmax,ymin,ymax,zmin,zmax

C*** ATTRIBUTESet,1,96mp,murx,1,1

C*** MESH BLOCKtype,1real,1

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esiz,eszvmes,all

C*** BC's => UNIFORM Bcsysasel,s,loc,y,yminda,all,magasel,s,loc,y,ymaxda,all,mag,MSPfini

/soluallseplosolvfini

/post1esel,s,type,,1nsleplve,b,,,,vect,,on

Sample code 4: Create Uniform Magnetic Field in a 3-D Model by MSP Formulation and Source Coil

/out,coil-msp,out fini /nerr,0,1e5 /cle

/prep7 /vie,1,1,2,3 /esha,1 mname='case2' /title,UNIFORM B FIELD USING THE 3-D MSP C*** DIMENSIONS

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len = 3.86 !m, =152 inchesrad = 0.80 !m, >30 inchesxmin=-radxmax=radymin=-rad ymax=rad zmin = -lenzmax= lenesz=0.2

C*** DESIRED VALUE OF B FIELD B_uniform=2e-4 !Teslapi=acos(-1) mu0=pi*4e-7

coilr=100coilz=100000coilthk=0.1 !has very little effect on final Binamp=-B_uniform*1e12/(4*pi) !negative Z direction mag field

C*** GEOMETRY /prep7

cylind,0,xmax,zmin,zmax,0,360lcomb,1,2lcomb,3,4lcomb,5,6lcomb,7,8

C*** ATTRIBUTES et,1,96 mp,murx,1,1 et,2,36 et,3,mesh200,7

!create the coil as current sourcer,2,1,inamp,coilthk,coilz,

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n,1,coilr,0,0n,2,0,coilr,0 n,3type,2 real,2 e,1,2,3 /eshap,1 eplo C*** MESH BLOCK type,3mshk,2msha,0esize,eszamesh,2

type,1real,1esiz,eszextopt,esize,2*eszvsweep,1

esel,,type,,1 nsle nsel,u,loc,z,zmin+.00001,zmax-.00001 d,all,mag alls

fini

C*** SOLVE /solu alls eplo *get,_cpu1,active,,time,cpu magsolv,2,,,,,1 fini *get,_cpu2,active,,time,cpu

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a_scpu=_cpu2-_cpu1

C*** POSTPROCESS /post1 esel,s,type,,1 nsle /title,%mname% plns,b,z

path,zvar,2,,100 ppath,1,,0,0,zmin ppath,2,,0,0,zmax pdef,bz_z,b,z plpa,bz_z

path,xvar,2,,100 ppath,1,,xmin,0,0 ppath,2,,xmax,0,0 pdef,bz_x,b,z plpa,bz_x

/vie,1,1,2,3 /esha,1 /out

Sample code 5: Create Uniform Magnetic Field in a 3-D Model by Edge-based Formulation and Restraining DOFs

fini/cle/vie,1,1,2,3/esha,1

/title,UNIFORM B FIELD USING THE 3-D EDGE POTENTIAL

C*** DIMENSIONSlen = 0.95

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xmin=-lenxmax=lenymin=-lenymax=lenzmin=-lenzmax=lenesz=0.1

C*** DESIRED VALUE OF B FIELDB_uniform=2

C*** GEOMETRY/prep7bloc,xmin,xmax,ymin,ymax,zmin,zmax

C*** ATTRIBUTESet,1,117et,2,mesh200,7mp,murx,1,1et,36,36 ! WILL NOT RUN UNLESS SOURC36 IS DEFINED

C*** MESH BLOCKtype,2mshk,2msha,0esize,eszamesh,2type,1real,1esiz,eszextopt,esize,2*eszvmes,all !CANNOT have both hexahedral and tetrahedral elements in the model

C*** UNDOCUMENTED DREC TO CREATE UNIFORM B FIELDC***type "drec,help" in ANSYS command window, you'll get the following secret recipecsysalls

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drec,dele,1drec,defi,1,node(xmin,ymin,zmin),node(xmin,ymin,zmax),node(xmin,ymax,zmin),B_uniform*(zmax-zmin) asel,s,loc,z,zminasel,a,loc,x,xmaxasel,a,loc,z,zmaxda,all,azfini

/soluallseplosolvfini

/post1esel,s,type,,1nsleplve,b,,,,vect,,on

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c100 cryomodule end can pipeline design per asme b31tnweb.jlab.org/tn/2008/08-015.doc · web...

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