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Electro-thermal FEM simulations of the 13 kA LHC joints
Cryogenics 53 (2013) 119–127
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Electro-thermal FEM simulations of the 13 kA LHC joints D. Molnar ⇑, A.P. Verweij, E.R. Bielert CERN, CH-1211 Geneve 23, Switzerland
a r t i c l e
i n f o
Article history: Available online 23 April 2012 Keywords: LHC 13 kA Joint FEM analysis Safe operation Shunt Electro-thermal
a b s t r a c t The interconnections between the superconducting main dipole and main quadrupole magnets are made of soldered joints of two superconducting Nb–Ti cables embedded in a copper busbar stabilizer. The primary cause of the September 2008 incident in the LHC was a defect in an interconnection between two dipole magnets. Analyses of the incident show that possibly more defects might be present in the 13 kA circuits, which can lead to unprotected resistive transitions. To avoid the reoccurrence of such an event, thorough experimental and numerical investigations have taken place to determine the safe operating conditions of the LHC. However to show measured curves is beyond the scope of this article. Furthermore, improvements in the design have been proposed in the form of additional parallel copper pieces, or shunts, which bridge the possible voids in the soldering and offer a bypass for the current in case of a quench. The purpose of this work is to support the design choices and to indicate the sensitivity to some of the free parameters in the design. Electro-thermal Finite Element Method (FEM) simulations are performed, making use of COMSOL Multiphysics. The use of FEM allows for a profound three-dimensional analysis and some interesting features of the shunted busbar can only be revealed this way. Especially current redistribution in the shunted area of the interconnect gives important insights in the problem. The results obtained using the model are very sensitive to the exact geometrical properties as well as to the material properties, which drive the Joule heating inside the interconnection. Differences as compared to a onedimensional model, QP3, are presented. QP3 is also used for simulations of non-shunted busbar joints as well as shunted busbars. Furthermore, margins are given for the soldering process and the quality control of the shunted interconnections, since the contact area between the stabilizer pieces and the shunt is an important quality aspect during the manufacturing of a safe interconnection. Ó 2012 Published by Elsevier Ltd.
1. Introduction The main dipole and quadrupole magnets in each of the eight sectors of the LHC are powered in series (see Fig. 1 for a schematic layout of the dipole circuit) [1]. Each magnet is individually protected by a quench detection system (QDS), and quench-heaters spreading the resistive transitions over the volume of the magnet coils. The parallel-connected diode over a magnet acts as a current bypass during the fast current discharge. This discharge has a time constant sRB of about 100 s for the dipole circuit and a time constant sRQ of about 30 s for the quadrupole circuits. The diodes however do not encompass the sections of the superconducting (SC) busbars between the magnets nor the interconnections. Their protection is based on heavy stabilization by soldered copper which, in case of a quench of the cable, would bypass the current and conduct the heat away. On 19 September 2008, during powering tests ⇑ Corresponding author. Address: 1192 Hu, Budapest, Garay koz 12, Hungary. Tel.: +36 304851792. E-mail addresses: [email protected], [email protected] (D. Molnar), [email protected] (A.P. Verweij), [email protected] (E.R. Bielert). 0011-2275/$ - see front matter Ó 2012 Published by Elsevier Ltd. http://dx.doi.org/10.1016/j.cryogenics.2012.03.008
of the main dipole circuit in sector 3–4 of the LHC, an electrical fault occurred in the 13 kA busbar. An electrical arc was produced and resulted in mechanical and electrical damage, release of helium from the magnet cold mass and contamination of the insulation and beam vacuum enclosures [2]. The most likely cause of the accident was a badly soldered joint, with large resistance between the two superconducting cables and a lack of continuity of the copper stabilizer. These joints consist of two superconducting Nb–Ti Rutherford type cables (LHC type 02 [1]), which are embedded in a copper busbar stabilizer [3,4], see Fig. 2. About 10,000 13 kA joints are present in the LHC. Since the September 2008 incident, the stability of the busbar interconnections has been thoroughly reassessed. In the LHC tunnel, quality control measurements revealed the presence of joints with unexpectedly high resistances. Imaging techniques were used to look into the structure of the joints and showed that voids were present between the superconducting cable and the copper stabilizer [5,6]. Also the continuity of the stabilizer itself was not always guaranteed, so that even in the case of a quench the current has to flow through the cable over several millimeters [7]. In such a defective joint the local Joule heating after a quench
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busbar
51mH 51mH B1
busbar joint
B2
B1
Dipole 1
busbar
51mH 51mH B1
51mH 51mH B2
Dipole 3
busbar joint
B2
Dipole 2
51mH 51mH B1
B2
Dipole 4
51mH 51mH B1
busbar
B2
Dipole 153
51mH 51mH B1
busbar
B2
Dipole 154
Fig. 1. The schematic of one of the eight main dipole circuits in the LHC.
results in excessive high temperatures, causing the solder to melt. Eventually the busbar may evaporate, similar to what happened in September 2008. The stability of the joint thus directly influences the maximum allowable operating current and therefore the collision energy of the LHC [8]. Following the considerations about the joint stability, the LHC is presently exploited at half of the nominal beam energy, i.e. 3.5 TeV. To be able to safely operate the LHC at full energy (7 TeV) consolidation actions are required [9]. This mainly involves the soldering of an additional copper stabilizer piece, or shunt, to the existing copper elements. The detailed layouts of the busbar and the shunted and non-shunted joints are given in Section 2. The safe operation thus strongly depends on the quality of the stabilizer pieces of the busbars, which have to carry all the current in the circuit. The safe current is defined as the current that limits the peak temperature in the bus to below 300 K for all operating conditions. This is a conservative definition, since the melting point of the tin silver (SnAg) solder is 494 K. Furthermore we consider conservative values for the RRRs (see Table 2), and we disregard possible cooling to the surrounding helium (adiabatic approach) [10]. In this paper, we describe the implementation of localized fast thermal runaways (see [7]) in a 3D COMSOL Multiphysics model. Section 2 reports on the design of the joints. The situations with and without a shunt are discussed here. In Section 3, the physics and the governing equations are introduced. The differences be-
tween the 1D and 3D implementation of the problem are discussed in Section 4. In Section 5 we explain how the geometries are implemented in the model, and we report on the used material properties, the used boundary – and initial conditions and on the implemented mesh. In Section 6 we present the results on simulations performed for a joint without shunt. The results are also compared to results obtained from the other codes as mentioned before. Results for the shunted busbar joints are given in Section 7. Shunted joints can intrinsically only be properly simulated with a 3D model since current redistribution plays a key role in this more complex geometry. These simulations are therefore not compared to results obtained by means of 1D models. The safe current as a function of the most important shunt design parameters is reported in this section. The main quality aspect of a shunt concerns the homogeneity and quality of the soldered connection. In Section 7 we discuss the effect of a partially soldered shunt.
2. Overview of designs The superconducting cables, busbar stabilizer, copper U-profile and copper wedge are soldered together using tin-silver (SnAg) solder (see Fig. 2). All the areas where the tin-silver should be present in order to assure a good thermal and electrical contact between the Rutherford cables and the copper stabilizer parts, are at the same time possible areas for voids, in case the soldering procedure was not successful [7]. In Fig. 4 we can see a possible worst case configuration of voids, when there is no solder at all between the stabilizer elements, while at the same time the superconducting cable is not stabilized (i.e. not soldered to copper parts) for a certain length, denoted as lNS. The precise dimensions of the pieces and their material properties are very important for the numerical models, since the stability is very sensitive to these input parameters. Table 1 summarizes the cross sectional areas of the copper stabilizer, the Nb–Ti superconducting Rutherford cable and the tin-silver solder in the busbar for
Table 1 The cross-sections of different materials in a joint in mm2.
Fig. 2. Layout of a LHC 13 kA joint between two superconducting Rutherford cables.
Copper including matrix Nb–Ti SnAg
RB bus
RB joint
RQ bus
RQ joint
281.3 6.5 26.8
291.8 13 9.8
161.3 6.5 26.8
171.8 13 9.8
D. Molnar et al. / Cryogenics 53 (2013) 119–127
16mm
Note that the electrical conductivity is a function of temperature. The coupling of the electro-dynamic and thermal models thus occurs naturally via temperature dependent material properties. The thermal problem is described by the following partial differential equation, the heat equation:
10mm
20mm
20mm
qm ðP; TÞC p ðB; TÞ
Fig. 3. The schematic of the cross section of the RB joint (left) and the RQ joint (right).
the RB and RQ circuits. Fig. 3 shows schematically the cross-sections of the RB and RQ joints. The smaller cross-section of the copper stabilizer in the RQ busbars are due to the smaller time constant of the circuit, resulting in much less dissipated energy during the current discharge. Note that the busbars of other circuits are positioned on top of the quadrupole busbars, hence making it practically impossible to solder a shunt on top of the RQ joints. Another important parameter is the RRR of the different copper parts, including the copper matrix of the superconducting cable. Since in the machine RRR values between 200 and 300 were measured [11], the RRR values were used for the analysis are conservative and are summarized in Table 2. The coordinate axes are shown in Fig. 4, where the origin (x = 0, y = 0, z = 0) is fixed in the middle of the joint. The only difference between the non-shunted and the shunted design is the presence of additional shunts which are soldered with SnPb to the stabilizer pieces. The shunts for the RB and RQ lines are identical. Four shunts will be soldered on a dipole joint, while there will be only two shunts on the quadrupole joint because there is no possibility to solder an upper shunt due to the presence of other busbar lines (see Fig. 3). Figs. 5 and 6 show the configurations of the shunted joints for the RB and RQ respectively. The shunt is 50 mm long, 15 mm wide and 3 mm thick. Each joint has two holes with a diameter of 7 mm, which are used to facilitate the soldering process.
3. Physics and governing equations The electro-thermal behavior of a joint can, in good approximation be described by coupling an electro-dynamic model with a heat transfer model. Taking Maxwell’s equations as a starting point for the electro-dynamic problem, one can express the electrical field E as the gradient of a scalar potential V (Eq. (2)), since the curl of the electrical field equals zero when no varying magnetic fields are present:
r E ¼ 0; E ¼ rV:
ð1Þ ð2Þ
Furthermore, current density J and electrical field E are linearly related by the electrical conductivity r via Ohm’s law:
J ¼ rðTÞE:
ð3Þ
Table 2 The assumed conservative RRR values of the copper pieces.
RRR RRR RRR RRR RRR
of of of of of
copper matrix bus stabilizer U-profile wedge shunt
121
RB
RQ
80 200 200 200 200
80 200 200 200 200
@T r ðkðB; P; TÞrTÞ ¼ Q ; @t
ð4Þ
qm(P, T) is the mass density in kg m3, which is a function of pressure P (in Pa) and temperature T (in K). Cp(B, T) is the specific heat at constant pressure in J kg1 K1, which is a function of the magnetic field B and temperature. t is time in s. k is the thermal conductivity in W m1 K1 which is a function of magnetic field, pressure and temperature. The right-hand side of the equation represents the heat source in W m3. Joule heating is assumed to be the only heat source, which gives the possibility to couple the two models also via the source term in the heat equation by the following relation: Q ¼ J E ¼ rjrVj2 :
ð5Þ
The obtained coupled system is strongly non-linear since the material properties depend strongly on the temperature and vice versa. Because of the very non-linear nature of the problem, numerical methods are needed to solve these equations. In this article a commercial tool Comsol 4.1 [12] was used. Comparison to another computer code, QP3 [13] is given for a particular case. 4. 3D and 1D implementations The bus including a (defective) non-shunted joint can be approximated by a 1 dimensional model, but for the correct analysis of the shunted busbars one needs a 3D implementation. The main advantage of a 3D model is the possibility to analyze the shunt and the current redistribution into it, which cannot be directly modeled in 1D. Furthermore, 3D modeling makes it possible to calculate the effect of partial soldering of the shunt or the presence of (small) contacts between different parts of the stabilizer, so the current could take parallel paths as indicated by the red1 arrows in Fig. 7. The main difference in the implemented geometry between 1D and the 3D models is explained in Fig. 8. The slightly different geometry can however lead to quite different results for the safe operating current of the joint, since the stability is very sensitive to especially the length of the non-stabilized cable. 1D models neglect the existence of the copper stabilizer along the non-stabilized cable, whereas in the 3D model the copper stabilizer is still present. No current is flowing in this part and therefore the simplification of the 1D model is allowed for the electro-dynamical part of the problem. However, from a thermal point of view both models are not exactly the same. The small volume of copper which is neglected in the 1D models has a finite heat capacity and therefore, the 3D model should return a slightly higher safe operating current. The second and more important difference between a 1D and a 3D model is indicated at the bottom of Fig. 8, and is related to the current redistribution inside the stabilizer just before the non-stabilized part of the cable. The 1D models assume that the current is homogeneously distributed over the full cross-sectional area of the copper stabilizer all the way up to the non-stabilized cable. The gap size is thus defined as the length of the non-stabilized cable. In the 3D model, current redistribution occurs and therefore the current is not homogeneously distributed over the full cross-sectional area in the last few mm before the non-stabilized part of the cable. The 1 For interpretation of color in Figs. 1–14, the reader is referred to the web version of this article.
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Y
Z
X
Stabilized cable
wedge BUS
BUS U-profile
Y
Non stabilized cable Z
15mm
Z=0
Z=60mm
Z=75mm
Fig. 4. Definition of the coordinate system and layout of the joint.
Top shunt
50mm
50mm
Holes wedge
BUS
BUS U-profile
Bottom shunt
Y Z
15mm
15mm
Fig. 5. Configuration of the shunted joint for the dipole busbar, notice that the non-stabilized cable (l = 15 mm) is assumed to have infinite resistance in case of a conservative approach.
50mm
50mm wedge
BUS
BUS U-profile
Bottom shunt
Y
Holes 15mm
Z
15mm
Fig. 6. Configuration of the shunted joint for the quadrupole busbar, notice that the non-stabilized cable (l = 15 mm) is assumed to have infinite resistance in case of a conservative analysis.
BUS
wedge
length elongated by the area of current redistribution. So far, the mentioned 1D models do not take into consideration this behavior, while in the 3D model, it is clearly present. Of course, current distribution effects are even more pronounced for shunted joints.
5. Modeling
BUS U-profile Partially soldered pieces Fig. 7. The partially soldered joint case.
physical gap size is the same, but, the effective gap size is slightly larger. The 3D model should give therefore a lower safe operating current, since the effective gap length equals the physical gap
One of the advantages of using a 3D COMSOL Multiphysics model is that the geometry of the model can be checked visually before any physics is introduced. Different subdomains can be introduced in a natural way. The various subdomains are provided with the correct material properties and boundary conditions afterwards. A detailed treatment of the implementation of a nonshunted joint can be found in [14]. The model described in that work has since been updated to a new version of COMSOL Multiphysics (version 4.1 versus 3.5a) and includes different types of shunts. The total simulated length of the model is 1.5 m from the
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at one end of the busbar (z = 1.5 m) a current density is applied and at the other end (z = 0 m) the electrical potential is set to zero. 5.2. Initial conditions The initial condition for the thermal problem is a homogeneous temperature of 10 K over the complete sample. In other words, since the superconducting material is Nb–Ti, a normal zone over the complete length has been initiated and iterations start from a quenched state. The cause of the quench or the propagation of the normal zone is not important for this analysis. This assumption again represents the worst case scenario. Since adiabatic thermal boundaries are considered, the cable will not recover its superconducting state. The voltage is calculated automatically in the first time-step by Comsol from the resistivity and the boundary conditions. 5.3. Material properties As becomes clear from the partial differential equations introduced in Section 3, the important material properties are the mass density, the specific heat, the thermal conductivity, and the electrical resistivity. The temperature and magnetic field dependence are taken into account. For copper, the fits by NIST are used, which include the temperature dependence and the RRR [15]. The magnetoresistivity is included by assuming uniform magnetic field. Furthermore, the method of volume averaging [16] is used to obtain effective properties for the cable, which consists of Nb-Ti filaments in a copper matrix in a ratio of 1:1.95 [1]. The properties of the different solders are not well known [17], but the same input is used in simulations performed with QP3 and COMSOL Multiphysics. 5.4. Mesh
Fig. 8. (Top) Physical situation in the non-shunted joint. (Middle) Simplification of 1D models neglecting some small parts of stabilizer which carry no current. (Bottom) current redistribution as present in the 3D simulations. 1D models should include a transition area, to capture this physical behavior.
middle of the joint, such that end effects in the busbar do not influence the result. In order to solve the partial differential equations introduced in Section 3, correct boundary conditions at all the interfaces between subdomains (contact resistances) and outer boundaries need to be given. Also the initial values of the dependent variables (temperature and electric potential or voltage) need to be set.
5.1. Boundary conditions From a safety point of view and a robust design, worst case thermal boundary conditions are implemented in the form of adiabatic walls. Furthermore, no thermal boundary resistance is assumed between the various parts of the joints. In this work only adiabatic conditions are applied. There are three different electro-dynamic boundary conditions implemented. Over the surface around the complete sample electrical insulation is applied (i.e. current conservation). Furthermore,
The mesh has a strong influence on both the solution and the computational time of the problem. The optimum balance between precision of the solution and used CPU time has resulted in a mapped mesh over the busbar end, consisting of 50 elements, which is extruded along the length of the busbar. To be able to use these brick shaped (hexahedral) mesh elements, the real geometry has to be simplified. The real geometry has rounded corners, while the model has ninety degree angles. The cross-sectional area of the model, however, corresponds to the real cross-sectional area of the busbar (see Table 1). Close to the discontinuity in the copper stabilizer, the length of the elements is 0.5 mm, while further away from this discontinuity the elements have a length of 10 mm. A linear shape function is used to interpolate the solution over the elements. The use of a minimum allowed number of mesh elements as well as the smallest order of the interpolation function are verified and little gain in the precision of the solution is obtained if either of them is increased. 6. Simulations of non-shunted joints The most interesting results from the non-shunted situation can be summarized in a graph relating the safe operating current to the physical non-stabilized length or gap length lNS (i.e. the non-soldered length of cable where there is no thermal and electrical contact between the cable and the stabilizer pieces). The gap starts at the discontinuity between the copper wedge and the busbar stabilizing copper, see Fig. 4. Using the boundary conditions mentioned before, the results are shown in Figs. 9 and 10. As was explained in Fig. 8 the relative thickness of the copper stabilizer compared to the cable has a strong influence on the effective gap length. For the RB bus this results in a difference of about 2 mm between
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er than the experimentally obtained results [21] furthermore the QP3 code has been validated thoroughly. A possible upgrade involves the parallel computation of the self-field and the application of a possible background field. The influence of the magneto-resistivity on the current re-distribution can then be investigated as well. As these curves indicate, safe operation at ultimate operating current of 13 kA is guaranteed if lNS is less than 4 mm for the RB and less than 8 mm for the RQ. It is important to point out that these values are calculated for rather conservative RRR values and disregarding possible cooling to helium. Also note that for lNS = 15 mm the dipole and quadrupole joints are capable to carry 8 kA and 9 kA respectively. This is important because the calculations on shunted joints assume this length of non-stabilized cable.
16000
Sa afe curre ent [A]
14000 12000 QP3 RB non shunted
10000 8000 Comsol RB non shunted
6000 4000 0
10 20 30 Non stabilized lenght of cable [mm]
40
Fig. 9. Safe operating current as a function of gap size for the RB interconnection for a current decay time constant of 100 s.
17000 15000
Safe current [A]
13000 QP3 RQ non shunted
11000 9000 7000
Comso RQ non shunted
5000 0
10
20
30
40
Non stabilized length of cable [mm] Fig. 10. Safe operating current as a function of gap size for the RQ interconnection for a current decay time constant of 30 s.
the 3D and 1D model and for the RQ which is much thinner it is much less, since the thickness of the stabilizer is about the same order of thickness as the cable itself. When cooling to liquid helium is introduced, the curves in Figs. 9 and 10 shift upward, allowing a higher operating current. Simulations similar to the ones discussed here were performed with another one-dimensional code [18]. These simulations take into consideration cooling to the helium bath as well [19]. Important input parameters such as RRR and maximum allowed temperature are however different, such that direct comparison of the results is not possible and therefore not mentioned here. A comparison between QP3 and Comsol is however possible, since the authors used both codes. Differences between these two models are due to the assumption of uniform current distribution over the cross-section of the bus in the 1D model, giving a slightly larger safe current. This effect becomes relatively larger for smaller physical length of the non-stabilized cable. For the RQ joint the effect is less present because of the shorter current decay time constant. The coupled electro-dynamic and thermal behavior of the non-shunted joint have been tested at several applied fields [20]. Comparisons with this experimentally obtained data are only possible when cooling is implemented in the model. The presented COMSOL Multiphysics model is already capable of performing such simulations [14]. However, here we discuss only the worst case, adiabatic conditions. The calculated safe operating currents with adiabatic case are systematically low-
7. Simulations of shunted joints In this section the safe operational current for various shunt designs is reported. The influence of a partly soldered shunt is analyzed, where the percentage of soldered area is important for quality control. The results presented here assume that the shunt needs to carry the full current of the circuit during a discharge and that the non-stabilized cable carries no current. Figs. 5 and 6 give an overview of the analyzed geometry, while Fig. 11 shows the details for a shunted joint, especially regarding the definition of the uniformity of the SnPb solder. The defect length is defined as the length of solder which is lacking over the complete width of the shunt. Also underneath the soldering holes, there is no contact between the shunt and the stabilizer part. This assumption is realistic since, according to experiments, the quality of the solder underneath the holes is very low compared to other parts. In principle the shunted joint can only be analyzed using a 3D code. However, coupled parallel 1D models (1.5D) can solve the problem as well. Additional features have been added to QP3 to allow its use for the shunted case too [13]. The shunt itself needs to be soldered to the existing interconnections of the LHC. During this process, unsoldering of the existing SnAg solder inside the joint should be avoided. This is achieved by using a soldering material with a lower melting point. It has been decided to use SnPb, which has a melting point of 461 K which is small enough as compared to the melting temperature of SnAg (494 K). Because the soldering process is a critical step in the repair of the joints, the quality of this new soldering layer needs to be assured. The main goals of this work are to define the dimensions and properties of the shunt, but also to give margins for the soldering process as well as for the quality control of the shunted joints. In Fig. 12, the safe operating current as a function of the defect length of the solder is shown for both the RB and RQ circuits. The defect length is defined as the length over which solder is lacking over the complete width of the shunt, compared to the nominal design. This means that the void of SnPb is symmetrical with respect to the void between the bus and the wedge (for the top shunt) or between the bus and the U-profile (for the bottom shunt), see Fig. 11. This configuration represents the worst possible situation, since all the current is bypassed via the shunt. Defects in the soldering of the top shunt give a less stable configuration as defects in the soldering of the bottom shunt. This is mainly caused by the intrinsically smaller total contact area between the top shunt and the wedge as compared to the total contact area between the bottom shunt and the U-profile. Therefore the top shunt was analyzed as a worst scenario for the RB joints. Since there is no possibility for a top shunt for quadrupole joints (see Section 2 and Fig. 3) the bottom shunt is only considered. Note that these results represent a configuration with a non-stabilized
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SnPb
Voids in SnPb solder
BUS
lSnPb defect
Top shunt
wedge
BUS U-profile
Bottom shunt
Voids in SnPb solder
SnPb
Fig. 11. Schematic overview of the shunted joint.
Safe operating current [A]
19000 18000
RQ bottom shunt
17000 16000 15000 RB top shunt
14000 13000 12000 0
5
10
15
20
25
Defect length of SnPB [mm] Fig. 12. The safe operating current as a function of the defect length of the shunt solder.
length of the cable being equal to 15 mm on both sides of the joint. The shunt is present on both sides of the joint as well, therefore a completely symmetrical geometry relative to the center of the joint is analyzed. The kinks in the RQ curve are caused by a sudden increase in effective defect length when the defect length of the SnPb reaches the hole (see Fig. 11). The quadrupole joints have a much larger margin, which is obvious because of the decay time constant of the RQ circuit is much smaller than for the RB circuit, while the dimensions of the RB and RQ shunts are identical. For safe operation at ultimate current the maximum allowed defect length of SnPb soldering layer is 14 mm for the RB while it is 24 mm for the RQ. Optimization possibilities include the variation of the length of the shunt and the diameter of the solder reservoir holes. However simulations showed that the proposed 50 mm length of the shunt is sufficient, since there is no gain in safe operating current by elongating the shunt. The bottleneck in the coupled electro-thermal problem is the non-soldered length of the shunt. A qualitative proof for this is shown in Fig. 13, where the y-component of the current density is plotted as a function of the length of the shunt for an RB top shunt with lsold-def = 10 mm. A schematic configura-
tion of the shunt and voids of the SnPb soldering layer (including the holes) is shown as well. The horizontal line crossing the shunt represents the line where the current density component was evaluated, i.e. in the middle of the shunt. When the stabilizer is interrupted by a void, the current which was still flowing in the stabilizer is also forced into the shunt. Therefore, the vertical component of the current density shows two peaks: one at the start of the shunt and one at the void of the stabilizer. In the bridging part of the shunt, the current distribution is homogeneous, so the vertical component of the current density equals zero. Of course, also at the position of the holes the y-component of the current is zero. The influence of the diameter of the soldering reservoir holes is rather limited. Simulations show that a smaller hole, and thus a larger contact surface, allows slightly higher safe operational currents. However, reducing the size of the holes gives practical difficulties during the soldering, since it may jeopardize the quality of the rest of the contact surface. The last part of the analysis considers possibilities for redundant shunts for the RQ circuit. As mentioned before (see Fig. 3), the RQ joint has limited access from the top, since the 600 A busbars are located there. Therefore the only possible position for an additional shunt is on the side of the copper stabilizer parts. Two possible designs are shown in Fig. 14: ‘‘type_a (bridge)’’, with limited contact surface, and ‘‘type_b’’. Several calculations are performed varying the geometry of the shunts. The width of the bridge shunt was fixed to 8 mm, while the type_b shunt’s all parameters are varied. The results are summarized in Tables 3 and 4. In these analyses, the SnPb soldering layer is assumed to be perfect with no voids in it. The results show that the safe operational current of 13 kA can be attained. However, implementation of such shunt in parallel with the main bottom shunt turns out to be very difficult in practice. Furthermore, proper quality control will be difficult. Also for the shunted joint, experiments have been carried out [21]. One of the most important results of these tests is that under certain operational conditions, the busbar which is embedded in a longitudinal slot in the iron yoke is less stable than the shunted joint.
8. Conclusion We have shown how the thermo-electrical behavior of a superconducting 13 kA busbar joint, with and without additional shunts, is implemented in a 3D FEM model. The numerically obtained re-
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Void of
hole
hole
SnPb
Fig. 13. Current redistribution from the stabilizer into the shunt and from the shunt into the stabilizer.
Fig. 14. Photographs and schematics of the side shunts for the RQ circuit (top) ‘‘type_a, (bridge)’’, (bottom) ‘‘type_b’’.
Table 3 Results for the ‘‘bridge type’’.
Table 4 Results ‘‘type_b’’ side shunt.
zl (mm)
zm (mm)
zr (mm)
x (mm)
Safe current (A)
4 8 7 8 4
6 6 6 6 6
4 4 7 8 4
3 3 3 3 10
10,500 11,600 12,500 12,900 13,000
sults are validated by comparison to other numerical codes, where a good agreement is found. The 3D model is an important tool for the understanding of the stability behavior of the joints, especially
x (mm)
y (mm)
zb (mm)
zj (mm)
Safe current (A)
3 4 3 3 3 3
6 6 7 6 6 6
4 4 4 8 8 8
4 4 4 4 20 25
10,000 11,780 12,400 12,050 13,450 13,500
because the current redistribution is modeled more correctly as compared to existing 1D models.
D. Molnar et al. / Cryogenics 53 (2013) 119–127
During the splice consolidation in the machine, every joint which has a larger non-stabilized cable length than 4 mm will be re-soldered (see Fig. 9 and 10). Furthermore, two shunts will be soldered onto each die of all the joints in the main dipole circuits, and one shunt will be soldered on each side of all the joints in the main quadrupole circuits. The results of the simulations clearly show that a joint with a non-stabilized cable length smaller than 4 mm is intrinsically safe, i.e. after a quench its temperature will remain below 300 K during an exponential current decay from 13 kA. Furthermore, the results show that a joint with a single shunt offers a fully redundant bypass for the current for nominal LHC operating conditions assuming conservative RRR values and adiabatic conditions. Therefore, the proposed consolidation of the dipole joints offers a double redundancy. For the quadrupole joints a second (side) shunt could mean a double redundancy, but implementation of such a shunt in parallel with the main bottom shunt turns out to be very difficult in practice.
References [1] Bruening OS, Collier P, Lebrun P, Myers S, Ostojic R, Poole J, et al. LHC design report – the LHC main ring, vol. 1. Geneva, Switzerland: CERN; 2004. [2] Belova L, Genet M, Perinet-Marquet J-L, Ivanov P, Urpin C. Design and manufacture of the superconducting bus-bars for the LHC main magnets. IEEE Trans Appl Supercond 2002;12:1305–9. [3] Main bus bars interconnections between cryomagnets of the LHC arcs. LHC engineering specification. EDMS 10810; 2005. [4] Lebrun P, et al. Report of the task force on the incident of 19 September 2008 at the LHC. LHC project report 1168, CERN, Geneva, Switzerland; 2009. [5] Scheuerlein C et al. Production and quality assurance of main busbar interconnection splices during the LHC 2008–2009 shutdown. IEEE Trans Appl Supercond 2011;21:1786–90.
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[6] Rossi L. Superconductivity: its role, its success and its setbacks in the large hadron collider of CERN. Supercond Sci Technol 2010;23:1–17. [7] Verweij AP. Busbar and joints stability and protection. In: Proceedings of the Chamonix 2009 workshop on LHC performance, Geneva, Switzerland; 2009. 113–9p. [8] Verweij AP. Minimum requirements for the 13 kA splices for 7 TeV operation. In: Proceedings of the Chamonix 2010 workshop on LHC performance, Geneva, Switzerland; 2010. 65–72p. [9] Verweij AP et al. Consolidation of the 13 kA interconnects in the LHC for operation at 7 TeV. IEEE Trans Appl Supercond 2011;21:2376–9. [10] Verweij AP. Probability of burn-through of defective 13 kA splices at increased energy levels. In: Proceedings of the Chamonix 2011 workshop on LHC performance, Geneva, Switzerland; 2011. 144–8p. [11] Heck S, Scheuerlein C, Fessia P, Principe R. The RRR of the Cu components of the LHC main bus bar splices. CERN TE-note-2010-005, CERN, Geneva, Switzerland; 2010. [12]. Visited October 2011. [13] Verweij AP. QP3, Computer code for the calculation of quench process, propagation and protection. 2009. [14] Berkelaar R. 2D and 3D simulations of a 13 kA interconnect in the LHC. CERN internship report at University of Twente; 2008. [15] . Visited October 2011. [16] Whitaker S. The method of volume averaging. 1st ed. New York: Springer; 1998. [17] Heck S, Scheuerlein C, Fessia P, Triquet S, Bonasia A. Resistivity of different solder alloys at cryogenic temperatures. Internal note 2011–03, CERN, Geneva, Switzerland; 2011. [18] Granieri PP et al. Stability analysis of the interconnection of the LHC main superconducting bus bars. Cryogenics 2012. [19] Granieri PP, Casali M, Richter D. Heat transfer in the LHC main superconducting bus bars. In: Proceedings of the 23rd ICEC and ICMC 2010, Wroclaw, Poland; 2010. 411–6p. [20] Willering GP, Fessia P, Bottura L, Scheuerlein C, Verweij AP. Thermal runaways in LHC interconnections: experiments. IEEE Trans Appl Supercond 2011;21:1781–5. [21] Willering GP, et al. Electro-thermal and mechanical validation experiment on the LHC main busbar splice consolidation, TE-note, CERN, Geneva, Switzerland, 2012.
Contents lists available at SciVerse ScienceDirect
Cryogenics journal homepage: www.elsevier.com/locate/cryogenics
Electro-thermal FEM simulations of the 13 kA LHC joints D. Molnar ⇑, A.P. Verweij, E.R. Bielert CERN, CH-1211 Geneve 23, Switzerland
a r t i c l e
i n f o
Article history: Available online 23 April 2012 Keywords: LHC 13 kA Joint FEM analysis Safe operation Shunt Electro-thermal
a b s t r a c t The interconnections between the superconducting main dipole and main quadrupole magnets are made of soldered joints of two superconducting Nb–Ti cables embedded in a copper busbar stabilizer. The primary cause of the September 2008 incident in the LHC was a defect in an interconnection between two dipole magnets. Analyses of the incident show that possibly more defects might be present in the 13 kA circuits, which can lead to unprotected resistive transitions. To avoid the reoccurrence of such an event, thorough experimental and numerical investigations have taken place to determine the safe operating conditions of the LHC. However to show measured curves is beyond the scope of this article. Furthermore, improvements in the design have been proposed in the form of additional parallel copper pieces, or shunts, which bridge the possible voids in the soldering and offer a bypass for the current in case of a quench. The purpose of this work is to support the design choices and to indicate the sensitivity to some of the free parameters in the design. Electro-thermal Finite Element Method (FEM) simulations are performed, making use of COMSOL Multiphysics. The use of FEM allows for a profound three-dimensional analysis and some interesting features of the shunted busbar can only be revealed this way. Especially current redistribution in the shunted area of the interconnect gives important insights in the problem. The results obtained using the model are very sensitive to the exact geometrical properties as well as to the material properties, which drive the Joule heating inside the interconnection. Differences as compared to a onedimensional model, QP3, are presented. QP3 is also used for simulations of non-shunted busbar joints as well as shunted busbars. Furthermore, margins are given for the soldering process and the quality control of the shunted interconnections, since the contact area between the stabilizer pieces and the shunt is an important quality aspect during the manufacturing of a safe interconnection. Ó 2012 Published by Elsevier Ltd.
1. Introduction The main dipole and quadrupole magnets in each of the eight sectors of the LHC are powered in series (see Fig. 1 for a schematic layout of the dipole circuit) [1]. Each magnet is individually protected by a quench detection system (QDS), and quench-heaters spreading the resistive transitions over the volume of the magnet coils. The parallel-connected diode over a magnet acts as a current bypass during the fast current discharge. This discharge has a time constant sRB of about 100 s for the dipole circuit and a time constant sRQ of about 30 s for the quadrupole circuits. The diodes however do not encompass the sections of the superconducting (SC) busbars between the magnets nor the interconnections. Their protection is based on heavy stabilization by soldered copper which, in case of a quench of the cable, would bypass the current and conduct the heat away. On 19 September 2008, during powering tests ⇑ Corresponding author. Address: 1192 Hu, Budapest, Garay koz 12, Hungary. Tel.: +36 304851792. E-mail addresses: [email protected], [email protected] (D. Molnar), [email protected] (A.P. Verweij), [email protected] (E.R. Bielert). 0011-2275/$ - see front matter Ó 2012 Published by Elsevier Ltd. http://dx.doi.org/10.1016/j.cryogenics.2012.03.008
of the main dipole circuit in sector 3–4 of the LHC, an electrical fault occurred in the 13 kA busbar. An electrical arc was produced and resulted in mechanical and electrical damage, release of helium from the magnet cold mass and contamination of the insulation and beam vacuum enclosures [2]. The most likely cause of the accident was a badly soldered joint, with large resistance between the two superconducting cables and a lack of continuity of the copper stabilizer. These joints consist of two superconducting Nb–Ti Rutherford type cables (LHC type 02 [1]), which are embedded in a copper busbar stabilizer [3,4], see Fig. 2. About 10,000 13 kA joints are present in the LHC. Since the September 2008 incident, the stability of the busbar interconnections has been thoroughly reassessed. In the LHC tunnel, quality control measurements revealed the presence of joints with unexpectedly high resistances. Imaging techniques were used to look into the structure of the joints and showed that voids were present between the superconducting cable and the copper stabilizer [5,6]. Also the continuity of the stabilizer itself was not always guaranteed, so that even in the case of a quench the current has to flow through the cable over several millimeters [7]. In such a defective joint the local Joule heating after a quench
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busbar
51mH 51mH B1
busbar joint
B2
B1
Dipole 1
busbar
51mH 51mH B1
51mH 51mH B2
Dipole 3
busbar joint
B2
Dipole 2
51mH 51mH B1
B2
Dipole 4
51mH 51mH B1
busbar
B2
Dipole 153
51mH 51mH B1
busbar
B2
Dipole 154
Fig. 1. The schematic of one of the eight main dipole circuits in the LHC.
results in excessive high temperatures, causing the solder to melt. Eventually the busbar may evaporate, similar to what happened in September 2008. The stability of the joint thus directly influences the maximum allowable operating current and therefore the collision energy of the LHC [8]. Following the considerations about the joint stability, the LHC is presently exploited at half of the nominal beam energy, i.e. 3.5 TeV. To be able to safely operate the LHC at full energy (7 TeV) consolidation actions are required [9]. This mainly involves the soldering of an additional copper stabilizer piece, or shunt, to the existing copper elements. The detailed layouts of the busbar and the shunted and non-shunted joints are given in Section 2. The safe operation thus strongly depends on the quality of the stabilizer pieces of the busbars, which have to carry all the current in the circuit. The safe current is defined as the current that limits the peak temperature in the bus to below 300 K for all operating conditions. This is a conservative definition, since the melting point of the tin silver (SnAg) solder is 494 K. Furthermore we consider conservative values for the RRRs (see Table 2), and we disregard possible cooling to the surrounding helium (adiabatic approach) [10]. In this paper, we describe the implementation of localized fast thermal runaways (see [7]) in a 3D COMSOL Multiphysics model. Section 2 reports on the design of the joints. The situations with and without a shunt are discussed here. In Section 3, the physics and the governing equations are introduced. The differences be-
tween the 1D and 3D implementation of the problem are discussed in Section 4. In Section 5 we explain how the geometries are implemented in the model, and we report on the used material properties, the used boundary – and initial conditions and on the implemented mesh. In Section 6 we present the results on simulations performed for a joint without shunt. The results are also compared to results obtained from the other codes as mentioned before. Results for the shunted busbar joints are given in Section 7. Shunted joints can intrinsically only be properly simulated with a 3D model since current redistribution plays a key role in this more complex geometry. These simulations are therefore not compared to results obtained by means of 1D models. The safe current as a function of the most important shunt design parameters is reported in this section. The main quality aspect of a shunt concerns the homogeneity and quality of the soldered connection. In Section 7 we discuss the effect of a partially soldered shunt.
2. Overview of designs The superconducting cables, busbar stabilizer, copper U-profile and copper wedge are soldered together using tin-silver (SnAg) solder (see Fig. 2). All the areas where the tin-silver should be present in order to assure a good thermal and electrical contact between the Rutherford cables and the copper stabilizer parts, are at the same time possible areas for voids, in case the soldering procedure was not successful [7]. In Fig. 4 we can see a possible worst case configuration of voids, when there is no solder at all between the stabilizer elements, while at the same time the superconducting cable is not stabilized (i.e. not soldered to copper parts) for a certain length, denoted as lNS. The precise dimensions of the pieces and their material properties are very important for the numerical models, since the stability is very sensitive to these input parameters. Table 1 summarizes the cross sectional areas of the copper stabilizer, the Nb–Ti superconducting Rutherford cable and the tin-silver solder in the busbar for
Table 1 The cross-sections of different materials in a joint in mm2.
Fig. 2. Layout of a LHC 13 kA joint between two superconducting Rutherford cables.
Copper including matrix Nb–Ti SnAg
RB bus
RB joint
RQ bus
RQ joint
281.3 6.5 26.8
291.8 13 9.8
161.3 6.5 26.8
171.8 13 9.8
D. Molnar et al. / Cryogenics 53 (2013) 119–127
16mm
Note that the electrical conductivity is a function of temperature. The coupling of the electro-dynamic and thermal models thus occurs naturally via temperature dependent material properties. The thermal problem is described by the following partial differential equation, the heat equation:
10mm
20mm
20mm
qm ðP; TÞC p ðB; TÞ
Fig. 3. The schematic of the cross section of the RB joint (left) and the RQ joint (right).
the RB and RQ circuits. Fig. 3 shows schematically the cross-sections of the RB and RQ joints. The smaller cross-section of the copper stabilizer in the RQ busbars are due to the smaller time constant of the circuit, resulting in much less dissipated energy during the current discharge. Note that the busbars of other circuits are positioned on top of the quadrupole busbars, hence making it practically impossible to solder a shunt on top of the RQ joints. Another important parameter is the RRR of the different copper parts, including the copper matrix of the superconducting cable. Since in the machine RRR values between 200 and 300 were measured [11], the RRR values were used for the analysis are conservative and are summarized in Table 2. The coordinate axes are shown in Fig. 4, where the origin (x = 0, y = 0, z = 0) is fixed in the middle of the joint. The only difference between the non-shunted and the shunted design is the presence of additional shunts which are soldered with SnPb to the stabilizer pieces. The shunts for the RB and RQ lines are identical. Four shunts will be soldered on a dipole joint, while there will be only two shunts on the quadrupole joint because there is no possibility to solder an upper shunt due to the presence of other busbar lines (see Fig. 3). Figs. 5 and 6 show the configurations of the shunted joints for the RB and RQ respectively. The shunt is 50 mm long, 15 mm wide and 3 mm thick. Each joint has two holes with a diameter of 7 mm, which are used to facilitate the soldering process.
3. Physics and governing equations The electro-thermal behavior of a joint can, in good approximation be described by coupling an electro-dynamic model with a heat transfer model. Taking Maxwell’s equations as a starting point for the electro-dynamic problem, one can express the electrical field E as the gradient of a scalar potential V (Eq. (2)), since the curl of the electrical field equals zero when no varying magnetic fields are present:
r E ¼ 0; E ¼ rV:
ð1Þ ð2Þ
Furthermore, current density J and electrical field E are linearly related by the electrical conductivity r via Ohm’s law:
J ¼ rðTÞE:
ð3Þ
Table 2 The assumed conservative RRR values of the copper pieces.
RRR RRR RRR RRR RRR
of of of of of
copper matrix bus stabilizer U-profile wedge shunt
121
RB
RQ
80 200 200 200 200
80 200 200 200 200
@T r ðkðB; P; TÞrTÞ ¼ Q ; @t
ð4Þ
qm(P, T) is the mass density in kg m3, which is a function of pressure P (in Pa) and temperature T (in K). Cp(B, T) is the specific heat at constant pressure in J kg1 K1, which is a function of the magnetic field B and temperature. t is time in s. k is the thermal conductivity in W m1 K1 which is a function of magnetic field, pressure and temperature. The right-hand side of the equation represents the heat source in W m3. Joule heating is assumed to be the only heat source, which gives the possibility to couple the two models also via the source term in the heat equation by the following relation: Q ¼ J E ¼ rjrVj2 :
ð5Þ
The obtained coupled system is strongly non-linear since the material properties depend strongly on the temperature and vice versa. Because of the very non-linear nature of the problem, numerical methods are needed to solve these equations. In this article a commercial tool Comsol 4.1 [12] was used. Comparison to another computer code, QP3 [13] is given for a particular case. 4. 3D and 1D implementations The bus including a (defective) non-shunted joint can be approximated by a 1 dimensional model, but for the correct analysis of the shunted busbars one needs a 3D implementation. The main advantage of a 3D model is the possibility to analyze the shunt and the current redistribution into it, which cannot be directly modeled in 1D. Furthermore, 3D modeling makes it possible to calculate the effect of partial soldering of the shunt or the presence of (small) contacts between different parts of the stabilizer, so the current could take parallel paths as indicated by the red1 arrows in Fig. 7. The main difference in the implemented geometry between 1D and the 3D models is explained in Fig. 8. The slightly different geometry can however lead to quite different results for the safe operating current of the joint, since the stability is very sensitive to especially the length of the non-stabilized cable. 1D models neglect the existence of the copper stabilizer along the non-stabilized cable, whereas in the 3D model the copper stabilizer is still present. No current is flowing in this part and therefore the simplification of the 1D model is allowed for the electro-dynamical part of the problem. However, from a thermal point of view both models are not exactly the same. The small volume of copper which is neglected in the 1D models has a finite heat capacity and therefore, the 3D model should return a slightly higher safe operating current. The second and more important difference between a 1D and a 3D model is indicated at the bottom of Fig. 8, and is related to the current redistribution inside the stabilizer just before the non-stabilized part of the cable. The 1D models assume that the current is homogeneously distributed over the full cross-sectional area of the copper stabilizer all the way up to the non-stabilized cable. The gap size is thus defined as the length of the non-stabilized cable. In the 3D model, current redistribution occurs and therefore the current is not homogeneously distributed over the full cross-sectional area in the last few mm before the non-stabilized part of the cable. The 1 For interpretation of color in Figs. 1–14, the reader is referred to the web version of this article.
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Y
Z
X
Stabilized cable
wedge BUS
BUS U-profile
Y
Non stabilized cable Z
15mm
Z=0
Z=60mm
Z=75mm
Fig. 4. Definition of the coordinate system and layout of the joint.
Top shunt
50mm
50mm
Holes wedge
BUS
BUS U-profile
Bottom shunt
Y Z
15mm
15mm
Fig. 5. Configuration of the shunted joint for the dipole busbar, notice that the non-stabilized cable (l = 15 mm) is assumed to have infinite resistance in case of a conservative approach.
50mm
50mm wedge
BUS
BUS U-profile
Bottom shunt
Y
Holes 15mm
Z
15mm
Fig. 6. Configuration of the shunted joint for the quadrupole busbar, notice that the non-stabilized cable (l = 15 mm) is assumed to have infinite resistance in case of a conservative analysis.
BUS
wedge
length elongated by the area of current redistribution. So far, the mentioned 1D models do not take into consideration this behavior, while in the 3D model, it is clearly present. Of course, current distribution effects are even more pronounced for shunted joints.
5. Modeling
BUS U-profile Partially soldered pieces Fig. 7. The partially soldered joint case.
physical gap size is the same, but, the effective gap size is slightly larger. The 3D model should give therefore a lower safe operating current, since the effective gap length equals the physical gap
One of the advantages of using a 3D COMSOL Multiphysics model is that the geometry of the model can be checked visually before any physics is introduced. Different subdomains can be introduced in a natural way. The various subdomains are provided with the correct material properties and boundary conditions afterwards. A detailed treatment of the implementation of a nonshunted joint can be found in [14]. The model described in that work has since been updated to a new version of COMSOL Multiphysics (version 4.1 versus 3.5a) and includes different types of shunts. The total simulated length of the model is 1.5 m from the
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at one end of the busbar (z = 1.5 m) a current density is applied and at the other end (z = 0 m) the electrical potential is set to zero. 5.2. Initial conditions The initial condition for the thermal problem is a homogeneous temperature of 10 K over the complete sample. In other words, since the superconducting material is Nb–Ti, a normal zone over the complete length has been initiated and iterations start from a quenched state. The cause of the quench or the propagation of the normal zone is not important for this analysis. This assumption again represents the worst case scenario. Since adiabatic thermal boundaries are considered, the cable will not recover its superconducting state. The voltage is calculated automatically in the first time-step by Comsol from the resistivity and the boundary conditions. 5.3. Material properties As becomes clear from the partial differential equations introduced in Section 3, the important material properties are the mass density, the specific heat, the thermal conductivity, and the electrical resistivity. The temperature and magnetic field dependence are taken into account. For copper, the fits by NIST are used, which include the temperature dependence and the RRR [15]. The magnetoresistivity is included by assuming uniform magnetic field. Furthermore, the method of volume averaging [16] is used to obtain effective properties for the cable, which consists of Nb-Ti filaments in a copper matrix in a ratio of 1:1.95 [1]. The properties of the different solders are not well known [17], but the same input is used in simulations performed with QP3 and COMSOL Multiphysics. 5.4. Mesh
Fig. 8. (Top) Physical situation in the non-shunted joint. (Middle) Simplification of 1D models neglecting some small parts of stabilizer which carry no current. (Bottom) current redistribution as present in the 3D simulations. 1D models should include a transition area, to capture this physical behavior.
middle of the joint, such that end effects in the busbar do not influence the result. In order to solve the partial differential equations introduced in Section 3, correct boundary conditions at all the interfaces between subdomains (contact resistances) and outer boundaries need to be given. Also the initial values of the dependent variables (temperature and electric potential or voltage) need to be set.
5.1. Boundary conditions From a safety point of view and a robust design, worst case thermal boundary conditions are implemented in the form of adiabatic walls. Furthermore, no thermal boundary resistance is assumed between the various parts of the joints. In this work only adiabatic conditions are applied. There are three different electro-dynamic boundary conditions implemented. Over the surface around the complete sample electrical insulation is applied (i.e. current conservation). Furthermore,
The mesh has a strong influence on both the solution and the computational time of the problem. The optimum balance between precision of the solution and used CPU time has resulted in a mapped mesh over the busbar end, consisting of 50 elements, which is extruded along the length of the busbar. To be able to use these brick shaped (hexahedral) mesh elements, the real geometry has to be simplified. The real geometry has rounded corners, while the model has ninety degree angles. The cross-sectional area of the model, however, corresponds to the real cross-sectional area of the busbar (see Table 1). Close to the discontinuity in the copper stabilizer, the length of the elements is 0.5 mm, while further away from this discontinuity the elements have a length of 10 mm. A linear shape function is used to interpolate the solution over the elements. The use of a minimum allowed number of mesh elements as well as the smallest order of the interpolation function are verified and little gain in the precision of the solution is obtained if either of them is increased. 6. Simulations of non-shunted joints The most interesting results from the non-shunted situation can be summarized in a graph relating the safe operating current to the physical non-stabilized length or gap length lNS (i.e. the non-soldered length of cable where there is no thermal and electrical contact between the cable and the stabilizer pieces). The gap starts at the discontinuity between the copper wedge and the busbar stabilizing copper, see Fig. 4. Using the boundary conditions mentioned before, the results are shown in Figs. 9 and 10. As was explained in Fig. 8 the relative thickness of the copper stabilizer compared to the cable has a strong influence on the effective gap length. For the RB bus this results in a difference of about 2 mm between
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er than the experimentally obtained results [21] furthermore the QP3 code has been validated thoroughly. A possible upgrade involves the parallel computation of the self-field and the application of a possible background field. The influence of the magneto-resistivity on the current re-distribution can then be investigated as well. As these curves indicate, safe operation at ultimate operating current of 13 kA is guaranteed if lNS is less than 4 mm for the RB and less than 8 mm for the RQ. It is important to point out that these values are calculated for rather conservative RRR values and disregarding possible cooling to helium. Also note that for lNS = 15 mm the dipole and quadrupole joints are capable to carry 8 kA and 9 kA respectively. This is important because the calculations on shunted joints assume this length of non-stabilized cable.
16000
Sa afe curre ent [A]
14000 12000 QP3 RB non shunted
10000 8000 Comsol RB non shunted
6000 4000 0
10 20 30 Non stabilized lenght of cable [mm]
40
Fig. 9. Safe operating current as a function of gap size for the RB interconnection for a current decay time constant of 100 s.
17000 15000
Safe current [A]
13000 QP3 RQ non shunted
11000 9000 7000
Comso RQ non shunted
5000 0
10
20
30
40
Non stabilized length of cable [mm] Fig. 10. Safe operating current as a function of gap size for the RQ interconnection for a current decay time constant of 30 s.
the 3D and 1D model and for the RQ which is much thinner it is much less, since the thickness of the stabilizer is about the same order of thickness as the cable itself. When cooling to liquid helium is introduced, the curves in Figs. 9 and 10 shift upward, allowing a higher operating current. Simulations similar to the ones discussed here were performed with another one-dimensional code [18]. These simulations take into consideration cooling to the helium bath as well [19]. Important input parameters such as RRR and maximum allowed temperature are however different, such that direct comparison of the results is not possible and therefore not mentioned here. A comparison between QP3 and Comsol is however possible, since the authors used both codes. Differences between these two models are due to the assumption of uniform current distribution over the cross-section of the bus in the 1D model, giving a slightly larger safe current. This effect becomes relatively larger for smaller physical length of the non-stabilized cable. For the RQ joint the effect is less present because of the shorter current decay time constant. The coupled electro-dynamic and thermal behavior of the non-shunted joint have been tested at several applied fields [20]. Comparisons with this experimentally obtained data are only possible when cooling is implemented in the model. The presented COMSOL Multiphysics model is already capable of performing such simulations [14]. However, here we discuss only the worst case, adiabatic conditions. The calculated safe operating currents with adiabatic case are systematically low-
7. Simulations of shunted joints In this section the safe operational current for various shunt designs is reported. The influence of a partly soldered shunt is analyzed, where the percentage of soldered area is important for quality control. The results presented here assume that the shunt needs to carry the full current of the circuit during a discharge and that the non-stabilized cable carries no current. Figs. 5 and 6 give an overview of the analyzed geometry, while Fig. 11 shows the details for a shunted joint, especially regarding the definition of the uniformity of the SnPb solder. The defect length is defined as the length of solder which is lacking over the complete width of the shunt. Also underneath the soldering holes, there is no contact between the shunt and the stabilizer part. This assumption is realistic since, according to experiments, the quality of the solder underneath the holes is very low compared to other parts. In principle the shunted joint can only be analyzed using a 3D code. However, coupled parallel 1D models (1.5D) can solve the problem as well. Additional features have been added to QP3 to allow its use for the shunted case too [13]. The shunt itself needs to be soldered to the existing interconnections of the LHC. During this process, unsoldering of the existing SnAg solder inside the joint should be avoided. This is achieved by using a soldering material with a lower melting point. It has been decided to use SnPb, which has a melting point of 461 K which is small enough as compared to the melting temperature of SnAg (494 K). Because the soldering process is a critical step in the repair of the joints, the quality of this new soldering layer needs to be assured. The main goals of this work are to define the dimensions and properties of the shunt, but also to give margins for the soldering process as well as for the quality control of the shunted joints. In Fig. 12, the safe operating current as a function of the defect length of the solder is shown for both the RB and RQ circuits. The defect length is defined as the length over which solder is lacking over the complete width of the shunt, compared to the nominal design. This means that the void of SnPb is symmetrical with respect to the void between the bus and the wedge (for the top shunt) or between the bus and the U-profile (for the bottom shunt), see Fig. 11. This configuration represents the worst possible situation, since all the current is bypassed via the shunt. Defects in the soldering of the top shunt give a less stable configuration as defects in the soldering of the bottom shunt. This is mainly caused by the intrinsically smaller total contact area between the top shunt and the wedge as compared to the total contact area between the bottom shunt and the U-profile. Therefore the top shunt was analyzed as a worst scenario for the RB joints. Since there is no possibility for a top shunt for quadrupole joints (see Section 2 and Fig. 3) the bottom shunt is only considered. Note that these results represent a configuration with a non-stabilized
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SnPb
Voids in SnPb solder
BUS
lSnPb defect
Top shunt
wedge
BUS U-profile
Bottom shunt
Voids in SnPb solder
SnPb
Fig. 11. Schematic overview of the shunted joint.
Safe operating current [A]
19000 18000
RQ bottom shunt
17000 16000 15000 RB top shunt
14000 13000 12000 0
5
10
15
20
25
Defect length of SnPB [mm] Fig. 12. The safe operating current as a function of the defect length of the shunt solder.
length of the cable being equal to 15 mm on both sides of the joint. The shunt is present on both sides of the joint as well, therefore a completely symmetrical geometry relative to the center of the joint is analyzed. The kinks in the RQ curve are caused by a sudden increase in effective defect length when the defect length of the SnPb reaches the hole (see Fig. 11). The quadrupole joints have a much larger margin, which is obvious because of the decay time constant of the RQ circuit is much smaller than for the RB circuit, while the dimensions of the RB and RQ shunts are identical. For safe operation at ultimate current the maximum allowed defect length of SnPb soldering layer is 14 mm for the RB while it is 24 mm for the RQ. Optimization possibilities include the variation of the length of the shunt and the diameter of the solder reservoir holes. However simulations showed that the proposed 50 mm length of the shunt is sufficient, since there is no gain in safe operating current by elongating the shunt. The bottleneck in the coupled electro-thermal problem is the non-soldered length of the shunt. A qualitative proof for this is shown in Fig. 13, where the y-component of the current density is plotted as a function of the length of the shunt for an RB top shunt with lsold-def = 10 mm. A schematic configura-
tion of the shunt and voids of the SnPb soldering layer (including the holes) is shown as well. The horizontal line crossing the shunt represents the line where the current density component was evaluated, i.e. in the middle of the shunt. When the stabilizer is interrupted by a void, the current which was still flowing in the stabilizer is also forced into the shunt. Therefore, the vertical component of the current density shows two peaks: one at the start of the shunt and one at the void of the stabilizer. In the bridging part of the shunt, the current distribution is homogeneous, so the vertical component of the current density equals zero. Of course, also at the position of the holes the y-component of the current is zero. The influence of the diameter of the soldering reservoir holes is rather limited. Simulations show that a smaller hole, and thus a larger contact surface, allows slightly higher safe operational currents. However, reducing the size of the holes gives practical difficulties during the soldering, since it may jeopardize the quality of the rest of the contact surface. The last part of the analysis considers possibilities for redundant shunts for the RQ circuit. As mentioned before (see Fig. 3), the RQ joint has limited access from the top, since the 600 A busbars are located there. Therefore the only possible position for an additional shunt is on the side of the copper stabilizer parts. Two possible designs are shown in Fig. 14: ‘‘type_a (bridge)’’, with limited contact surface, and ‘‘type_b’’. Several calculations are performed varying the geometry of the shunts. The width of the bridge shunt was fixed to 8 mm, while the type_b shunt’s all parameters are varied. The results are summarized in Tables 3 and 4. In these analyses, the SnPb soldering layer is assumed to be perfect with no voids in it. The results show that the safe operational current of 13 kA can be attained. However, implementation of such shunt in parallel with the main bottom shunt turns out to be very difficult in practice. Furthermore, proper quality control will be difficult. Also for the shunted joint, experiments have been carried out [21]. One of the most important results of these tests is that under certain operational conditions, the busbar which is embedded in a longitudinal slot in the iron yoke is less stable than the shunted joint.
8. Conclusion We have shown how the thermo-electrical behavior of a superconducting 13 kA busbar joint, with and without additional shunts, is implemented in a 3D FEM model. The numerically obtained re-
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Void of
hole
hole
SnPb
Fig. 13. Current redistribution from the stabilizer into the shunt and from the shunt into the stabilizer.
Fig. 14. Photographs and schematics of the side shunts for the RQ circuit (top) ‘‘type_a, (bridge)’’, (bottom) ‘‘type_b’’.
Table 3 Results for the ‘‘bridge type’’.
Table 4 Results ‘‘type_b’’ side shunt.
zl (mm)
zm (mm)
zr (mm)
x (mm)
Safe current (A)
4 8 7 8 4
6 6 6 6 6
4 4 7 8 4
3 3 3 3 10
10,500 11,600 12,500 12,900 13,000
sults are validated by comparison to other numerical codes, where a good agreement is found. The 3D model is an important tool for the understanding of the stability behavior of the joints, especially
x (mm)
y (mm)
zb (mm)
zj (mm)
Safe current (A)
3 4 3 3 3 3
6 6 7 6 6 6
4 4 4 8 8 8
4 4 4 4 20 25
10,000 11,780 12,400 12,050 13,450 13,500
because the current redistribution is modeled more correctly as compared to existing 1D models.
D. Molnar et al. / Cryogenics 53 (2013) 119–127
During the splice consolidation in the machine, every joint which has a larger non-stabilized cable length than 4 mm will be re-soldered (see Fig. 9 and 10). Furthermore, two shunts will be soldered onto each die of all the joints in the main dipole circuits, and one shunt will be soldered on each side of all the joints in the main quadrupole circuits. The results of the simulations clearly show that a joint with a non-stabilized cable length smaller than 4 mm is intrinsically safe, i.e. after a quench its temperature will remain below 300 K during an exponential current decay from 13 kA. Furthermore, the results show that a joint with a single shunt offers a fully redundant bypass for the current for nominal LHC operating conditions assuming conservative RRR values and adiabatic conditions. Therefore, the proposed consolidation of the dipole joints offers a double redundancy. For the quadrupole joints a second (side) shunt could mean a double redundancy, but implementation of such a shunt in parallel with the main bottom shunt turns out to be very difficult in practice.
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[6] Rossi L. Superconductivity: its role, its success and its setbacks in the large hadron collider of CERN. Supercond Sci Technol 2010;23:1–17. [7] Verweij AP. Busbar and joints stability and protection. In: Proceedings of the Chamonix 2009 workshop on LHC performance, Geneva, Switzerland; 2009. 113–9p. [8] Verweij AP. Minimum requirements for the 13 kA splices for 7 TeV operation. In: Proceedings of the Chamonix 2010 workshop on LHC performance, Geneva, Switzerland; 2010. 65–72p. [9] Verweij AP et al. Consolidation of the 13 kA interconnects in the LHC for operation at 7 TeV. IEEE Trans Appl Supercond 2011;21:2376–9. [10] Verweij AP. Probability of burn-through of defective 13 kA splices at increased energy levels. In: Proceedings of the Chamonix 2011 workshop on LHC performance, Geneva, Switzerland; 2011. 144–8p. [11] Heck S, Scheuerlein C, Fessia P, Principe R. The RRR of the Cu components of the LHC main bus bar splices. CERN TE-note-2010-005, CERN, Geneva, Switzerland; 2010. [12]