PFC/RR-83-21 DOE/ET-51013-92 MFTFB+T MAGNETOSTATIC AND CIRCUIT FAULT INDUCED FORCES R. D. Pillsbury, Jr., R. J. Thome W. R. Mann, and W. G. Langton Massachusetts Institute of Technology Plasma Fusion Center Cambridge, MA 02139 August 1983 Foreword This work was performed for the Fusion Engineering Design Center, Oak Ridge, Tennessee in support of their activi-:y for the Mirror Fusion Test Facility at the Lawrence Livermore National Laboratory. The effort was carried out by the Plasma Fusion Center Magnet Technology Division under contract no. DOE-AC02-78ET-51013. TABLE OF CONTENTS Page No. 0.0 INTRODUCTION. . . . . . . . . . . 1 1.0 SUMMARY . . . . . . . . . . . . . 3 2.0 COIL AND CIRCUIT MODELS . . . . . 22 3.0 MAGNETOSTATIC LOAD ANALYSES . . . 30 4.0 TRANSIENT LOAD ANALYSES . . . . . 41 5.0 CONCLUSIONS . . . . . . . . . . . 64 0.0 INTRODUCTION Magnet systems consisting of multiple, inductively coupled coils can experience substantial changes in their usual operating load patterns in the event of a fault condition such as a short circuit followed by a rapid system discharge. The methods for determining the load changes are straightforward, but time consuming and the number of cases requiring consideratlrn grows rapidly as the number of coils and circuits in a system increases. As magnet systems become larger and more complex, the electromagnetic load redistribution or other effects such as excessive temperature rise can become so severe that a thorough fault condition examination is essential. The Magnet Technology Division at the Plasma Fusion Center has been developing codes to improve the efficiency and turn around time for model construction and fault condition analysis. In this report the codes were applied to a system of 24 coils in nine circuits which constitute MVTFB+T, a joule mirror fusion system under consideration by LLJL. The process begins by system field/force model construction using sufficient detail to analyze parameters selected as indicative of the severity of a fault condition (e.g. - total load in a particular direction on a coil or load per unit length at a point in a coil), but not so detailed that turn around time is unattractive. If a severe condition is found it is assumed that the design croup will investigate the condition with a more detailed model. An estimation of "severity" of a fault condition requires a well defined set of "usual' operating conditions for comparison. We define the latter as the extreme maximum or minimum values of the critical parameters for any combination of the circuits in a fully "on" or "off" condition. In itself, this magnetostatic analysis is nontrivial in a complex system. For example, for the nine circuits in MFTFB+T, there are 512 (2 to the ninth power) usual operating conditions. It should be emphasized that these represent feasible conditions since it is conceivable that any combination of circuits :ould be fully charged during shakedown tests or system operation. This is indicative of the need for an efficient procedure and codes for fault analysis since the number of credible faults is often many t imes the number of usual operating conditions in a multiple coil/multiple In this report, the fault conditions which have been selected arise from assuming that all circuits are charged to their operating level, a short circuiu occurs across one coil and a discharge of the entire system follows. Each case requires a transient circuit analysis required by em load determination as a function of time because, in general, the extreme loads do not necessarily occur at the time a discharge current in a circuit passes throuch its maximum value. NOW& In general, the four C-shaped magnets at each machine end (I4'2, 1I11, WT2, and WTI) experience the worst case loading under static current conditions. The central cell solenoids (WS6, WS5, WS4, and WS3) experience their peak loads during discharge transients with a neighboring coil short-circuited. The coils at the machine center (WS2, WS1, WCC1, WTDFS2, etc.) have peak axial loads that occur primarily in the static condition. However, the peak radial loads occur during the discharge transients. The currient scenarios chosen for the analyses were by no means exhaustive from a fault condition standpoint. An entire class of faults which requires consideration involves system behavior during discharge execution with a section of one of the superconducting coils in the resistive state. Even though the coils are designed to be stable under usual conditions, that is, complete LHe coolant immersion, a resistive region is possible in the event of a fault in the form of a low helium level. The tEimperature rise in a resistive region which is not immersed is strongly dependent on the coupled discharge character of the circuits and the level of operating current and dump voltage selected. Substantial progress has been made in the ability to turn around certain classes of fault conditions as evidenced by the cases treated in this report. is indicated above, however, other classes of severe conditions ex. st and development of codes for rapid turnaround of these cases should continue. -2- I I 1. 0 SLMVY This report presents the results of work performed to date on the estimation of the Lorentz forces acting on the various coils in the MFTFB+T mirror machine. The analyses include: (1) static loading under normal operating conditions; (2) transient loading during a normal discharge; and (3) transient loading for one coil short circuits with all coils discharging. For the purposes of this memo, normal operation is defined as any possible combination of circuits fully charged to their operating current level or at zero current. This definition would then include any possible scenario for the entire system or partial system at full operating current. Figure 1.1 shows both an isometric and side view of the coils in the machine. Txwenty four coils are shown and consist of two large central solenoids, iwo high field choke coils, and twelve identical solenoids in the central cell. Each of the machine ends has four coils: two transition coils and a yin-yang pair. Only the coil centerlines are shown.Superimposed are the coordinate system, the coil numbering system and coil nomenclature adopted for this effort. The coils are numbered consecutively from the coil with the largest positive axial (z) coordinate (coil 1) to the largest negative coordinate (coil 24). Table 1.1 lists the coil number, name, their circuit number, and full operating current. The circuit numbering is arbitrary, but collects the 24 coils into nine circuits corresponding to the expected power supply configuration for this machine. Note that each of the four yin-yang coils are in an independent circuit whereas other similar coils are in series in the same circuit. Results may change considerably if different current levels or circuit configurations are postulated. The models of the coils and circuits are described in section 2.0. The results froff the static analyses are given in section 3.0. The transient analyses are presented in section 4.0. The remainder of this section summarizes the results. Table 1.2 summarizes the peak values of the net axial force which can act on each coil out of the possible normal operating conditions. Both the largest positive and largest negative loads are given along with the current scenario that produces those forces. The current scenarios are gii'en as a nine digit number. Each digit represents the current multiplier in each circiit. For example, the current scenario 110011001 implies that circuits 1,2,5,6, and 9 are at full current, while circuits 3,4,7, and 8 are at zero :urrent. The forces given represent the total axial load acting on the coil. It can be seen that, except for the two end coils, the worst case do rot occur when all coils are at full operating current. Similarly, none of the cases of the single circuit on - all others off generates maimun or minimum forces. In general, the worst case loading occurs when as many coils as possible to one side of the coil under II:adings -3- High Field Choke Coils FR (y =0) Transition -(X z y Pair FR(x y =o) x Cc4 D N I- w~ w CY VM 04 C-1 1 N V'OWNWOVM r- VN p-T 19 0N N Figure 1.1 -T C :D -. ~. NT-O0ONO~fle . MFTF+T Coil Centerlines, Numbers and Nomenclature -4- z rable 1.1 Coil/Circuit Numbering and Nomenclature coil # coil name 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 WM2 WM1 WT2 WT1 WS6 WS5 WS4 WS3 WS2 WS1 WCC1 WTDFS2 ETDFS2 ECC1 ESI ES2 ES3 ES4 ESS ES6 ETI ET2 1 2 3 4 5 5 5 5 5 5 6 7 7 6 5 5 5 5 5 5 4 3 4403 3872 5206 2322 1823 1823 1823 1823 1823 1823 107190 8000 8000 107190 1823 1823 1823 1823 1823 1823 2328 5206 3 [Ml1 8 3872 24 EM2 9 4403 Circuit # -5- Operating Current (A) Table 1.2 coi I # 1 3 4 5 6 7 6 9 16 11 12 13 14 15 16 17 18 19 20 21 23 n4A coil name WM2 WM1 WT2 WT1 WS 6 WSS WS4 WS3 WS2 WS1 WCC1 WTDF32 ETDF32 ECC1 ES1 ES2 ES3 ES4 ES5 ES6 ETI ET2 EMI E- Ic Peak Axial Loads Under Normal Operating Conditions Maximum Fz (MN) 0 4.75 4.96 1.04 0 0 Current Scenario* Minimum Fz (M) Current Scenario* 110000000 -5.27 -5.02 -1.51 -0.48 011111111 -4.44 000011111 000011111 111110000 111110000 111110000 -2.17 -1.63 -1.84 -2.80 -4.82 111111000 -1.68 111000000 111100000 0 0.43 1.41 3.91 0.21 -162. 0 102. 1.68 4.82 2.66 1.84 1.63 2.17 4.44 0.48 1.51 5.02 110000100 110001100 5.27 111111111 110011100 110011100 110011100 110011100 110011100 110011100 110111100 111111100 111111110 + each diqit -epresents a circuit on (1) 111111111 661111111 000111111 000011111 000011111 000011111 000011111 000001111 000000111 0 -0.21 001111011 -3.91 001110011 001110011 001110011 -1.41 -0.43 0 0 0 -1.04 -4.% -4.75 0 001100011 001000011 000000011 or off (0) e.g. 116011100 means circuits 1,2,5,6,7 are on and circuits 3,4,8,9 are off consideratiOn have zero current and as many as possible on the other side have full cirrent. Due to the connection symmetry of most of the circuits the worst case load does not correspond to all coils on one side on and all coils on the other off. Force; that are listed as 0 imply there is no scenario that gives a force of that sign or direction on that coil. For example, WS6 (coil #5) has a zero maximum (positive) force. This means that there is no possible combination of circuits completely on or-off that produces a net force on WS6 that is away from the machine center. However, there are several combination; that produce a net force on WS6 toward the machine center. The worst case .oad is -4.44 MN and occurs when circuits 1,2,3 and 4 are off and circuits 5-9 are on (i.e. a current scenario of 000011111). Figure 1.2 shows the same information in bar chart form. The worst case maximu (positive) and minimum (negative) net axial force on each coil is shown. For scaling purposes the forces on the large solenoids have been clipped and the peak value written adjacent to the bars. There is anti-symmetry about the machine center, as is expected. Table 1.3 summarizes the peak radial loading per unit length acting on each coil for normal operating conditions. In a solenoid, the forces per unit length are indeed radial. For C-shaped coils, these forces are local running loads (N/m) which contribute to the lobe-opening forces. For the purposes of this memo these forces are denoted as radial for all coils. There are tuo values presented. The first is in the X=0 plane; the second in the Y=0 plane. The two radial force directions are illustrated in Figure 1.1 for a typical C-shaped magnet and for a typical solenoid. Note that the force in the X=G plane is y-directed and the force in the y=0 plane is x-directed. In a purely solenoidal system, these two forces would be equal. The lack of equality is a function of the non-solenoidal fields produced by the C-shaped magnets in the system. The radial forces are pu.It~ie fur dll cases and are usually extreme for all circuits on. However, som of the coils (e.g. WT2) experience the worst case radial loading when an adjacent coil is off and unable to hold the axial flux from the system away from the winding in question. Figure 1.3 shows the information from this table in bar chart form. The sclid lines represent the radial forces (per unit length) in the X-0 plane; and the dashed lines the Y=0 plane. Only the C-shaped coils at the machine ends experience a significant loading difference in the two planes. The end solenoids do experience a slight difference in force, but the difference it; too small to see at this scale and the solid lines hide the dashed ones. A more detailed discussion and presentation of some of the individual current scenarios for usual operating conditions can be found in section 3.0. The cases considered in detail were all coils on, and individual circuits off with all others on. -7- 11 X a4vi U.0 -D c) - C-C--D I I I I I I..ILI f I I I M4 C I I I 101.8 CO z IZI .LLLLI N IL .7 - I m . I . I . . i I . -iOt.9 . i I 24232221 20 19181716151413 i I 9I 211.10 I COIL P Figure 1.2 Peak Axial Loads - Static -8- 8I 7I 8 ' I ' 5 4 I 3 I 2 1 Table 1.3 coil # 2 3 4 5 6 8 9 10 11 12 13 14 15 16 coi l name Peak Radial Loads per Unit Length Under Normal Operating Conditions X=6 Plane Fr (M/m) WM2 WM1 4.95 6.03 WT2 WT1 WS6 WS5 WS4 0.80 WS2 WS1 WCC L WTDFS2 ETDFS2 ES I ES2 0.87 0.67 0.75 0.82 0.90 1.01 1.16 34.0 28.1 28.1 34.0 1.16 1.01 F' 0.90 18 L4 19 ESS 0.83 0.75 0.65 0.66 1.34 3.99 5.41 20 21 22 23 24 ET1 ET2 E 1I E12 Current Scenar 1o* Y-0 Plane Fr (MN/m) Current Scenario* 111111111 5.41 111111111 111111111 10111111 111111111 3.99 1.34 0.66 0.65 0.75 1111111 111111 1111111 116111111 11111111 111111111 111611111 111611111 111111111 111111111 111111111 111110111 111111111 111110111 111110111 111111111 111110111 111111111 111111111 111111111 111111111 116111111 111111111 111111111 111111111 111111111 * each di9 it represents a circuit on (1) 0.83 0.90 1.01 1.16 34.0 28.1 28.1 34.0 1.16 1.01 0.90 0.82 0.75 0.67 0.87 0.80 6.03 4.95 111111111 111111111 111116111 111111111 111116111 111116111 111111111 111116111 111111111 111111111 111111111 111611111 111611111 111111111 111111161 111111111 111111111 or off (0) e.g. 110011166 means circuits 1,2,5,6,7 are on and circuits 3,4,8,9 are off -9- w wu W WWW UWWLWJI*Jt i. CC- * V3 C4 -01M G'-ww~q V V OC C C" 0a .f-oU4 ca Lo X = 0 Plane Y = 0 Plane 0- (v) in i E z CLL C), 0 ,;T N42 22 01 1 7I 1 41 CO 121I 10 9 Figure 1.3 8 7 e 5 4 3 2 Peak Radial Loads Per Unit Length - Static -10- 1 The next set of analyses investigated the coil loading experienced during discharge transients. The lumped circuit parameter model used is discussed in section 2.0. The scenarios considered were: (1) all coils on and then discharged simultaneously, and (2) all coils on then a single coil short-circuited with all others discharging. The extreme loads on different coils can occur at different times during the transient, and, therefore, cannot be used to represent a subsystem loading - e.g. peak axial loads on coils 1 and 2 (WM2 and WM1) cannot be summed to get a worst case loading on the set. Such an assumption would be conservative, but possibly too much so. Table 1.4 presents the worst case axial forces acting on each coil for the normal discharge case. Some coils actually experience a load reversal during discharge, because all coils do not discharge at identical rates. Figure 1.4 shows the same information in bar chart form. Table 1.5 and Figure 1.5 present the worst case radial forces per unit length in the X-0 plane (solid lines) and Y-0 plane (dashed lines) for the normal discharge c'ase. Similarly, Tables 1.6 and 1.7 and Figures 1.6 and 1.7 present the worst case loads on each coil for all the single coil short-circuit transients, Each coil from 1 to 12 (M2 to WTFDS2) in turn was assumed to have a short across the entire coil with a short resistance of 1 micro-Ohm. The other coils discharge through their dump resistors. The case numbers correspond to the coil number that contains the short during the worst transient v'or the coil. Case 0 is the normal discharge of all coils. The notation 0+ implies a small load (order of kN). WT2 experiences a small load reversal in the radial force per unit length in the X-O plane. Since only half the coils were shorted individually because of the system symmetry, the worst case forces on the coils are tabulated for coils 1-12 only. The loads on all the coils are presented in the figures. A mort detailed discussion of the transient analyses is given in Also presented are the loadings for the individual current scenarios. Snetiui 4.A. Finally, Tables 1.8 and 1.9 list the worst case loadings for each coil from all the usual and fault current scenarios investigated. If the load is from a static scenario, the scenario is given as the nine digit number describlng which circuits are charged and which are not. If the load arises during a ccil short-circuit transient, the coil being shorted is given. Only the first 12 coils are listed. The peak forces on the other coils will have the expected syimmetry or anti-symmetry. These worst case loads are sho'wn in Figures 1.8 and 1.9. All coils are shown. -11- 11 1 Table 1.4 Peak Axial Loads Under Normal Discharge Conditions coil # coil name Maximum Fz (MN) Minimum Fz (MN) 1 0 0 3.44 0.56 0 0 0 0 0.15 0+ 0 0 -5.27 -0.28 5 6 WM2 WMIl WT2 WT1 WS6 W35 2 3 4 7 WS4 8 9 WS3 WS2 10 11 WS1 13 14 WCC 1 WTDFS.? ETDFS2 ECCI 15 ESI 16 17 18 19 20 ES2 ES3 ES4 ESS ES6 ETI 12 21 22 23 24 90.3 1.47 4.78 2.75 1.74 1.46 1.84 0 0 -3.89 -1.84 -1.46 -1.74 -2.75 -4.78 -1.47 -90.3 0 0 0+ -0.15 3.89 0 0 0 0 ET2 EMIl 0 0 -0.56 -3.44 0.28 EM2 5.27 0 0 0+ denotes a small force on the order of kN. -12- X £4~~ ~ Z~ -4 I I I I I I I I I - I- 'O6I-S w4V. 44 N~ M I I N .4( ho ~ QI.9.fV io.b * 0) fC I I 9I- I I I *I II II II I I I z LL Si 24 23 22 21 20 19 18 17 16 15 14 13 12 11 10 9 Figure 1.4 II 8 7 0 i 5 Peak Axial Forces - Normal Discharge -13- I 4 * I 3 2 1 Table 1.5 Peak Radial Loads per Unit Length Under Normal Discharge Conditions coil # 1 C- 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 2- I 22 23 24 coil name WM2 WMIl WT2 WT1 WS6 WSS WS4 WS3 WS2 WS1 WCCI1 WTDFS2 ETDFS2 ECC 1 ESI ES2 ES3 ES4 ES5 ES6 ETI ET2 EM1 EM2 X=0 Plane Fr (MN. m) Y=0 Plane Fr (MN/m) 5.41 3.99 1.34 0.66 0.65 0.75 0.83 0.90 1.01 4.95 6.03 0.47 0.87 0.64 0.75 0.82 0.90 1.01 1.18 34.0 28.1 28.1 34.0 1.18 1.01 0.90 0.83 0.75 0.65 0.66 1.34 3.99 5.41 1.18 34.0 28.1 28.1 34.0 1.18 1.01 0.90 0.82 0.75 0.64 0.37 0.47 6.03 4.95 -14- x N iu w It w O wwwtWW 64 n C4CIv -j Inj X Ln- = 0 Plane -Y =O0Plane 0 UI) C4 E , ,n z LL Ca In v-4 24 2-322 Figure 1.5 2120 19 18 17 18 15 14 19 21 L O 8 7 0 Peak Radial Forces Per Unit Length - -15- 5 3 2 1 Normal Discharge Table 1.6 Coil # Coil Name 1 WM2 W41 WT2 WTI 2 3 4 5 6 1436 7 W34 WS5 8 9 10 W:.31 11 WCC1 12 wTrDSF2 Table 1.7 Coil # Coil Name Peak Axial Loads On Coils Due to Single Coil Short-Circuits Maximum Fz(MN) Case # Minimum 0 0.56 0+ -0.04 -3.99 4 0.56 0.75 5 0.89 1.12 7 8 9 1.85 0 0.90 -5.27 -1.39 -1.12 1 2 0 1.09 3.60 6 10 X=0 Plane Maximum Fr (M/m) Case # ll WM2 4.95 6.03 3 WT2 WTI 0.51/-.03 A 0.87 WS" WS!; 1.15 0 5 1.53 1.78 6 7 2.05 2.46 6 9 6 7 8 9 10 11 12 WS4 IA& WS2 WSJ, wCc1 WTEISF2 5 -2.29 -1.86 6 8 -2.10 8 -3.06 -4.83 -1.47 -90.3 10 12 3.23 49.0 30.4 Y-0 Plane Minimum Fr (t./m) 5.41 0 0 4.13 1.34 o.66 1.15 1.53 1.78 2.05 2.46 3.23 49.0 30.4 3/2 10 11 12 0+ denotes a simall force on the order of kN. A 12 3 4 4 9 12 Peak Radial Loads Per Unit Length On Coils Due to Single Coil Short-Circuits 1 2 4 5 Case Fz(MN) a slight foroie reversal -16- Case * 0 2 0 0 5 6 7 8 9 10 11 12 N x C (*VC4 cIIIII.0 IN~~ff N I N N SS Np~y~p .5h!; fi p.Cp N .OS~ Cc:: p ... 90 * CO - I) .4 z E N I= CL) 411 -111111 , In -90.3 24 23 22 21 20 19 I 17 16 15 14 13 12 1I LO 9 8 7 6 5 4 3 2 1 COIL # Figure 1.6 Peak Axial Forces Due To A Single Coil Short Circuit -17- x w w cj CflwflCI~Oi- 5 3:3I0CflI-4 3.- ca Cc : C1 I0I I-EOIf I I z 0 I I I I I .1 I44~ I I 49.0 = -x - X I 0 Plane = 0 Plane 0- an In z C3 In 242022.2 9I 1 61 . 3121 COL S7 10 Figure 1.7 432 9 a 7 6 5 4 3 f2 Peak Radial Forces Per Unit Length Due To A Single Coil Short -18- ,11 Peak Axial Loads Under All Conditions Table 1.8 coil coil Maximum # name Fz (MN) 1 2 Wi2 Wi 1 3 W72 0 4.75 4.96 1.04 0+ 0.56 0.75 0.89 1.41 3.91 0.21 0.90 4 5 6 7 8 9 10 11 12 W26 WS4 WE3 WS2 W1 WCCI Wi DFS2 Table 1.9 Current Scenario* 11000 11100600 liltn m short 4 short 5 short 6 short 7 111110000 11111600 11111100 short 10 name X=6 Plane Fr (MN/m) Current Scenario* 1 2 3 4 5 6 7 8 9 10 11 12 WM2 WHi 4.95 6.03 W12 W1 W6 0.80/-.03 A 111111111 111111111 161111111 111111111 short 5 WS2 14,1 W( Cl WTDFS2 111111111 011111111 001111111 000111111 000011111 short 6 short 8 short 8 0011111 short 10 00001111 600000111 Peak Radial Loads Per Unit Length All Conditions coii W$3 -5.27 -5.02 -1.51 -0.48 -4.44 -2.29 -1.86 -2.10 -2.60 -4.83 -1.68 # WS4 Current Scenario* -102. coil WS5 Minimum Fz (MN) 0.87 1.15 1.53 1.78 2.05 2.46 3.23 49.0 30.4 short 6 short 7 short 8 short 9 short 10 short 11 short 12 Y-0 Plane Fr (Mf/m) 5.41 4.13 1.34 0.66 1.15 1.53 1.78 2.05 2.46 3.23 49.0 30.4 Current Scenario* 111111111 short 2 111111111 111111111 short 5 short short short short short short short 6 7 8 9 10 11 12 or off (0) e.g. 11011100 means circuits 1,2,5,6,7 are on and circuits 3,4,8,9 are off * each dig it represents a circuit on (1) 0+ denotesl a small force of the order of kN. ^ force rtversal for short 2. -19- 1%I x C C V 4 I -4 I ~I-4--iS S S IS 0 N 4 IS g 'O NN- 0-- S S I I 8C - I fqS r CMI - - a*6l. U~w I V N 0 .L.~ I z Cc I I~ S I i02. 0 In- $ L t - t - - - 1 t - I - t - I '-'t -4. - 4 4 -- - + -4. - 4 '4. 4 - I - I 4. -, 9 4- I ()- ca- IT -j---r-Fp -v-VI i 24 23 22 21 20 19 I8 r~- u-rT--1-- i 17 -102.0 i fv 16 15 14 19 i i ! i j i ff 1 0 12 11 10 9 8 7 8 5 4 3 2 1 COIL M1 Figure 1.8 Peak Axial Loads For All Current Scenarios Considered -20- x OLL0 JZ; "goA VM" W~ ww w O-00 " 531W3 1d 2 . 1. It~ ; V q, i m e.. a p..1. 'O0e-*at9n4100 I I4 I ,---. 49.6 .I . .. 0' a----. A 49. b -- 31 I i i oW i v v ? X = 0 Plane Y = 0 Plane 1E IN z L La. D I C I I 2 24 23 - . 2 15 i i 2 21 20 19 IS 17 16 15 1 4 13 Figure 1.9 1211 10 9 8 7 8 COIL # 5 4 3 2 1 Peak Radial Loads Per Unit Length For All Current Scenarios -21- 2.0 COIL MD CIR UIT MODELS The individLal coils in the mirror machine were modeled with lumped current filaments made up of piecewise straight segments or sticks. The number of filamer ts used to represent the coil cross-section varied from coil to coil. Fil aments were used in the solenoids for convenience. Checks on the accuracy cf both inductance and force were made using uniform current density s olenoid models. Figure 2.1 shows the typical coil geometries for a C-shaped and solenoid magnet. Also indicated are the necessary inputs to generate a stick model of the coil. Table 2.1 lists the inputs and other critical parameters for each coil in the machine. In addition to the geometry, the table also lists the overall current density, the ampere-turns, the full operating current , the number of turns, the size of the dump resistor, and the coil self-ind uctance. The model usd for both the inductance and force calculations is shown in Figure 2.2. Th! coils WM2, WM1, EM2, and EMI were modeled(aith 6 filaments (2 by 3). The other four C-shaped magnets were modeled with 4 filaments (2 by 2). The central cell solenoids were modeled with 2 filaments (radially). The choke coils each had 4 filaments (2 by 2). Each layer of the larg' solenoids was modeled with 2 filaments (axially). Each filament was brok'n up into 40 sticks for both solenoids and C-shaped magnets. The effect o the number of filaments on the calculation is shown in Figure 2.3. The a:Aal field profile is shown for both the model described above as well as or a single filament model for each coil. Note that the peak field under ,he choke coils decreased from 14.7 to 12.7 T. The primary effect of a finer model is to determine more accurately the peak fields under the choke a8id C-shaped coils. Since the model was to be used for calculating induc lances and fields at the coils, the finer model was used. The fine mod4l was used to construct three force influence coefficient matrices. Each eliment of these 24 by 24 matrices represented the force on a coil (or force 1 er unit length at a point) due to another coil. The terms were per unit curd ent in all coils. Therefore, given a current scenario, the necessary mul iplication yields the axial force. That is: 24 F( )=IVk) Z f(k,j)*I(j), J=1 where I(k) is the current in the kth coil. f(k,j) is the force on coil k per unit current n coil k due to a unit current in coil j. Similar expressions hold for the radial forces per unit length. -22- Magnet Model of a C-Shaped x ROLL y E. G. to get f rom x R2 -z z to x 0=900 ) z d% x PITCH z E.G.to get from x R1 z to x '=180 0 44w z INPUTS C-Shaped: R,R 2 ,dR,dR2 , I PITCH R ROLL Figure 2.l.a C-Shaped Magnet Model -23- Solenoid Input dz r dr r zc VC ___ ___ __i______ INPUTS: zc, rc,dz,dr, Figure 2.1.b Solenoid Magnet -24- Model cnr m nc in ink 0 U" r_ a C 0 qr A 0 0 0 N - 0 0 2~ N L C r in 44i Ln V... 0 0 0D %0 in 44 10 .D 0V. o in 0 0 V. in CD -'," cc- . 0% 0 0 0% %0 0c in co ,PP ON 0) in 0D 0 n in in N~ V. L1 10 . 0 in +1 L n M. 10 o 0 +1 +1 +1 W. 0 0% L. n n 0%Vn in %a co as . n to vi . 0 I" m% m. C0 0DC in CYN CD -a0 tn C; in N' I 0% C- in cr 0, m% 0 a% % 0% ON N 0 E-V~V~ 0 Pr 0D Nl 03 0% 0 W0 + 0% 0 P, ~ CA m 0 0 0, - enV r- in = 0% 0 !- 0% N W; V. "%.% 0% 1M en m i Z 0M -7 0 n N ±1 inM f"4 10 10 o . V.D o . 0 40 0 0D 0 iM 40 in In I in In , VS i N +1 +1 I V) 0 N) -25- - D C o 6 0; 0; 0 (74 0 r)V. N 0 +9 0; W +1 - NL l o CD %a0 in in co NN %0 10 V- +4 0% %0 9%, i enV) +4 in N 10 U) N~ LO .1 + o 2520L 15 101 51 Ck II DCH II COC -511 -10 J -15, -201 -25'L - -- 201 - - +- - -- 10- - +- - - 0- -25 -1-s 5 -5 15 Z Figure 2. 2 Side View of Multiple Filament Model of MFTFB+T -26- 25 111,11.1 Islet aim mess, seem, 15111 ems am imesmi 'ii. v tea,, I Sing e Filament Peak Mult iple Filament Peak, -4 4 N ca - - 4 in - -30 25[ -20 -3-5 -10 -5 0 5 Single Filament 10 15 Z(m) Figure 2.3 Axial Field Profile for Two Models -27- Multiple Filament 20 a, The ax al force calculations are on a coil basis. That is, the J x B body force d nsities are integrated over the coil volume to obtain a total force. The r dial forces, on the other hand, are a local force calculated on a per uni, running length basis. The integrated radial force is, of course, zero The radial forces per unit length were calculated at two points in ea h coil. These points are in the X-0 and Y-0 planes and correspond t local y-directed and x-directed forces, respectively. In a purely solen idal system, these forces (per unit length) would be equal because of t e axial symmetry. The presence of the C-shaped coils perturbs the solenoid 1 nature of the field and produces nonuniform loadings on the "-shaped coi s and on the closest solenoids. The sta ic load analyses discussed in section 3.0 used these matrices along with a static current scenario vector to determine the forces on the coils. An inductance matrix was calculated using the fine model discussed above. This natrix was used in the transient load calculations along with the lumped cilcuit model discussed below. The transient currents were calculated using an eigenvalue/eigenvector expansion for each transient current case. These expansions were used to determine the current versus time behavior of each coil. These current versus time behavior then multiplies thl force influence matrices to get the force versus time. The maximum and minimum forces for each scenario were calculated throughout the transient to determine the extreme loads. The cir uit model for the machine is shown in Figure 2.4. As can be seen there ar, nine independent circuits. The four coils that form the two yin-yang pairs at either end of the machine are on individual circuits. The two transitio (C-shaped) coils at either end are connected across the machine to th mirror image coil at the other end. The ten solenoids are on one circuit. "he two choke coils are on a single circuit as are the two large solenoi s. Also shown are the circuit parameters assumed for the transient ana yses. The only transients considered for this effort were full coil sho ts with all other coils discharging through their individual dump resistor. . Under this assumption the circuits become 24 independent L-R circuits coupled only through the mutuals inductances from coil to coil. -28- MFTB+T £IP CIRCUITS EM2 WM2 0.085 =4403A L = 11.I H Mi EM L=ll.IH TL5 f 0.0444 ETI i'z ~ I 0.085 10 =3872A ET2 L = 0.86H WT I11*=2328 0851 L=2.6 H W2 1 1s WT2 1 A .0_ . -02 ES6 o~ozES5 o.02 * ES4 90.02 ES3 L =16.4 H 10=8000 A ETDFS2 o.125 .125T WTDFS2 H 4.65 x ES2 0.02 o.o2a ES I 0.02 9 WSI 0.02) WS2 0.029 WS3 0.029 WS4 02 9 WS5 1T2 9 L= 5.6 x 10- 4 H 'o = 107'90 4 Lu36HECCI L = 3.6 H lo==1823 WS6 Figure 2.4 0-4 MFTFB+T Circuits and Circuit Parameters -29- 4 - 3.0 MAGNETOSTA IC LOAD ANiALYSES The first Iset of analyses performed investigated the worst case loading on the :oils under various static normal operating conditions. A normal operat in scenario is defined as any combination of one to nine circuits at full current and the remaining circuits at zero current. The data obtained fOom this analysis are summarized in Tables 1.2 and 1.3 and Figures 1.2 and! 1.3. This secti yn presents the loading for a few of the individual current scenarios. The cenarios given are: (1) all circuits at full operating current; and (2 certain circuits at full current with all others at zero current. These Ire not necessarily the worst case scenarios. In the fol owing set of figures, the axial force on each coil is presented in on figure. For scaling purposes, the bars representing the two large solen ids are clipped and the peak values written. The two radial forces per unit length are presented in one figure. The radial force in the X-0 plane i sh wn as a solid line and the force in the Y-0 plane as a dashed line. For coils with little or no difference in the two forces, the dashed line is hidden by the solid one. Shown at the top of each figure is a side view of the machine with the coils numbered. The coils that have zero current are denoted with an asterisk (*). -30- .4 4' * I., . II S a a-I Ul -d S N.4 S tV4m aft 1. aim 0) c SSM- 9 0 'FJ a 0 ft CC *~ aSM 6 Q.33 O CS3 VS3SSI 9S3-U LL. 91. 6L. O U3 ; Z13n z o*aE s.tZ 0~ sc~ aoc scr icv o*s~ u-s s& s.a~ 03 s-c CWJIM) 'U a esm s~ UL a - a C (ts~j) E3 -31- 1 r .... rrT - 3 -, z - - a + -L I I 1 1 1 1 1 1 1 1 1 1 1 1 -I I , 1 1 1 1 1 1 , -4 -4 I., C-, S' zt 8 0 mi N N (4. 4LL LM LIM IL U C,, IISM 9 t'SM L0SM 9 6 '-ri ao'C S'Z a SC S* D*DC 5-tr CWA.&J) O'SrT oo- 'rF Slt WS S.C 0 (U J-1 OL LS3 ZL LL. CS9 Psa 9L LL 6& 9S3 Ili, 1 14 1z L13~ knJ Z1 .4 0 IL 4 8 I-) H .4 X. 4 TT4r IL -32- I em 4 8 - (n3 0 M- it I.. .4 a ZV4M ft 0 g IL 6I 8I 4 ft LILM 0 a U SSM- 9 eSMzSM- 9 6 &OOM 44- c O-OS S -L -sc s-cc roc S-l @-S S-'T 1 S 81 I's a' (W/' ' ) ' ' (1) -it S:1013- CL UL- 9& itL BI. 6L ZS3CS3 IIS39S3OS3 -O &aI U13 E.13 n M3d u ca 0 LL. H Ln Qi. (C M. LL r- V- 07 094) -33- I4 L Ar. -4 C3 a (n bi 0 0 LL -4 I~ N .4 A A I IAJM k LM I... a ) U aIm 9SM ssm t'SM eSM aSMLSM- £ 9 9 L Qo3m L03LS3 L SL. CS-- LL. SS3 9S3 L.L3 --C7- 6t. OZ &Z n z t3 U C 4- A A P 8 6 M LL. Z1 4- FJ LL. 2:_ t, ." 6- 0 SF S'M ,.1.r - iIIIIiI . GAS~ S'L. 0'u s*r 4 . * S-C WT , 0 J2-1 (W/W) £iLUJIiJ2tLI s~ .~ CT 0-s SL ODST o S, 0 c.'J LLL4LL&qLiif~LI±4~LLL1 S71] 7 ILn _________ ~~~1 --1 - ____ 0 8 H U*) (n XL IL----] Tr-ryrlT r T 'I 43 £. i :rr T~r uT~rrr rrr,r e c ip s rrrfrIrIr T o4 (jtA.) -34- rI j ,m r~r C_ TrTT ih-rr 9- rr+rrrrrri S- 9- ., L- a- trrr a-a6 .4 cc3 8 (44-~ 0 r cnr Nw ... .. ... .. W jJL, 0 4. (W/NW) zV4ml~ n 4)~ r.- 9 tSM eSM L &3M 9 a 0& it L333 UT. LL. CL3 153 SS39S3 U53 .4 N oz 91 (.3 LIZZIE 4. '3 IVY3 a U 1~ a a V4 U -J Aa 8 Aa 0 I.- 4. -J -4 a -4 r -4 -4 N ~ UT 0 5 1. 3 S 4. C U I -35- C- 8- p- S- 9- L. . . a- . .rT 0s- at- .rr.rrr. a tn LL.. USE iS 'E S4 'c ~ SC ,r ~T 4s (W/NW a" SL U " - J-- CC%,I ,.x "G.LA S. Iv u 1 LI. -- I.j .4 ft 0I '3 a 'S a S -4 0 LL ~zz 0 T-. M: .4 a IL -I Cl CI +rrrirrr OT 6 a 4 s S v Is ~ rrrhr-rrl-r.T-r-1r 1 v - ,rr I ... I . c .1 I 1 a -36- - 6 . . . . . . . . . . I IJ .4 (n Lid at L) 38 . 0 C .LJ 5c 0 C I 91LM 0~ ssm-.-- flS 9- aaS WAS S*Lc OS S'CC S0oc GIST ICT VI cwW.) SIL crT S* O59 JA 6 ZSM- &SM- ot SIM-1 M9 LL- SA133 - .7s3- CS3 -aS3SS39S3U43 P 9t LL 9L 61& oz* Z1L3n? 1&W.3 u 8t EL -4 in Cc -o m L- s v C. c 7 -7- a r- C- e- -rTT 4 rr+rTr :rT=T rr~ rr~+,r.1T lr-r, 1 or- ', g- L- rr4T-r-rTr, a- f3- or- LL F. . I I -L- .L . -I ' '1 1 1 1 1 1 1 .4 U, 0 a m a .4 Li tL L) F5 I zw LIPM -4 0 9..4 k)j ziLm r_ N £ 0 LIM SSM t'SMESM zsm LSM U 1* St 9 L USE 9 ii'CE 0-0 S'4C 'S S~ s= (W4.&J) 6 01. OfST S'Lr O D*S S4 OOMT ICT S' 4,4 aa -j I cn 4) '4- S:1013 CL. sI LS3- VS3 9S3 Z13 5 L.1 3 - 68t O n ? u c IL iT H 8 C in H- v11e9c I -38- r- a - W- P S- 9- L- 8- 0y- at- . ., ., . . . I.. -4 9, U' rEZZ C Is a a a -a n -I 8 a'. -4 a) &WM LIM U SSM-L IFSM CSM ZSM LSM- S Ir a dl 0 v -r 9 SIX 0,4Zoa S*IZ S' sc a' 9 6 & L S4013- C& Vs3SS39S3 .1.3 aa- IW S*/ 0*9i S.LL .4±4............... .L 9L. 6L. "I I., o U, z Z.i3n LAd3 Os-c JA cv.) .. CS3 a D S'ITGS (W44.4I ft 8 OL LOOM 0 0 a- U a a -4 0 IL a~ .4 -4 I N -.4 a -4 a .4 x C- ft m -4 ft A ft . 01 r- -0 8 L. QT rT-rS W Cr (Ik&4 -39- I III I L-"4-1-"L + A-L 1 4 - -1 --------T- , , .L- 1 --- , . . ! , 1 1 a , r C' 4 C IU U 0 -I L). N U -d It N I-C Cn LL x 0 a .4 0A C' 0 z IJ.M 4 '.4 -r 9 L 9 SSM Vsm CSM zsm 6 tsm OL L& LOOM - S"Z US1 S*4r 006 S= 0' S'lZ OAS Q'T S'LT 0'0-9 S'4 00 S.O WS w U- ZS3 CS3 IPS3 SS3 9S3-U L13 Z1 W - n U 9& Lt. 9L U O L LI + LI Lj. .. i14 LI.I.. s i.LI.fLi LIJ: I IlL I11 ~ LIJLI: iJ..U.I~±.LL±j-4.tILfIJ~LLJ..LL.L4.M ~II' CC C" 4 U z C C N a .4* a .4 0 S '-4 I.- .4 -:4 ----. -..-----.-. -------- - U a -4 U) C .4 02 d LH Lr 1I- ~*1 L TI ~t Ii' I . ~I -. TI ~ L 4 . . . . r . . # . -~ I I FCTv? Ii -. IIrrrI~rTvrrrrTtr yr?: IrIr? ~S~~- -40- V--r, L- ~1 -r-rrr'-rrr 8- d~- 9 4.0 TRAMSIET LOAD ALYSES The transient load analyses consisted of a sequence of runs in which all coils start from a fully charged condition; each coil from I to 12 (1411 to WTDFS2) was assumed to have a short across the entire coil while the other coils are assumed to discharge through their individual dump resistors. The two choke coils are resistive and have an internal resistance rather than an external dump resistor. Figure 2.4 shows the nine independent circuits in the machine. For a discharge scenario, the nine circuits become 24 independent L-R circuits coupled through the coil to coil mutual inductances. The matrix set of first order ordinary differential equations to be solved for the unknown current versus time is given by: [LJ(I(t)) + [RJCI(t)) - (0) where CU is the system inductance matrix. CRJ is a diagonal matrix of coil dump resistors. The initial condition for these runs was that each coil is at full operating current. For a coil short, the dump resistor value in [RJ is replaced by a small number (0 is unacceptable from a numeric standpoint). If the terms in the ELI and ER] matrices are constant, the set can be solved usini3 an eigenvalue/eigenvector approach. The current at any time can then be found from the eigenexpansion. Figure 4.1 shows the set of currents vesus time for the normal discharge case. Only the currents in 1-12 are shown since by symmetry the currents in 13-24 are identical. It can be seen that the current in coil 10 (WS1) initially increases. Because the force on a coil is a product of a row of the influence coefficient matrix and the current vector and then multiplied by the coil current, it is not obvious from the current plot when the peak forces occur. In order to find the peak forces during each scenario, the eigenexpansion was used to calculate currents at various times. The forces were calculated at each of these times and the maximum (positive) and minimum (negative) values found. The forces versus time are shown in Figure 4.2 through 4.4 for the normal discharge case. Only the forces on coils 1-12 are shown. Figure 4.2 shows the peak axial force acting on each coil. It can be seen that certain coils actually experience a force reversal during the discharge (e.g. coil #10, WS6). Figure 4.3 shows the radial forces per unit length acting on the coils in the X=0 plane and Figure 4.4 the radial forces per unit length in the Y=0 plane (dashed lines). -41- x )P Qn( oO)P U)i 1)( Ujw W C4 ~~~wwwuwwwwu1 3 * : i c4 - : 3 cN - r, U) a: H -12 = coil number 2 10 w4 115 0 50 150 100 200 TIME (sec) Figure 4. I Coil Currents vs Time for Normal Discharge -42- 250 T a a a a a * a a C4) 3 4 2 i '.- 1=coil number a 0 50 a a i , I50 -i----i---- 100 . . . --I 200 TIME (sec) Figure 4.2 Coil Axial Forces vs Time for Normal Discharge -43- x w w w LO) LUiWW a - 1 11 cC '-~)cl cC7 4 L 2 = coil number 10 11 0 so 100 150 200 TIME (sec) Figure 4.3 Coil Radial Force Per Unit Length (X = 0) Normal Discharge -44- w W LU C WW'-I. I II I I 1II c I I c: I :: I --- U) Cn C7 Cy z V) 12 L 1f) U, 1 coil number 2 3 1 -J I. 0 50 . 150 100 , , ......... .- 200 TIME (sec) Figure 4.4 Coil Radial Force Per Unit Length (Y = 0 ) Normal Discharge -45- 250 One of the more interesting cases was a short circuit across coil 2 (W14). Them! is a slight radial force reversal in coil #3 (14T2) in the X-0 plane. The current versus time for the coils is shown in Figure 4.5. The net axial load versus time for coils 1-12 is shown in Figure 4.6. The radial force per unit length in the X-0 plane for each of the coils is shown as a Punction of time in Figure 4.7. There is indeed a small reversal for this radial force in coil 3. Figure 4.8 shows the radial force per unit length in the Y-0 plane for coils 1-12. The remaining figures in this section are the peak loads during discharge fOr single coil shorts. The figures have a side view of the machine with coil numbers superimposed at the top. The coil with the short is denoted by an asterisk (*). The case number in the plot title corresponds to the coil with the short. Both the worst case axial forces and radial forces per unit length are shown. The radial force per unit length is the X-0 plane is denoted by a solid line; the the force per unit length in the Y-0 plane by a dashed line. The worst case loadings across all transient runs are summarized in Tables 1.7 and 1.8 and in Figures 1.7 and 1.8. -46- U N Cq N - N IL w w Wwwwwwww W Nv q, W 01 a * * * S* I i i m I * - Hc coI .4 . . I 0 so 100 .SO 200 250 TIME (sec) Figure 4.5 Coil Currents vs Time for Coil #2 Short-Circuited, All Others Discharging -47- "i n v)--94r. Q C I CA co 3 A. '"I 1 1-... .. . .. N 21 I If 50 0 Figure 4.15 100 150 TIME (sec) 200 250 Coil Axial Forces vs Time for Coil #2 Short-Circuited; All Others Discharging -48- CY C-C4 -V- N Cy I- - V- C) 9- 1 - V- i . , I I II In In In - 1-2 in 0 E 1 L- L. U, .1 7 1T vi 0n C; .3 1 0 50 £50 100 200 TIME (sec) Figure 4.7 Coil Radial Forces Per Unit Length (X = 0 Plane) for Coil #2 Short-Circuited; All Others Discharging -49- 3m ,I (f~ cfO( c-nn(j( c44 11*0 N' 44 qcm 14 0 4*4-OSSi.IDeOY ~ I- "00eP-ND law*t in in S U) in 2 In L 1 C2 C,' U, 'A 0 - - , I .0 I 82.5 I S S I *, 125.0 I I * 187.5 a -r - 2 0.0 TIME (sec) Figure 4.8 Coil Radial Forces Per Unit Length (Y = 0 Plane) for Coil #2 Short-Circuited; All Others Discharging -50- lit .4 QU -c - sWm lm U C0 LI EL S.-S 0-06 SL4Z 0*Sr S'CC nVaC STOST s-ra 'CT L 0 S*C I m SU/W~) J-1 CL &SM L3SM 911 LL ESM ZSM 93 S'a 0 - LDD3 611, oz LI. +LLLLSI U53 LLI+J-LL+ J-L+L" . LWS3U Z W3 k" Li C, LDI- i L.. J 8 r~rr-r" -,T,,N ... 1.rr+TZ,7 II I.1~ ON&) Z j ft *3 1' * .4 WI 0 4,- a a a.0 :1 8 tL -I 1'. M- .4 a U -o aft 1J.M 0* 9 tiM U io ft -s 9SMssmVSMeSMaSMtSM- 1r ri? 9 L 9 6 OI s-~ oas S*~ os~ s~ an~ *5~ SLT CW44.d) scr St CIT IS s-c cm .34 Lt *am sAIalm- U S~IO.3 t333 .Sa- UI - LL. 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CW/W LiLm Uv SSM CSM- 9 a IL- 6 0& ZSM &SMLOOM U L 4 S:1a13 CL iS3CS3 VS3SS3 9S3 S& - A..JLJ.4LLLL -4 LL. (4 Si 6L U) z U, LL~iLj.JL.L~i1I.......................... L1 U U LZ p. U U a -771 -I .4! 8 .CD .~ .4 A -S N -- 4 .5 .5a 's 'V A il-I -rrrTTrrrTl 1 r1-y-j-1-rrrrrr,......................................... WTr rrf 9h rrrs (NW)~ Z 3 -62- I I t e .1 ,I ~1 L*1 4 I' Ni a In T I.. U a .4 IL ~z. I- 8 -j -4 U- e-, S.- EC 0 U U. U.M C*-c 9 L 9 SSM t'SM CSM 7SM t33M a 5S S G sc L s,= S'ITa '*ST aO S*C G*I SIL 0" S*T 810 .Uj (W/MNW) 6 -Lt. S.- sd0J.3 CL LL CS3 GS3 9S3 L13 - -.4 z Z1 LV43 61. O L U C2 LU CD. I- L- 8 'r ... 'rTrrT~rT -4TTLTrr rj T-rrrT e c C- S- OW C H I.IL -63- T4. rr'7'. rrT r-Y q- 0 Z I L- HTT T"r r-r rT - a ir 5.0 CONCLUSIOI5 A large number of possible normal operating and fault conditions for the MFTFB+T mirror machine have been investigated to estimate the worst case coil loadings. The results from these analyses are summarized in section 1.0. More detailed results are presented in sections 2.0 through 4.0. In general, the four C-shaped magnets at each machine end (W112, WMi, WT2,and WT1) experience the worst case loading under static current conditions. The central cell solenoids (WS6, WS5, WS4, and WS3) experience peak loads during discharge transients with a neighboring coil shortcircuited. The coils at the machine center (WS2, WSI, WCC1, WTDFS2, etc.) have peak axial loads that occur primarily in the static condition. However, the peak radial loads occur during the discharge transients. The axial loading investigated was the net force on a coil and tells nothing of the distribution of the load. The radial loading was considered at two points within the coils as an indicator of when the worst case load probably occuro. The load conditions are predicated on a certain coil/circuit configuration. If this configuration changes or if a coil operating current is altered, the new static and transient load scenarios should be reconsidered. The current scenarios chosen for the analyses were by no means exhaustive from a fault condition standpoint. An entire class of faults which requires consideration involves system behavior during discharge execution with a section of one of the superconducting coils in the resistive state. Even though the coils are designed to be stable under usual conditions, that is complete LHe coolant immersion, a resistive region is possible in the event of a fault in the form of a low helium level. The temperature rise in a resistive region which is not immersed is strongly dependent on the coupled discharge character of the circuits and the level of operating current and dump voltage selected. -64- PFC BASE MAILING LIST Argonne National lahoratory, TIS, Reports Section Associazione EURATOM - CNEN Fusione, Italy, The Librarian CRPP, Switzerland, Troqon, Prof. F. Central Research Institute for Physics, Hungary, Preprint Library Chinese Academy of Sciences, China, The Library Eindhoven University of Technology, Netherlands, Schram, Prof. D. C The Flinders University of S.A., Australia, Jones, Prof. I.R. General Atomic Co., Overskei, Dr. D. International Atomic Energy Agency. Austria, Israel Atomic Energy Commission, Soreq Nucl. Res. Ctr., Israel JET, England, Gondhaltkar, Dr. A. Kernforschungsanlage Julich, FRG, Zentralbibliothek Kyushu University, Japari, Library Max-Planck-Inslitut fur Plasma Physik, FRG, Main Library Nagoya University, Institute of Plasma Physics, Japan Physical Research Laboratory, India. Sen, Dr. Abhijit Rensselaer Polytechnic bistitute, Plasma Dynamics Iab. South African Atomic Eiergy Board, S. Africa, Hayzen, Dr. A. UKAEA, Culham Laboratory, United Kingdom, Librarian Universite de Montreal, Lab. de Physique des Plasmas, Ca..ada University of Innsbruck, Inst. of Theoretical Physics, Austria University of Saskatchewan. Plasma Physics Lab., Canada University of Sydney. Wlls Plasma Physics Dept., Australia INTERNAL MAILINGS MIT libraries Industrial Liaison Office G. Bekefi, A. Bers, D. Cohn, B. Coppi, R.C. Davidson, T. Dupree, S. Foner, J. Freidberg, M.O. Hoenig, M. Kazimi, L. Lidsky, E. Marmar, J. McCune, J. Meyer, D.B. Montgomery, J. Moses, D. Pappas, R.IL Parker, N.T. Pierce, P. Politzer, M. Porkolab, R. Post, II Praddaude, D. Rose, J.C. Rose, R.M. Rose, B.B. Schwartz, R. Temkin, P. Wolff, T-F. Yang I