Unit 10 Electro-magnetic forces and stresses in superconducting accelerator magnets
|
|
|
- Rosalind Hancock
- 5 years ago
- Views:
Transcription
1 Uit Electo-mgetic oces d stesses i supecoductig cceleto mgets Soe Pestemo Lwece ekeley Ntiol Lbotoy (LNL) Polo Feci d Ezio Todesco Euope Ogiztio o Nucle Resech (CERN)
2 Outlie. Itoductio. Electo-mgetic oce. Deiitio d diectios. Mgetic pessue d oces. Appoximtios o pcticl widig coss-sectios. Thi shell, Thick shell, Secto 5. Stoed eegy d ed oces 6. Stess d sti 7. Pe-stess 8. Coclusios Supecoductig Acceleto Mgets, ue -6, 5. Electomgetic oces d stesses i supecoductig cceleto mgets
3 Reeeces [] Y. Iws, Cse studies i supecoductig mgets, New Yok, Pleum Pess, 99. [] M. Wilso, Supecoductig mgets, Oxod UK: Cledo Pess, 98. [] A.V. Tollestup, Supecoductig mget techology o cceletos, A. Reo. Nucl. Pt. Sci. 98., 7-8. [] K. Koepke, et l., Femilb double mget desig d bictio techiques, IEEE Ts. Mg., Vol. MAG-5, No. l, uy 979. [5] S. Wol, Supecoductig mget desig, AIP Coeece Poceedigs 9, edited by M. Moth d M. Diees, 99, pp [6] A. Deved, The mechics o SSC dipole mget pototypes, AIP Coeece Poceedigs 9, edited by M. Moth d M. Diees, 99, p [7] T. Ogitsu, et l., Mechicl peomce o 5-cm-petue, 5-m- log SSC dipole mget pototypes, IEEE Ts. Appl. Supecod., Vol., No. l, Mch 99, p [8]. Mutoe, NL, pivte commuictios. [9] LHC desig epot v.: the mi LHC ig, CERN---v-,. []A.V. Tollestup, Ce d tiig i supecoductig mgets, IEEE Ts. Mg.,Vol. MAGN-7, No. l, uy 98, p [] N. Adeev, K. Atoos, E. Csejos, T. Kutyk, C. Rthje, D. Peii, N. Siegel, D. Tommsii, I. Vekov, MT 5 (997) LHC PR 79. Supecoductig Acceleto Mgets, ue -6, 5. Electomgetic oces d stesses i supecoductig cceleto mgets
4 . Itoductio Supecoductig cceleto mgets e chcteized by high ields d high cuet desities. As esults, the coil is subjected to stog electo-mgetic oces, which ted to move the coducto d deom the widig. A good kowledge o the mgitude d diectio o the electomgetic oces, s well s o the stess o the coil, is mdtoy o the mechicl desig o supecoductig mget. I this uit we will descibe the eect o these oces o the coil though simpliied ppoximtio o pcticl widig, d we will itoduced the cocept o pe-stess, s wy to mitigte thei impct o mget peomce. Supecoductig Acceleto Mgets, ue -6, 5. Electomgetic oces d stesses i supecoductig cceleto mgets
5 . Electo-mgetic oce Deiitio I the pesece o mgetic ield (iductio), electic chged pticle q i motio with velocity v is cted o by oce F L clled electo-mgetic (Loetz) oce [N]: F L qv A coducto elemet cyig cuet desity (A/mm ) is subjected to oce desity L [N/m ] L The e.m. oce ctig o coil is body oce, i.e. oce tht cts o ll the potios o the coil (like the gvittiol oce). Supecoductig Acceleto Mgets, ue -6, 5. Electomgetic oces d stesses i supecoductig cceleto mgets 5
6 . Electo-mgetic oce Dipole mgets The e.m. oces i dipole mget ted to push the coil Towds the mid-ple i the veticl-zimuthl diectio (F y, F < ) Outwds i the dil-hoizotl diectio (F x, F > ) Tevto dipole HD Supecoductig Acceleto Mgets, ue -6, 5. Electomgetic oces d stesses i supecoductig cceleto mgets 6
7 . Electo-mgetic oce Qudupole mgets The e.m. oces i qudupole mget ted to push the coil Towds the mid-ple i the veticl-zimuthl diectio (F y, F < ) Outwds i the dil-hoizotl diectio (F x, F > ) TQ HQ Supecoductig Acceleto Mgets, ue -6, 5. Electomgetic oces d stesses i supecoductig cceleto mgets 7
8 . Electo-mgetic oce Ed oces i dipole d qudupole mgets I the coil eds the Loetz oces ted to push the coil Outwds i the logitudil diectio (F z > ) Similly s o the soleoid, the xil oce poduces xil tesio i the coil stight sectio. Supecoductig Acceleto Mgets, ue -6, 5. Electomgetic oces d stesses i supecoductig cceleto mgets 8
9 . Electo-mgetic oce Ed oces i dipole d qudupole mgets Nb-Ti LHC M (vlues pe petue) F x = t pe mete ~ compct cs Pecisio o coil positioig: -5 μm F z = 7 t ~weight o the cold mss Nb S dipole (HD) F x = 5 t pe mete F z = 85 t These oces e pplied to objet with coss-sectio o 5x mm!!! d by the wy, it is bittle Supecoductig Acceleto Mgets, ue -6, 5. Electomgetic oces d stesses i supecoductig cceleto mgets 9
10 . Electo-mgetic oce Soleoids The e.m. oces i soleoid ted to push the coil Outwds i the dil-diectio (F > ) Towds the mid ple i the veticl diectio (F y < ) Impott dieece betwee soleoids d dipole/qudupole mgets I dipole/qudupole mget the hoizotl compoet pushes outwdly the coil The oce must be tseed to suppot stuctue I soleoid the dil oce poduces cicumeetil hoop stess i the widig The coducto, i piciple, could suppot the oces with ectig tesio Supecoductig Acceleto Mgets, ue -6, 5. Electomgetic oces d stesses i supecoductig cceleto mgets
11 Outlie. Itoductio. Electo-mgetic oce. Deiitio d diectios. Mgetic pessue d oces. Appoximtios o pcticl widig coss-sectios. Thi shell, Thick shell, Secto 5. Stoed eegy d ed oces 6. Stess d sti 7. Pe-stess 8. Coclusios Supecoductig Acceleto Mgets, ue -6, 5. Electomgetic oces d stesses i supecoductig cceleto mgets
12 . Mgetic pessue d oces The mgetic ield is ctig o the coil s pessuized gs o its cotie. Let s coside the idel cse o iiitely log thi-wlled soleoid, with thickess d, dius, d cuet desity θ. The ield outside the soleoid is zeo. The ield iside the soleoid is uiom, diected log the soleoid xis d give by The ield iside the widig deceses liely om t to zeo t +. The vege ield o the coducto elemet is /, d the esultig Loetz oce is dil d give by L i o i Supecoductig Acceleto Mgets, ue -6, 5. Electomgetic oces d stesses i supecoductig cceleto mgets
13 . Mgetic pessue d oces We c theeoe deie mgetic pessue p m ctig o the widig suce elemet: L zi p m zi whee p m So, with T mget, the widigs udego pessue p m = ( )/( -7 ) = 7 P = 9 tm. The oce pessue icese with the sque o the ield. A pessue [N/m ] is equivlet to eegy desity [/m ]. Supecoductig Acceleto Mgets, ue -6, 5. Electomgetic oces d stesses i supecoductig cceleto mgets
14 Outlie. Itoductio. Electo-mgetic oce. Deiitio d diectios. Mgetic pessue d oces. Appoximtios o pcticl widig coss-sectios. Thi shell, Thick shell, Secto 5. Stoed eegy d ed oces 6. Stess d sti 7. Pe-stess 8. Coclusios Supecoductig Acceleto Mgets, ue -6, 5. Electomgetic oces d stesses i supecoductig cceleto mgets
15 . Appoximtios o pcticl widig coss-sectios I ode to estimte the oce, let s coside thee dieet ppoximtios o -ode mget Thi shell (see Appedix I) Cuet desity = cos (A pe uit cicumeece) o iiitely thi shell Odes o mgitude d popotiolities Thick shell (see Appedix II) Cuet desity = cos (A pe uit e) o shell with iite thickess Fist ode estimte o oces d stess Secto (see Appedix III) Cuet desity = cost (A pe uit e) o secto with mximum gle = 6º/º o dipole/qudupole Fist ode estimte o oces d stess Supecoductig Acceleto Mgets, ue -6, 5. Electomgetic oces d stesses i supecoductig cceleto mgets 5
16 . Appoximtios o pcticl widig coss-sectios: thi shell We ssume = cos whee [A/m] is to the coss-sectio ple Rdius o the shell/coil = No io The ield iside the petue is i si The vege ield i the coil is The Loetz oce ctig o the coil [N/m ] is x i si cos si cos si cos y si cos Supecoductig Acceleto Mgets, ue -6, 5. Electomgetic oces d stesses i supecoductig cceleto mgets 6
17 . Appoximtios o pcticl widig coss-sectios: thi shell (dipole) I dipole, the ield iside the coil is y The totl oce ctig o the coil [N/m] is F x y F y y The Loetz oce o dipole coil vies with the sque o the boe ield liely with the mgetic pessue liely with the boe dius. I igid stuctue, the oce detemies zimuthl displcemet o the coil d cetes septio t the pole. The stuctue sees F x. Supecoductig Acceleto Mgets, ue -6, 5. Electomgetic oces d stesses i supecoductig cceleto mgets 7
18 . Appoximtios o pcticl widig coss-sectios: thi shell (qudupole) I qudupole, the gdiet [T/m] iside the coil is G The totl oce ctig o the coil [N/m] is c F x c 5 G 5 F y c 8 5 G 8 5 The Loetz oce o qudupole coil vies with the sque o the gdiet o coil pek ield with the cube o the petue dius (o ixed gdiet). Keepig the pek ield costt, the oce is popotiol to the petue. Supecoductig Acceleto Mgets, ue -6, 5. Electomgetic oces d stesses i supecoductig cceleto mgets 8
19 . Appoximtios o pcticl widig coss-sectios: thick shell We ssume = cos whee [A/m ] is to the coss-sectio ple Ie (oute) dius o the coils = () No io The ield iside the petue is The ield i the coil is The Loetz oce ctig o the coil [N/m ] is Supecoductig Acceleto Mgets, ue -6, 5. Electomgetic oces d stesses i supecoductig cceleto mgets 9 i si i cos si cos cos cos si si cos x cos si y
20 . Appoximtios o pcticl widig coss-sectios: secto (dipole) We ssume = is the coss-sectio ple Ie (oute) dius o the coils = () Agle = 6º (thid hmoic tem is ull) No io The ield iside the petue The ield i the coil is Supecoductig Acceleto Mgets, ue -6, 5. Electomgetic oces d stesses i supecoductig cceleto mgets si si si si cos si cos si si si si si cos si cos si
21 . Appoximtios o pcticl widig coss-sectios: compiso NbS ss mu.566e-6 A/m 86 lmbd. A/m sc 7 A/mm sc 7 m. m.55 m w.5 T.75 pek/. T pek.75 N/m Fx (qud) 7 N/m Fy (qud) - N/m Fx tot 8666 NbS ss mu.566e-6 Degee lph 6 A/m 786 lmbd. A/m sc 565 A/mm sc 56 m. m.555 m w.55 T.75 pek/. T pek. N/m Fx (qud) 5969 N/m Fy (qud) N/m Fx tot 7879 Roxie mu.566e-6 Degee lph A/m 796 lmbd. A/m sc A/mm sc 56 m. m.598 m w.98 T.7699 pek/.959 T pek.787 N/m Fx (qud) 7 N/m Fy (qud) -96 N/m Fx tot 85 Supecoductig Acceleto Mgets, ue -6, 5. Electomgetic oces d stesses i supecoductig cceleto mgets
22 Outlie. Itoductio. Electo-mgetic oce. Deiitio d diectios. Mgetic pessue d oces. Appoximtios o pcticl widig coss-sectios. Thi shell, Thick shell, Secto 5. Stoed eegy d ed oces 6. Stess d sti 7. Pe-stess 8. Coclusios Supecoductig Acceleto Mgets, ue -6, 5. Electomgetic oces d stesses i supecoductig cceleto mgets
23 5. Stoed eegy d ed oces The mgetic ield possesses eegy desity [/m ] U The totl eegy [] is give by E dv ll _ spce O, cosideig oly the coil volume, by E A jdv V Kowig the iductce L, it c lso be expesses s E LI The totl eegy stoed is stogly elted to mechicl d potectio issues. Supecoductig Acceleto Mgets, ue -6, 5. Electomgetic oces d stesses i supecoductig cceleto mgets
24 5. Stoed eegy d ed oces The stoed eegy c be used to evlute the Loetz oces. I ct F E This mes tht, cosideig log mget, oe c compute the ed oce F z [N] om the stoed eegy pe uit legth W [/m]: W whee A Z is the vecto potetil, give by F E F z E z Az jda coil _ e z LI zm A z,, A z Supecoductig Acceleto Mgets, ue -6, 5. Electomgetic oces d stesses i supecoductig cceleto mgets
25 5. Stoed eegy d ed oces Thi shell Fo dipole, the vecto potetil withi the thi shell is d, theeoe, The xil oce o dipole coil vies with the sque o the boe ield liely with the mgetic pessue with the sque o the boe dius. Fo qudupole, the vecto potetil withi the thi shell is d, theeoe, A z A z F z y cos c Fz eig the pek ield the sme, qudupole hs hl the F z o dipole. cos G Supecoductig Acceleto Mgets, ue -6, 5. Electomgetic oces d stesses i supecoductig cceleto mgets 5
26 Outlie. Itoductio. Electo-mgetic oce. Deiitio d diectios. Mgetic pessue d oces. Appoximtios o pcticl widig coss-sectios. Thi shell, Thick shell, Secto 5. Stoed eegy d ed oces 6. Stess d sti 7. Pe-stess 8. Coclusios Supecoductig Acceleto Mgets, ue -6, 5. Electomgetic oces d stesses i supecoductig cceleto mgets 6
27 6. Stess d sti Deiitios A stess o [P] is itel distibutio o oce [N] pe uit e [m ]. Whe the oces e pepedicul to the ple the stess is clled oml stess () ; whe the oces e pllel to the ple the stess is clled she stess (). Stesses c be see s wy o body to esist the ctio (compessio, tesio, slidig) o extel oce. A sti (l/l ) is oced chge dimesio l o body whose iitil dimesio is l. A stetch o shoteig e espectively tesile o compessive sti; gul distotio is she sti. Supecoductig Acceleto Mgets, ue -6, 5. Electomgetic oces d stesses i supecoductig cceleto mgets 7
28 6. Stess d sti Deiitios The elstic modulus (o Youg modulus, o modulus o elsticity) E [P] is pmete tht deies the stiess o give mteil. It c be expessed s the te o chge i stess with espect to sti (Hook s lw): = /E The Poisso s tio is the tio betwee xil to tsvesl sti. Whe body is compessed i oe diectio, it teds to elogte i the othe diectio. Vice ves, whe body is elogted i oe diectio, it teds to get thie i the othe diectio. = - xil / ts Supecoductig Acceleto Mgets, ue -6, 5. Electomgetic oces d stesses i supecoductig cceleto mgets 8
29 6. Stess d sti Deiitios y combiig the pevious deiitios, o bixil stess stte we get d x x x E E y E x y Compessive stess is egtive, tesile stess is positive. The Poisso s tio couples the two diectios A stess/sti i x lso hs eect i y. Fo give stess, the highe the elstic modulus, the smlle the sti d displcemet. y y E y E x E y x Supecoductig Acceleto Mgets, ue -6, 5. Electomgetic oces d stesses i supecoductig cceleto mgets 9
30 6. Stess d sti Filue/yield citei The popotiolity betwee stess d sti is moe complicted th the Hook s lw A: limit o popotiolity (Hook s lw) : yield poit Pemet deomtio o. % C: ultimte stegth D: ctue poit Sevel ilue citei e deied to estimte the ilue/yield o stuctul compoets, s Equivlet (Vo Mises) stess v yield, whee v Supecoductig Acceleto Mgets, ue -6, 5. Electomgetic oces d stesses i supecoductig cceleto mgets
31 6. Stess d sti Mechicl desig piciples The e.m oces push the coducto towds mid-ples d suppotig stuctue. The esultig sti is idictio o chge i coil shpe eect o ield qulity displcemet o the coducto potetil elese o ictiol eegy d cosequet quech o the mget The esultig stess must be ceully moitoed I Nb-Ti mgets, possible dmge o kpto isultio t bout 5- MP. I Nb S mgets, possible coducto degdtio t bout 5- MP. I geel, l the compoets o the suppot stuctue must ot exceed the stess limits. Mechicl desig hs to ddess ll these issues. Supecoductig Acceleto Mgets, ue -6, 5. Electomgetic oces d stesses i supecoductig cceleto mgets
32 6. Stess d sti Mechicl desig piciples LHC dipole t T LHC dipole t 9 T Displcemet sclig = 5 Usully, i dipole o qudupole mget, the highest stesses e eched t the mid-ple, whee ll the zimuthl e.m. oces ccumulte (ove smll e). Supecoductig Acceleto Mgets, ue -6, 5. Electomgetic oces d stesses i supecoductig cceleto mgets
33 6. Stess d sti Thick shell Stess o mid-ple (MP) Fo dipole, Fo qudupole, 57.8 midd ( ) _ mid ple_ v / d 5 l 6 6 _ mid ple _ mid ple_ v / d l 7 9 l _ mid ple Rdius (m) Supecoductig Acceleto Mgets, ue -6, 5. Electomgetic oces d stesses i supecoductig cceleto mgets No she
34 Outlie. Itoductio. Electo-mgetic oce. Deiitio d diectios. Mgetic pessue d oces. Appoximtios o pcticl widig coss-sectios. Thi shell, Thick shell, Secto 5. Stoed eegy d ed oces 6. Stess d sti 7. Pe-stess 8. Coclusios Supecoductig Acceleto Mgets, ue -6, 5. Electomgetic oces d stesses i supecoductig cceleto mgets
35 7. Pe-stess A.V. Tollestup, [] Supecoductig Acceleto Mgets, ue -6, 5. Electomgetic oces d stesses i supecoductig cceleto mgets 5
36 7. Pe-stess Tevto mi dipole Let s coside the cse o the Tevto mi dipole ( om =. T). I iiitely igid stuctue without pe-stess the pole would move o bout - m, with stess o the mid-ple o -5 MP. Supecoductig Acceleto Mgets, ue -6, 5. Electomgetic oces d stesses i supecoductig cceleto mgets 6
37 7. Pe-stess Tevto mi dipole We c plot the displcemet d the stess log pth movig om the mid-ple to the pole. I the cse o o pe-stess, the displcemet o the pole duig excittio is bout - m. Supecoductig Acceleto Mgets, ue -6, 5. Electomgetic oces d stesses i supecoductig cceleto mgets 7
38 7. Pe-stess Tevto mi dipole We ow pply to the coil pe-stess o bout - MP, so tht o septio occus t the pole egio. The displcemet t the pole duig excittio is ow egligible, d, withi the coil, the coductos move t most o - m. Supecoductig Acceleto Mgets, ue -6, 5. Electomgetic oces d stesses i supecoductig cceleto mgets 8
39 7. Pe-stess Tevto mi dipole We ocus ow o the stess d displcemet o the pole tu (high ield egio) i dieet pe-stess coditios. The totl displcemet o the pole tu is popotiol to the pe-stess. A ull pe-stess coditio miimizes the displcemets. Supecoductig Acceleto Mgets, ue -6, 5. Electomgetic oces d stesses i supecoductig cceleto mgets 9
40 No pe-stess, o e.m. oce Displcemet sclig = 5 Supecoductig Acceleto Mgets, ue -6, 5. Electomgetic oces d stesses i supecoductig cceleto mgets
41 No pe-stess, with e.m. oce Displcemet sclig = 5 About μm o Tevto mi dipole ( om =. T) Supecoductig Acceleto Mgets, ue -6, 5. Electomgetic oces d stesses i supecoductig cceleto mgets
42 Pe-stess, o e.m. oce Pole shim Displcemet sclig = 5 Supecoductig Acceleto Mgets, ue -6, 5. Electomgetic oces d stesses i supecoductig cceleto mgets
43 Pe-stess, with e.m. oce Pole shim Displcemet sclig = 5 Coil pe-stess pplied to ll the cceleto dipole mgets Supecoductig Acceleto Mgets, ue -6, 5. Electomgetic oces d stesses i supecoductig cceleto mgets
![Tevto [] HERA [5] SSC [6]-[7] RHIC [8] LHC [9] The pe-stess is](/docs-images/89/98622064/images/44-3.jpg "chose i such wy tht the coil emis i cotct with the pole t omil")
44 7. Pe-stess Oveview o cceleto dipole mgets The pctice o pe-stessig the coil hs bee pplied to ll the cceleto dipole mgets Tevto [] HERA [5] SSC [6]-[7] RHIC [8] LHC [9] The pe-stess is chose i such wy tht the coil emis i cotct with the pole t omil ield, sometime with mechicl mgi o moe th MP. Supecoductig Acceleto Mgets, ue -6, 5. Electomgetic oces d stesses i supecoductig cceleto mgets
45 7. Pe-stess Geel cosidetios As we poited out, the pestess educes the coil motio duig excittio. This esue tht the coil boudies will ot chge s we mp the ield, d, s esults, mio ield qulity petubtios will occu. Wht bout the eect o pestess o quech peomce? I piciple less motio mes less ictiol eegy dissiptio o esi ctue. Nevetheless the impct o pestess o quech iititio emis cotovesil Supecoductig Acceleto Mgets, ue -6, 5. Electomgetic oces d stesses i supecoductig cceleto mgets 5
46 7. Pe-stess Expeiece i Tevto Above movemets o. mm, thee is coeltio betwee peomce d movemet: the lge the movemet, the loge the tiig. mm Coclusio: oe hs to pe-stess to void movemets tht c limit peomce A.V. Tollestup, [] Supecoductig Acceleto Mgets, ue -6, 5. Electomgetic oces d stesses i supecoductig cceleto mgets 6
47 7. Pe-stess Expeiece i LHC shot dipoles Study o vitio o pe-stess i sevel models evidece o ulodig t 75% o omil, but o quech N. Adeev, [] It is woth poitig out tht, i spite o the complete ulodig o the ie lye t low cuets, both low pestess mgets showed coect peomce d queched oly t much highe ields Supecoductig Acceleto Mgets, ue -6, 5. Electomgetic oces d stesses i supecoductig cceleto mgets 7
48 7. Pe-stess Expeiece i LARP TQ qudupole With low pe-stess, ulodig but still good quech peomce With high pe-stess, stble plteu but smll degdtio TQS low pestess TQSb high pestess Supecoductig Acceleto Mgets, ue -6, 5. Electomgetic oces d stesses i supecoductig cceleto mgets 8
49 8. Coclusios We peseted the oce poiles i supecoductig mgets A soleoid cse c be well epeseted s pessue vessel I dipole d qudupole mgets, the oces e diected towds the mid-ple d outwdly. They ted to septe the coil om the pole d compess the mid-ple egio Axilly they ted to stetch the widigs We povided seies o lyticl omuls to detemie i ist ppoximtio oces d stesses. The impotce o the coil pe-stess hs bee poited out, s techique to miimize the coducto motio duig excittio. Supecoductig Acceleto Mgets, ue -6, 5. Electomgetic oces d stesses i supecoductig cceleto mgets 9
50 Appedix I Thi shell ppoximtio Supecoductig Acceleto Mgets, ue -6, 5. Electomgetic oces d stesses i supecoductig cceleto mgets 5
51 Appedix I: thi shell ppoximtio Field d oces: geel cse We ssume = cos whee [A/m] is Rdius o the shell/coil = No io The ield iside the petue is i si The vege ield i the coil is to the coss-sectio ple The Loetz oce ctig o the coil [N/m ] is x i si cos si cos si cos y si cos Supecoductig Acceleto Mgets, ue -6, 5. Electomgetic oces d stesses i supecoductig cceleto mgets 5
52 Appedix I: thi shell ppoximtio Field d oces: dipole I dipole, the ield iside the coil is y The totl oce ctig o the coil [N/m] is F x y F y y The Loetz oce o dipole coil vies with the sque o the boe ield liely with the mgetic pessue liely with the boe dius. I igid stuctue, the oce detemies zimuthl displcemet o the coil d cetes septio t the pole. The stuctue sees F x. Supecoductig Acceleto Mgets, ue -6, 5. Electomgetic oces d stesses i supecoductig cceleto mgets 5
53 Appedix I: thi shell ppoximtio Field d oces: qudupole I qudupole, the gdiet [T/m] iside the coil is G The totl oce ctig o the coil [N/m] is c F x c 5 G 5 F y c 8 5 G 8 5 The Loetz oce o qudupole coil vies with the sque o the gdiet o coil pek ield with the cube o the petue dius (o ixed gdiet). Keepig the pek ield costt, the oce is popotiol to the petue. Supecoductig Acceleto Mgets, ue -6, 5. Electomgetic oces d stesses i supecoductig cceleto mgets 5
54 Appedix I: thi shell ppoximtio Stoed eegy d ed oces: dipole d qudupole Fo dipole, the vecto potetil withi the thi shell is d, theeoe, The xil oce o dipole coil vies with the sque o the boe ield liely with the mgetic pessue with the sque o the boe dius. Fo qudupole, the vecto potetil withi the thi shell is d, theeoe, A z A z F z y cos c Fz eig the pek ield the sme, qudupole hs hl the F z o dipole. cos G Supecoductig Acceleto Mgets, ue -6, 5. Electomgetic oces d stesses i supecoductig cceleto mgets 5
55 Appedix I: thi shell ppoximtio Totl oce o the mid-ple: dipole d qudupole I we ssume om ch coditio, whee ll the θ ccumultes o the mid-ple, we c compute totl oce tsmitted o the mid-ple F θ [N/m] Fo dipole, Fo qudupole, F y d F c d G eig the pek ield the sme, qudupole hs hl the F θ o dipole. Keepig the pek ield costt, the oce is popotiol to the petue. Supecoductig Acceleto Mgets, ue -6, 5. Electomgetic oces d stesses i supecoductig cceleto mgets 55
56 Appedix II Thick shell ppoximtio Supecoductig Acceleto Mgets, ue -6, 5. Electomgetic oces d stesses i supecoductig cceleto mgets 56
57 Appedix II: thick shell ppoximtio Field d oces: geel cse We ssume = cos whee [A/m ] is to the coss-sectio ple Ie (oute) dius o the coils = () No io The ield iside the petue is The ield i the coil is The Loetz oce ctig o the coil [N/m ] is Supecoductig Acceleto Mgets, ue -6, 5. Electomgetic oces d stesses i supecoductig cceleto mgets 57 i si i cos si cos cos cos si si cos x cos si y
58 Appedix II: thick shell ppoximtio Field d oces: dipole I dipole, the ield iside the coil is The totl oce ctig o the coil [N/m] is Supecoductig Acceleto Mgets, ue -6, 5. Electomgetic oces d stesses i supecoductig cceleto mgets 58 y l F x l 9 7 F y
59 Appedix II: thick shell ppoximtio Field d oces: qudupole I qudupole, the ield iside the coil is G y l beig l The totl oce ctig o the coil [N/m] is F x l 5 F y l Supecoductig Acceleto Mgets, ue -6, 5. Electomgetic oces d stesses i supecoductig cceleto mgets 59
60 Appedix II: thick shell ppoximtio Stoed eegy, ed oces: dipole d qudupole Fo dipole, d, theeoe, Fo qudupole, d, theeoe, Supecoductig Acceleto Mgets, ue -6, 5. Electomgetic oces d stesses i supecoductig cceleto mgets 6 cos A z 6 F z cos l A z l 8 8 F z
61 Stess o mid-ple (MP) Appedix II: thick shell ppoximtio Stess o the mid-ple: dipole d qudupole Fo dipole, Fo qudupole, 57.8 midd ( ) _ mid ple_ v / d 5 l 6 6 _ mid ple / l d 7 9 v l _ mid ple _ mid ple_ Rdius (m) Supecoductig Acceleto Mgets, ue -6, 5. Electomgetic oces d stesses i supecoductig cceleto mgets 6 No she
62 Appedix III Secto ppoximtio Supecoductig Acceleto Mgets, ue -6, 5. Electomgetic oces d stesses i supecoductig cceleto mgets 6
63 Appedix III: secto ppoximtio Field d oces: dipole We ssume = is the coss-sectio ple Ie (oute) dius o the coils = () Agle = 6º (thid hmoic tem is ull) No io The ield iside the petue The ield i the coil is Supecoductig Acceleto Mgets, ue -6, 5. Electomgetic oces d stesses i supecoductig cceleto mgets 6 si si si si cos si cos si si si si si cos si cos si
64 Appedix III: secto ppoximtio Field d oces: dipole The Loetz oce ctig o the coil [N/m ], cosideig the bsic tem, is The totl oce ctig o the coil [N/m] is Supecoductig Acceleto Mgets, ue -6, 5. Electomgetic oces d stesses i supecoductig cceleto mgets 6 cos si si si si cos x cos si y 6 6 l 6 F x l F y
65 Appedix III: secto ppoximtio Field d oces: qudupole We ssume = is the coss-sectio ple Ie (oute) dius o the coils = () Agle = º (thid hmoic tem is ull) No io The ield iside the petue The ield i the coil is Supecoductig Acceleto Mgets, ue -6, 5. Electomgetic oces d stesses i supecoductig cceleto mgets 65 si si si si l cos si cos si l si si si si l cos si cos si l
66 Appedix III: secto ppoximtio Field d oces: qudupole The Loetz oce ctig o the coil [N/m ], cosideig the bsic tem, is The totl oce ctig o the coil [N/m] pe octt is Supecoductig Acceleto Mgets, ue -6, 5. Electomgetic oces d stesses i supecoductig cceleto mgets 66 si cos x cos si y cos l si si l si l 6 7 F x 9 l F y
67 Appedix III: secto ppoximtio Stoed eegy, ed oces: dipole d qudupole Fo dipole, d, theeoe, Fo qudupole, d, theeoe, Supecoductig Acceleto Mgets, ue -6, 5. Electomgetic oces d stesses i supecoductig cceleto mgets 67 cos si A z 6 F z cos l si A z l 8 F z
68 Appedix III: secto ppoximtio Stess o the mid-ple: dipole d qudupole Fo dipole, Fo qudupole, / d 5 v 6 l 6 _ mid ple _ mid ple_ l 8 /6 _ mid ple d _ mid ple_ v l No she Stess o mid-ple (MP) 7.5 midd ( ) Rdius (m) Supecoductig Acceleto Mgets, ue -6, 5. Electomgetic oces d stesses i supecoductig cceleto mgets 68
Mechanical Design of Superconducting Accelerator Magnets
Mechicl Desig of Supecoductig Acceleto Mgets F. Tol CIEMAT, Mdid, Spi Abstct This ppe is bout the mechicl desig of supecoductig cceleto mgets. Fist, we give bief eview of the bsic cocepts d tems. I the
Macroscopic Fields in Accelerators
48 E hs simil effect s v. d q E v Fo eltivistic ticles T hs simil effect s dt E c 3 8 V/m such Electic field is beod techicl limits. Electic fields e ol used fo ve lo eegies o Fo setig to coute ottig bems
ANSWER KEY PHYSICS. Workdone X
ANSWER KEY PHYSICS 6 6 6 7 7 7 9 9 9 0 0 0 CHEMISTRY 6 6 6 7 7 7 9 9 9 0 0 60 MATHEMATICS 6 66 7 76 6 6 67 7 77 7 6 6 7 7 6 69 7 79 9 6 70 7 0 90 PHYSICS F L l. l A Y l A ;( A R L L A. W = (/ lod etesio
1. The 0.1 kg particle has a speed v = 10 m/s as it passes the 30 position shown. The coefficient of kinetic friction between the particle and the
1. The 0.1 kg pticle h peed v = 10 m/ it pe the 30 poitio how. The coefficiet of kietic fictio betwee the pticle d the veticl ple tck i m k = 0.0. Detemie the mgitude of the totl foce exeted by the tck
Semiconductors materials
Semicoductos mteils Elemetl: Goup IV, Si, Ge Biy compouds: III-V (GAs,GSb, ISb, IP,...) IV-VI (PbS, PbSe, PbTe,...) II-VI (CdSe, CdTe,...) Tey d Qutey compouds: G x Al -x As, G x Al -x As y P -y III IV
Multi-Electron Atoms-Helium
Multi-lecto Atos-Heliu He - se s H but with Z He - electos. No exct solutio of.. but c use H wve fuctios d eegy levels s sttig poit ucleus sceeed d so Zeffective is < sceeig is ~se s e-e epulsio fo He,
Mathematical Statistics
7 75 Ode Sttistics The ode sttistics e the items o the dom smple ed o odeed i mitude om the smllest to the lest Recetl the impotce o ode sttistics hs icesed owi to the moe equet use o opmetic ieeces d
PROGRESSION AND SERIES
INTRODUCTION PROGRESSION AND SERIES A gemet of umbes {,,,,, } ccodig to some well defied ule o set of ules is clled sequece Moe pecisely, we my defie sequece s fuctio whose domi is some subset of set of
SOLUTIONS ( ) ( )! ( ) ( ) ( ) ( )! ( ) ( ) ( ) ( ) n r. r ( Pascal s equation ). n 1. Stepanov Dalpiaz
STAT UIU Pctice Poblems # SOLUTIONS Stepov Dlpiz The followig e umbe of pctice poblems tht my be helpful fo completig the homewo, d will liely be vey useful fo studyig fo ems...-.-.- Pove (show) tht. (
SULIT 3472/2. Rumus-rumus berikut boleh membantu anda menjawab soalan. Simbol-simbol yang diberi adalah yang biasa digunakan.
SULT 347/ Rumus-umus eikut oleh memtu d mejw sol. Simol-simol yg diei dlh yg is diguk. LGER. 4c x 5. log m log m log 9. T d. m m m 6. log = log m log 0. S d m m 3. 7. log m log m. S, m m logc 4. 8. log.
Physics 11b Lecture #11
Physics 11b Lectue #11 Mgnetic Fields Souces of the Mgnetic Field S&J Chpte 9, 3 Wht We Did Lst Time Mgnetic fields e simil to electic fields Only diffeence: no single mgnetic pole Loentz foce Moving chge
Force and Motion. Force. Classifying Forces. Physics 11- Summer /21/01. Chapter 4 material 1. Forces are vector quantities!
Force d Motio Cocept of Force Newto s hree Lws ypes of Forces Free body lysis Equilibrium Noequilibrium Frictio Problem Solvig Force A Force is push or pull tht is exerted o object by some other object.
Force and Motion. Force
Force d Motio Cocept of Force Newto s hree Lws ypes of Forces Free body lysis Equilibrium Noequilibrium Frictio Problem Solvig Force A Force is push or pull tht is exerted o object by some other object.
We show that every analytic function can be expanded into a power series, called the Taylor series of the function.
10 Lectue 8 We show tht evey lytic fuctio c be expded ito powe seies, clled the Tylo seies of the fuctio. Tylo s Theoem: Let f be lytic i domi D & D. The, f(z) c be expessed s the powe seies f( z) b (
Electric Potential. and Equipotentials
Electic Potentil nd Euipotentils U Electicl Potentil Review: W wok done y foce in going fom to long pth. l d E dl F W dl F θ Δ l d E W U U U Δ Δ l d E W U U U U potentil enegy electic potentil Potentil
Chapter 28 Sources of Magnetic Field
Chpte 8 Souces of Mgnetic Field - Mgnetic Field of Moving Chge - Mgnetic Field of Cuent Element - Mgnetic Field of Stight Cuent-Cying Conducto - Foce Between Pllel Conductos - Mgnetic Field of Cicul Cuent
Expansion by Laguerre Function for Wave Diffraction around an Infinite Cylinder
Joul of Applied Mthemtics d Physics, 5, 3, 75-8 Published Olie Juy 5 i SciRes. http://www.scip.og/joul/jmp http://dx.doi.og/.436/jmp.5.3 Expsio by Lguee Fuctio fo Wve Diffctio oud Ifiite Cylide Migdog
Advanced Higher Maths: Formulae
: Fomule Gee (G): Fomule you bsolutely must memoise i ode to pss Advced Highe mths. Remembe you get o fomul sheet t ll i the em! Ambe (A): You do t hve to memoise these fomule, s it is possible to deive
U>, and is negative. Electric Potential Energy
Electic Potentil Enegy Think of gvittionl potentil enegy. When the lock is moved veticlly up ginst gvity, the gvittionl foce does negtive wok (you do positive wok), nd the potentil enegy (U) inceses. When
Summary: Binomial Expansion...! r. where
Summy: Biomil Epsio 009 M Teo www.techmejcmth-sg.wes.com ) Re-cp of Additiol Mthemtics Biomil Theoem... whee )!!(! () The fomul is ville i MF so studets do ot eed to memoise it. () The fomul pplies oly
ENGINEERING MATHEMATICS I QUESTION BANK. Module Using the Leibnitz theorem find the nth derivative of the following : log. e x log d.
ENGINEERING MATHEMATICS I QUESTION BANK Modle Usig the Leibit theoem id the th deivtive o the ollowig : b si c e d e Show tht d d! Usig the Leibit theoem pove the ollowig : I si b the pove tht b I si show
Physics 235 Final Examination December 4, 2006 Solutions
Physics 35 Fi Emitio Decembe, 6 Soutios.. Fist coside the two u quks. They e idetic spi ½ ptices, so the tot spi c be eithe o. The Pui Picipe equies tht the ove wvefuctio be echge tisymmetic. Sice the
CHAPTER 18: ELECTRIC CHARGE AND ELECTRIC FIELD
ollege Physics Student s Mnul hpte 8 HAPTR 8: LTRI HARG AD LTRI ILD 8. STATI LTRIITY AD HARG: OSRVATIO O HARG. ommon sttic electicity involves chges nging fom nnocoulombs to micocoulombs. () How mny electons
4.2 Boussinesq s Theory. Contents
00477 Pvement Stuctue 4. Stesses in Flexible vement Contents 4. Intoductions to concet of stess nd stin in continuum mechnics 4. Boussinesq s Theoy 4. Bumiste s Theoy 4.4 Thee Lye System Weekset Sung Chte
Advanced Higher Maths: Formulae
Advced Highe Mths: Fomule Advced Highe Mthemtics Gee (G): Fomule you solutely must memoise i ode to pss Advced Highe mths. Rememe you get o fomul sheet t ll i the em! Ame (A): You do t hve to memoise these
I. Exponential Function
MATH & STAT Ch. Eoetil Fuctios JCCSS I. Eoetil Fuctio A. Defiitio f () =, whee ( > 0 ) d is the bse d the ideedet vible is the eoet. [ = 1 4 4 4L 4 ] ties (Resf () = is owe fuctio i which the bse is the
Chapter 21: Electric Charge and Electric Field
Chpte 1: Electic Chge nd Electic Field Electic Chge Ancient Gees ~ 600 BC Sttic electicit: electic chge vi fiction (see lso fig 1.1) (Attempted) pith bll demonsttion: inds of popeties objects with sme
10 m, so the distance from the Sun to the Moon during a solar eclipse is. The mass of the Sun, Earth, and Moon are = =
Chpte 1 nivesl Gvittion 11 *P1. () The un-th distnce is 1.4 nd the th-moon 8 distnce is.84, so the distnce fom the un to the Moon duing sol eclipse is 11 8 11 1.4.84 = 1.4 The mss of the un, th, nd Moon
Numerical integration
Numeicl itegtio Alyticl itegtio = ( ( t)) ( t) Dt : Result ( s) s [0, t] : ( t) st ode odiy diffeetil equtio Alyticl solutio ot lwys vilble d( ) q( ) = σ = ( d ) : t 0 t = Numeicl itegtio 0 t t 2. t. t
Physics 505 Fall 2005 Midterm Solutions. This midterm is a two hour open book, open notes exam. Do all three problems.
Physics 55 Fll 5 Midtem Solutions This midtem is two hou open ook, open notes exm. Do ll thee polems. [35 pts] 1. A ectngul ox hs sides of lengths, nd c z x c [1] ) Fo the Diichlet polem in the inteio
[5 points] (c) Find the charge enclosed by the cylindrical surface of radius ρ 0 = 9 mm and length L = 1 m. [2
![[5 points] (c) Find the charge enclosed by the cylindrical surface of radius ρ 0 = 9 mm and length L = 1 m. [2](/thumbs/85/91744669.jpg "[5 points] (c) Find the charge enclosed by the cylindrical surface of radius ρ 0 = 9 mm and length L = 1 m. [2")
STUDENT NAME: STUDENT ID: ELEC ENG FH3: MIDTERM EXAMINATION QUESTION SHEET This emitio is TWO HOURS log. Oe double-sided cib sheet is llowed. You c use the McMste ppoved clculto Csio f99. You c tke y mteil
Fluids & Bernoulli s Equation. Group Problems 9
Goup Poblems 9 Fluids & Benoulli s Eqution Nme This is moe tutoil-like thn poblem nd leds you though conceptul development of Benoulli s eqution using the ides of Newton s 2 nd lw nd enegy. You e going
This immediately suggests an inverse-square law for a "piece" of current along the line.
Electomgnetic Theoy (EMT) Pof Rui, UNC Asheville, doctophys on YouTube Chpte T Notes The iot-svt Lw T nvese-sque Lw fo Mgnetism Compe the mgnitude of the electic field t distnce wy fom n infinite line
BINOMIAL THEOREM SOLUTION. 1. (D) n. = (C 0 + C 1 x +C 2 x C n x n ) (1+ x+ x 2 +.)
BINOMIAL THEOREM SOLUTION. (D) ( + + +... + ) (+ + +.) The coefficiet of + + + +... + fo. Moeove coefficiet of is + + + +... + if >. So. (B)... e!!!! The equied coefficiet coefficiet of i e -.!...!. (A),
School of Electrical and Computer Engineering, Cornell University. ECE 303: Electromagnetic Fields and Waves. Fall 2007
School of Electicl nd Compute Engineeing, Conell Univesity ECE 303: Electomgnetic Fields nd Wves Fll 007 Homewok 4 Due on Sep. 1, 007 by 5:00 PM Reding Assignments: i) Review the lectue notes. ii) Relevnt
ELECTRO - MAGNETIC INDUCTION
NTRODUCTON LCTRO - MAGNTC NDUCTON Whenee mgnetic flu linked with cicuit chnges, n e.m.f. is induced in the cicuit. f the cicuit is closed, cuent is lso induced in it. The e.m.f. nd cuent poduced lsts s
Physics 1502: Lecture 2 Today s Agenda
1 Lectue 1 Phsics 1502: Lectue 2 Tod s Agend Announcements: Lectues posted on: www.phs.uconn.edu/~cote/ HW ssignments, solutions etc. Homewok #1: On Mstephsics this Fid Homewoks posted on Msteingphsics
Homework 3 MAE 118C Problems 2, 5, 7, 10, 14, 15, 18, 23, 30, 31 from Chapter 5, Lamarsh & Baratta. The flux for a point source is:
. Homewok 3 MAE 8C Poblems, 5, 7, 0, 4, 5, 8, 3, 30, 3 fom Chpte 5, msh & Btt Point souces emit nuetons/sec t points,,, n 3 fin the flux cuent hlf wy between one sie of the tingle (blck ot). The flux fo
DRAFT. Formulae and Statistical Tables for A-level Mathematics SPECIMEN MATERIAL. First Issued September 2017
Fist Issued Septembe 07 Fo the ew specifictios fo fist techig fom Septembe 07 SPECIMEN MATERIAL Fomule d Sttisticl Tbles fo A-level Mthemtics AS MATHEMATICS (7356) A-LEVEL MATHEMATICS (7357) AS FURTHER
School of Electrical and Computer Engineering, Cornell University. ECE 303: Electromagnetic Fields and Waves. Fall 2007
School of Electicl nd Compute Engineeing, Conell Univesity ECE 303: Electomgnetic Fields nd Wves Fll 007 Homewok 3 Due on Sep. 14, 007 by 5:00 PM Reding Assignments: i) Review the lectue notes. ii) Relevnt
Lecture 10. Solution of Nonlinear Equations - II
Fied point Poblems Lectue Solution o Nonline Equtions - II Given unction g : R R, vlue such tht gis clled ied point o the unction g, since is unchnged when g is pplied to it. Whees with nonline eqution
STD: XI MATHEMATICS Total Marks: 90. I Choose the correct answer: ( 20 x 1 = 20 ) a) x = 1 b) x =2 c) x = 3 d) x = 0
STD: XI MATHEMATICS Totl Mks: 90 Time: ½ Hs I Choose the coect nswe: ( 0 = 0 ). The solution of is ) = b) = c) = d) = 0. Given tht the vlue of thid ode deteminnt is then the vlue of the deteminnt fomed
DEPARTMENT OF CIVIL AND ENVIRONMENTAL ENGINEERING FLUID MECHANICS III Solutions to Problem Sheet 3
DEPATMENT OF CIVIL AND ENVIONMENTAL ENGINEEING FLID MECHANICS III Solutions to Poblem Sheet 3 1. An tmospheic vote is moelle s combintion of viscous coe otting s soli boy with ngul velocity Ω n n iottionl
Chapter 7. Kleene s Theorem. 7.1 Kleene s Theorem. The following theorem is the most important and fundamental result in the theory of FA s:
Chpte 7 Kleene s Theoem 7.1 Kleene s Theoem The following theoem is the most impotnt nd fundmentl esult in the theoy of FA s: Theoem 6 Any lnguge tht cn e defined y eithe egul expession, o finite utomt,
Lecture 11: Potential Gradient and Capacitor Review:
Lectue 11: Potentil Gdient nd Cpcito Review: Two wys to find t ny point in spce: Sum o Integte ove chges: q 1 1 q 2 2 3 P i 1 q i i dq q 3 P 1 dq xmple of integting ove distiution: line of chge ing of
Vectors. Vectors in Plane ( 2
Vectors Vectors i Ple ( ) The ide bout vector is to represet directiol force Tht mes tht every vector should hve two compoets directio (directiol slope) d mgitude (the legth) I the ple we preset vector
EVALUATING DEFINITE INTEGRALS
Chpter 4 EVALUATING DEFINITE INTEGRALS If the defiite itegrl represets re betwee curve d the x-xis, d if you c fid the re by recogizig the shpe of the regio, the you c evlute the defiite itegrl. Those
8.1 Arc Length. What is the length of a curve? How can we approximate it? We could do it following the pattern we ve used before
8.1 Arc Legth Wht is the legth of curve? How c we pproximte it? We could do it followig the ptter we ve used efore Use sequece of icresigly short segmets to pproximte the curve: As the segmets get smller
Friedmannien equations
..6 Fiedmnnien equtions FLRW metic is : ds c The metic intevl is: dt ( t) d ( ) hee f ( ) is function which detemines globl geometic l popety of D spce. f d sin d One cn put it in the Einstein equtions
( ) ( ) Physics 111. Lecture 13 (Walker: Ch ) Connected Objects Circular Motion Centripetal Acceleration Centripetal Force Sept.
Physics Lectue 3 (Wlke: Ch. 6.4-5) Connected Objects Cicul Motion Centipetl Acceletion Centipetl Foce Sept. 30, 009 Exmple: Connected Blocks Block of mss m slides on fictionless tbletop. It is connected
Lecture 38 (Trapped Particles) Physics Spring 2018 Douglas Fields
Lecture 38 (Trpped Prticles) Physics 6-01 Sprig 018 Dougls Fields Free Prticle Solutio Schrödiger s Wve Equtio i 1D If motio is restricted to oe-dimesio, the del opertor just becomes the prtil derivtive
The Definite Riemann Integral
These otes closely follow the presettio of the mteril give i Jmes Stewrt s textook Clculus, Cocepts d Cotexts (d editio). These otes re iteded primrily for i-clss presettio d should ot e regrded s sustitute
S. Socrate 2013 K. Qian
S. Socrte 213 K. Qi odig Coditios o ech Sectio () pplied lodig oly log the is () of the br. The oly iterl resultt t y sectios is the il force N() Fid N()log the br (il force digrm) by cuttig the br t ech
Solutions to Midterm Physics 201
Solutions to Midtem Physics. We cn conside this sitution s supeposition of unifomly chged sphee of chge density ρ nd dius R, nd second unifomly chged sphee of chge density ρ nd dius R t the position of
2.Decision Theory of Dependence
.Deciio Theoy of Depedece Theoy :I et of vecto if thee i uet which i liely depedet the whole et i liely depedet too. Coolly :If the et i liely idepedet y oepty uet of it i liely idepedet. Theoy : Give
Pre-Calculus - Chapter 3 Sections Notes
Pre-Clculus - Chpter 3 Sectios 3.1-3.4- Notes Properties o Epoets (Review) 1. ( )( ) = + 2. ( ) =, (c) = 3. 0 = 1 4. - = 1/( ) 5. 6. c Epoetil Fuctios (Sectio 3.1) Deiitio o Epoetil Fuctios The uctio deied
General Physics II. number of field lines/area. for whole surface: for continuous surface is a whole surface
Genel Physics II Chpte 3: Guss w We now wnt to quickly discuss one of the moe useful tools fo clculting the electic field, nmely Guss lw. In ode to undestnd Guss s lw, it seems we need to know the concept
Parametric Methods. Autoregressive (AR) Moving Average (MA) Autoregressive - Moving Average (ARMA) LO-2.5, P-13.3 to 13.4 (skip
Pmeti Methods Autoegessive AR) Movig Avege MA) Autoegessive - Movig Avege ARMA) LO-.5, P-3.3 to 3.4 si 3.4.3 3.4.5) / Time Seies Modes Time Seies DT Rdom Sig / Motivtio fo Time Seies Modes Re the esut
Heat Transfar and Thermal Stress Analysis In Annular Cylinder under Steady State
IOSR ol o temtics IOSR- e-iss: 78-578p-ISS: 9-765X Volme 7 Isse 6 Sep. - Oct. PP 9-99 www.iosjols.og Het s d eml Stess Alysis I Al ylide de Stedy Stte P.H.jk..Desmk V.S.lki Deptmet o temtics Amedk Sciece
Step-index silica fiber
Modl lysis of step-idex fibes Itoductio C 46/566 Guided Wve Optics Step-idex silic fibe Mteil d fbictio Types d mig of modes Deivtio d solutio of the W Solutio of the W T/TM modes Hybid modes LP modes
Mapping Radius of Regular Function and Center of Convex Region. Duan Wenxi
d Iteatioal Cofeece o Electical Compute Egieeig ad Electoics (ICECEE 5 Mappig adius of egula Fuctio ad Cete of Covex egio Dua Wexi School of Applied Mathematics Beijig Nomal Uivesity Zhuhai Chia 363463@qqcom
3.1 Magnetic Fields. Oersted and Ampere
3.1 Mgnetic Fields Oested nd Ampee The definition of mgnetic induction, B Fields of smll loop (dipole) Mgnetic fields in mtte: ) feomgnetism ) mgnetiztion, (M ) c) mgnetic susceptiility, m d) mgnetic field,
Evaluation of the Proximity Effect upon the Impedance Characteristics of Subsea Power Transmission Cables
Poceedigs of the 6th WSEAS tetiol Cofeece o Powe Systems, Lisbo, Potugl, Septembe -4, 6 Evlutio of the Poximity Effect upo the mpedce Chcteistics of Subse Powe Tsmissio Cbles Chg Hsi CHEN d Richd BUCKNALL
Pearson Edexcel Level 3 Advanced Subsidiary and Advanced GCE Mathematics and Further Mathematics
Peso Edecel Level 3 Advced Subsidiy d Advced GCE Mthemtics d Futhe Mthemtics Mthemticl fomule d sttisticl tbles Fo fist cetifictio fom Jue 08 fo: Advced Subsidiy GCE i Mthemtics (8MA0) Advced GCE i Mthemtics
is completely general whenever you have waves from two sources interfering. 2
MAKNG SENSE OF THE EQUATON SHEET terferece & Diffrctio NTERFERENCE r1 r d si. Equtio for pth legth differece. r1 r is completely geerl. Use si oly whe the two sources re fr wy from the observtio poit.
Chapter 2: Electric Field
P 6 Genel Phsics II Lectue Outline. The Definition of lectic ield. lectic ield Lines 3. The lectic ield Due to Point Chges 4. The lectic ield Due to Continuous Chge Distibutions 5. The oce on Chges in
MATHEMATICIA GENERALLI
MATHEMATICIA GENERALLI (y Mhmmed Abbs) Lgithmi Reltis lgb ) lg lg ) b b) lg lg lg m lg m d) lg m. lg m lg m e) lg lg m lg g) lg lg h) f) lg lg f ( ) f ( ). Eetil Reltis ). lge. lge.... lge...!! b) e......
PhysicsAndMathsTutor.com
PhysicsAMthsTuto.com . M 6 0 7 0 Leve lk 6 () Show tht 7 is eigevlue of the mti M fi the othe two eigevlues of M. (5) () Fi eigevecto coespoig to the eigevlue 7. *M545A068* (4) Questio cotiue Leve lk *M545A078*
Induction. Induction and Recursion. Induction is a very useful proof technique
Iductio Iductio is vey useul poo techique Iductio d Recusio CSC-59 Discete Stuctues I compute sciece, iductio is used to pove popeties o lgoithms Iductio d ecusio e closely elted Recusio is desciptio method
Simultaneous Estimation of Adjusted Rate of Two Factors Using Method of Direct Standardization
Biometics & Biosttistics Itetiol Joul Simulteous Estimtio of Adjusted Rte of Two Fctos Usig Method of Diect Stddiztio Astct This ppe pesets the use of stddiztio o djustmet of tes d tios i compig two popultios
AQA Maths M2. Topic Questions from Papers. Circular Motion. Answers
AQA Mths M Topic Questions fom Ppes Cicul Motion Answes PhysicsAndMthsTuto.com PhysicsAndMthsTuto.com Totl 6 () T cos30 = 9.8 Resolving veticlly with two tems Coect eqution 9.8 T = cos30 T =.6 N AG 3 Coect
UNIT V: Z-TRANSFORMS AND DIFFERENCE EQUATIONS. Dr. V. Valliammal Department of Applied Mathematics Sri Venkateswara College of Engineering
UNIT V: -TRANSFORMS AND DIFFERENCE EQUATIONS D. V. Vllimml Deptmet of Applied Mthemtics Si Vektesw College of Egieeig TOPICS:. -Tsfoms Elemet popeties.. Ivese -Tsfom usig ptil fctios d esidues. Covolutio
Multivector Functions
I: J. Math. Aal. ad Appl., ol. 24, No. 3, c Academic Pess (968) 467 473. Multivecto Fuctios David Hestees I a pevious pape [], the fudametals of diffeetial ad itegal calculus o Euclidea -space wee expessed
Pearson Edexcel Level 3 Advanced Subsidiary and Advanced GCE Mathematics and Further Mathematics
Peso Edecel Level Advced Subsidiy d Advced GCE Mthemtics d Futhe Mthemtics Mthemticl fomule d sttisticl tbles Fo fist cetifictio fom Jue 08 fo: Advced Subsidiy GCE i Mthemtics (8MA0) Advced GCE i Mthemtics
Dynamically Equivalent Systems. Dynamically Equivalent Systems. Dynamically Equivalent Systems. ME 201 Mechanics of Machines
ME 0 Mechnics of Mchines 8//006 Dynmicy Equivent Systems Ex: Connecting od G Dynmicy Equivent Systems. If the mss of the connecting od m G m m B m m m. Moment out cente of gvity shoud e zeo m G m B Theefoe;
Chapter 10: The Z-Transform Adapted from: Lecture notes from MIT, Binghamton University Dr. Hamid R. Rabiee Fall 2013
Sigls & Systems Chpter 0: The Z-Trsform Adpted from: Lecture otes from MIT, Bighmto Uiversity Dr. Hmid R. Rbiee Fll 03 Lecture 5 Chpter 0 Lecture 6 Chpter 0 Outlie Itroductio to the -Trsform Properties
Radial geodesics in Schwarzschild spacetime
Rdil geodesics in Schwzschild spcetime Spheiclly symmetic solutions to the Einstein eqution tke the fom ds dt d dθ sin θdϕ whee is constnt. We lso hve the connection components, which now tke the fom using
Technical Report: Bessel Filter Analysis
Sasa Mahmoodi 1 Techical Repot: Bessel Filte Aalysis 1 School of Electoics ad Compute Sciece, Buildig 1, Southampto Uivesity, Southampto, S17 1BJ, UK, Email: sm3@ecs.soto.ac.uk I this techical epot, we
Answers to test yourself questions
Answes to test youself questions opic Descibing fields Gm Gm Gm Gm he net field t is: g ( d / ) ( 4d / ) d d Gm Gm Gm Gm Gm Gm b he net potentil t is: V d / 4d / d 4d d d V e 4 7 9 49 J kg 7 7 Gm d b E
ELECTROSTATICS. 4πε0. E dr. The electric field is along the direction where the potential decreases at the maximum rate. 5. Electric Potential Energy:
LCTROSTATICS. Quntiztion of Chge: Any chged body, big o smll, hs totl chge which is n integl multile of e, i.e. = ± ne, whee n is n intege hving vlues,, etc, e is the chge of electon which is eul to.6
«A first lesson on Mathematical Induction»
Bcgou ifotio: «A fist lesso o Mtheticl Iuctio» Mtheticl iuctio is topic i H level Mthetics It is useful i Mtheticl copetitios t ll levels It hs bee coo sight tht stuets c out the poof b theticl iuctio,
Ch 26 - Capacitance! What s Next! Review! Lab this week!
Ch 26 - Cpcitnce! Wht s Next! Cpcitnce" One week unit tht hs oth theoeticl n pcticl pplictions! Cuent & Resistnce" Moving chges, finlly!! Diect Cuent Cicuits! Pcticl pplictions of ll the stuff tht we ve
( ) ( ) ( ) ( ) ( ) # B x ( ˆ i ) ( ) # B y ( ˆ j ) ( ) # B y ("ˆ ( ) ( ) ( (( ) # ("ˆ ( ) ( ) ( ) # B ˆ z ( k )
Emple 1: A positie chge with elocit is moing though unifom mgnetic field s shown in the figues below. Use the ight-hnd ule to detemine the diection of the mgnetic foce on the chge. Emple 1 ˆ i = ˆ ˆ i
On the relation between tonal and broadband content of hull pressure spectra due to cavitating ship propellers
Joul of Physics: Cofeece Seies PAPER OPEN ACCESS O the eltio betwee tol d bodbd cotet of hull pessue spect due to cvittig ship popelles To cite this ticle: J Bossches 015 J. Phys.: Cof. Se. 656 01101 View
Theorem 5.3 (Continued) The Fundamental Theorem of Calculus, Part 2: ab,, then. f x dx F x F b F a. a a. f x dx= f x x
Chpter 6 Applictios Itegrtio Sectio 6. Regio Betwee Curves Recll: Theorem 5.3 (Cotiued) The Fudmetl Theorem of Clculus, Prt :,,, the If f is cotiuous t ever poit of [ ] d F is tiderivtive of f o [ ] (
Chapter Linear Regression
Chpte 6.3 Le Regesso Afte edg ths chpte, ou should be ble to. defe egesso,. use sevel mmzg of esdul cte to choose the ght cteo, 3. deve the costts of le egesso model bsed o lest sques method cteo,. use
DEPARTMENT OF ELECTRICAL &ELECTRONICS ENGINEERING SIGNALS AND SYSTEMS. Assoc. Prof. Dr. Burak Kelleci. Spring 2018
DEPARTMENT OF ELECTRICAL &ELECTRONICS ENGINEERING SIGNALS AND SYSTEMS Assoc. Prof. Dr. Bur Kelleci Sprig 8 OUTLINE The Z-Trsform The Regio of covergece for the Z-trsform The Iverse Z-Trsform Geometric
Plane Kinetics of Rigid Bodies 동역학 및 응용
Ple Kietics of igid odies 동역학 및 응용 EQUTONS O PLNE OTON esultt of the pplied etel foces : esultt foce (pss though ss cete) + ouple oets of the etel foces gul otio z ouple : sste of foces with esultt oet
S(x)along the bar (shear force diagram) by cutting the bar at x and imposing force_y equilibrium.
mmetric leder Bems i Bedig Lodig Coditios o ech ectio () pplied -Forces & z-omets The resultts t sectio re: the bedig momet () d z re sectio smmetr es the sher force () [ for sleder bems stresses d deformtio
Physics 604 Problem Set 1 Due Sept 16, 2010
Physics 64 Polem et 1 Due ept 16 1 1) ) Inside good conducto the electic field is eo (electons in the conducto ecuse they e fee to move move in wy to cncel ny electic field impessed on the conducto inside
f(bx) dx = f dx = dx l dx f(0) log b x a + l log b a 2ɛ log b a.
Eercise 5 For y < A < B, we hve B A f fb B d = = A B A f d f d For y ɛ >, there re N > δ >, such tht d The for y < A < δ d B > N, we hve ba f d f A bb f d l By ba A A B A bb ba fb d f d = ba < m{, b}δ
π,π is the angle FROM a! TO b
Mth 151: 1.2 The Dot Poduct We hve scled vectos (o, multiplied vectos y el nume clled scl) nd dded vectos (in ectngul component fom). Cn we multiply vectos togethe? The nswe is YES! In fct, thee e two
Review. I will give you these formulas: Sphere: V=frr Circle: A = rr2 Cone: V = I 2rr2h Cube: V = side3
You eed to kow: Rolle s Theoem: f ) f is cotiuous o [.bj, 2) f is diffeetible o (,b), d ) f()=f(b), the thee s oe c i (,b) whee f (c) = Me Vlue Theoem: l) f is cotiuous o [.b d 2) f is diffeetible o (,b),
M5. LTI Systems Described by Linear Constant Coefficient Difference Equations
5. LTI Systes Descied y Lie Costt Coefficiet Diffeece Equtios Redig teil: p.34-4, 245-253 3/22/2 I. Discete-Tie Sigls d Systes Up til ow we itoduced the Fouie d -tsfos d thei popeties with oly ief peview
BC Calculus Review Sheet
BC Clculus Review Sheet Whe you see the words. 1. Fid the re of the ubouded regio represeted by the itegrl (sometimes 1 f ( ) clled horizotl improper itegrl). This is wht you thik of doig.... Fid the re
Two dimensional polar coordinate system in airy stress functions
I J C T A, 9(9), 6, pp. 433-44 Intentionl Science Pess Two dimensionl pol coodinte system in iy stess functions S. Senthil nd P. Sek ABSTRACT Stisfy the given equtions, boundy conditions nd bihmonic eqution.in
Lecture 24: Observability and Constructibility
ectue 24: Obsevability ad Costuctibility 7 Obsevability ad Costuctibility Motivatio: State feedback laws deped o a kowledge of the cuet state. I some systems, xt () ca be measued diectly, e.g., positio
42. (20 pts) Use Fermat s Principle to prove the law of reflection. 0 x c
4. (0 ts) Use Femt s Piile t ve the lw eleti. A i b 0 x While the light uld tke y th t get m A t B, Femt s Piile sys it will tke the th lest time. We theee lulte the time th s uti the eleti it, d the tke
x a y n + b = 1 0<b a, n > 0 (1.1) x 1 - a y = b 0<b a, n > 0 (1.1') b n sin 2 + cos 2 = 1 x n = = cos 2 6 Superellipse (Lamé curve)
6 Supeellipse (Lmé cuve) 6. Equtios of supeellipse A supeellipse (hoizotlly log) is epessed s follows. Implicit Equtio y + b 0 0 (.) Eplicit Equtio y b - 0 0 (.') Whe 3, b, the supeellipses fo
ME 501A Seminar in Engineering Analysis Page 1
Fobeius ethod pplied to Bessel s Equtio Octobe, 7 Fobeius ethod pplied to Bessel s Equtio L Cetto Mechicl Egieeig 5B Sei i Egieeig lsis Octobe, 7 Outlie Review idte Review lst lectue Powe seies solutios/fobeius