Strong Shear Formation by Poloidal Chain of Magnetic Islands
|
|
- Rachel Watson
- 5 years ago
- Views:
Transcription
1 Stong Sha Fomation by Poloidal Chain of Magntic Islands V.I. Maslo, F. Poclli* NSC Khako Institut of Physics & Tchnology, Khako, Ukain * Politcnico di Toino, Italy
2 Objctis W will shown that: otical concti clls a naow fo lag sha and fo abupt plasma dnsity pofil. Also amplitud of otx satuation is insly popotional to sha. It pomots abupt plasma dnsity pofil and ITB fomation. plasma hating na low od ational sufac with poloidal chain of naow magntic islands can lad to sha fomation.
3 W consid ITB. J.W. Conno t al
4 Th is mchanism of tubulnc and anomalous tanspot damping, poiding sha of angula locity θ 0 of plasma paticls. In oth wods, poiding popagation of plasma lays lati to ach oth. By this way th plasma paticl bunchs o plasma paticl hols as pats of plasma ptubations a dampd. Minc otics and thi amplitud satuation by sha J.W. Conno t al
5 Spatial stuctu of otics But lt us at fist consid oth ffct of tubulnc and anomalous tanspot damping. Fo that w consid spatial stuctu of otics in cossd magntic H 0 and adial lctical E 0 filds in st-fam otatd with ph Vph. is adius of otx localization, V. Fo simplicity lt us consid singl ph = Vθ0 = chain of otics in cylindical appoximation. Anomalous tanspot is dtmind by st of chains. 5
6 Th concti diffusi tanspot, pfomd by otics Tap paticls by otics in plan appoximation. 6
7 Nglcting nonstationay and nonlina mmbs, fom lcton motion q w ha Both mmbs in ha th sam sign and ffct in on diction as against ions. Using and dcomposition on na w obtain q., dscibing lcton dynamics in otx [ ] [ ] z c z c 0 p, m n 1, m V V δ φ + = θ [ ] [ ] 0 z c o z c 0 p, m n 1 E, m V = θ V θ0 ph 1 t d t d + θ = θ ( ) V o θ δ () / V o o θ θ ( ) ( ) ( ) const n p m 4 o c = δ φ + δ = θ 7
8 ( ) Lt us connct φ δp n with q. of motion w di α z otv. Fom lcton 0 δ L T Δϕ ci α ( kρ ) ci V α thi ρ ci T Δϕ n 1 Δn If α θo fo kρ ci 1 δ ρ ci Fquncy of lcton oscillation in otx Ω = l θ m θo c = o ( ) n ( ) φ δp 0 1/ 8
9 ( ) ( ) 1/ 0 o o c n p m δ φ δ = θ It hlps ITB fomation. o 1 = θ δ 9
10 Votxs of lag amplituds Count-flows in lcton bunchs. Opposit otation of lcton hols and bunchs. ( ) ( ) ( ) 1/ 0 o o c b h n p m 8 δ φ δ = δ = θ 10
11 Radial dimnsion of slow otics V ph V θ0 Vph << Vθ0 fo xampl of Rossby kind V.D. Laich, G.М. Rznik At fist w di gnal nonlina q fo lctons. n V ϕ + ( n V) p = 0 + V V = + c, V t t m n m Simila М.V. Nzlin, G.P. Chniko α ot ( ) [ ] V d t α n c = 1 n ( )V ( α ) c W ha did without any appoachs a nonlina octoial q., dscibing otical lcton dynamics. 11
12 δ = co 1 n ( ) o c δn δ 1 n o It hlps abupt plasma dnsity pofil and ITB fomation. 1
13 Amplitud of otx satuation Votx is xcitd up to amplitud, at which lays, tappd by it, 1 duing γ a shiftd lati to ach oth du to sha δ θ 0 = on th angl not lag π l θ δ θ0 π l θ = γ 13
14 φ o n δp 0 ( ) = γπ l m θ θ o c = φ o δp n 0 ( ) 1 θ o = It pomots ITB fomation. Dcas of ll of fluctuations at ITB fomation has bn obsd, fo xampl, in E.D.Volko t al
15 n Concti diffusion quation θ At lag amplituds, whn fquncy of th lcton oscillations in otx, bcoms lag Ω > γ in icinity of cll bods n jumps a fomd, wh γ bcoms lag. Thfo at lag amplituds th instability is dlopd fo oding of otics and fo lattic fomation of otics. Ω 15
16 Lattic of otics 16
17 3 1 4 Insid otx odd concti lcton momnt. How, thy a ffctd by nionmntal otx filds and fluctuations and amplituds a not stationay. Instad of aag n o (t,), which dos not tak into account colations, w us fou lcton dnsitis n k (t,) aagd on smallscal oscillations: n 1 (t,), n (t,), n 3 (t,), n 4 (t,). 17
18 In otx following pocsss a alizd: platau fomation on n ( ) du to diffnc of angula spds. du to jump fomation on n ( ) acclatd diffusion in gions 1 and and an xchang by lctons btwn gions 1 and 3 (facto α), and also btwn gions and 4. ffct of fluctuations, gowth of amplituds. adjacnt otics fom intgatd bod. Paticls in spac btwn indiidual cll bods and intgatd bod mo in adial diction fom otx to otx fo th distanc min{, δτcoω }. π, l a τ co coth colation lngth and 3 tim of otical tubulnc. 1 l co 4 18
19 ( t + τ, ) = ( 1 α) n ( t, ) + n ( t, ) n1 αβ 3 ( t + τ, ) = ( 1 α) n ( t, ) + n ( t, ) n 1 αβ 4 ( t + τ, ) = αn ( t, ) + β( 1 α) n ( t, δ ) + 0.5( 1 β)[ n ] n n4 ( t + τ, ) = αn ( t, ) + β( 1 α) n ( t, + δ ) + 0.5( 1 β)[ n ] n n 4 H β is facto of concti xchang of otics by lctons. β is dtmind by atio of aa with concti lcton dynamics, locatd btwn indiidual otx bods and intgatd bods to all aa, locatd btwn indiidual otx bods and intgatd bods of adjacnt otics. 19
20 Enting ( n n ), n = δ = n n, n 3 4 on can di τ t t τ ( n n ), N 1 + t n δn + = δ = n n, = α N 1 ( N βn) ( β )( 1 α) δ δn, [ 1 β( 1 α) ] δn = αδn β( 1 α) δ n, τ N = α( βn N), τ δn + ( α) δn = αβδn t On can s that intoduction n is simila to aag n o (t,) but with taking into account colations. 0
21 Fom ths q.s w ha simila to A.S. Bakai following concti diffusion quation τ t δn = β + τ t [( 1 β( 1 α) ) δn αδn] β ( 1 α) δ α( N βn) ( 1 α) = δ δn β ( ) As is popotional to δ Δ δ thn at δ < Δ w ha β = 0 and th is no stong anomalous adial tanspot bcaus otics xchang by paticls disappas. 1
22 Sha fomation du to lcton hating na ational sufac with poloidal chain of islands
23 In this pat w discuss th angula locity sha θ 0 fomation by magntic islands. Not slf-consistnt islands but islands du to non-idal constuction o so-calld natual islands. Expimnts T. Shimozuma t al. Nucl. Fusion 45, 1396 (005). E.D.Volko t al. Czch. J. Phys. 53, 887 (003). show that naow magntic islands can impo plasma confinmnt. 3
24 Calculatd sults of flux sufacs with natual islands T. Shimozuma t al
25 Th btt confinmnt in xpimnts with sal chain of magntic islands du to sufficint hating E.D.Volko t al. 003 and in Lag Hlical Dic with nutal bam injction and with additional lcton cycloton hating, stongly focusd on ational sufac m/n = /1 with magntic islands T. Shimozuma t al Th a many instigations on magntic island fomation F. Poclli t al M Ottaiani t al and thi ffct on nucla fusion plasma K. Ida t al. 00. E.D.Volko t al. 003 T. Shimozuma t al
26 If at plasma lcton hating na low od ational sufac with poloidal chain of naow magntic islands π to ν < V ( hot) thn on th island dimnsion th adial distibution of th lctic fild E ( ) changs stongly and in plasma cosssction th stong sha is fomd. θo th S xpimnt E.D.Volko t al E 6
27 W suppos, that on wid intal 0 < < m lctical fild E in th cas of ITB absnc is popotional to E = πn 0 < m E 0 < N 0 n n i It mans, that th is no sha θo. Thn oscillations can b xcitd, which sult in anomalous adial tanspot. Anomalous tanspot lads to asi lcton follow fo ions and to smooth plasma paamt distibution on adius. 7
28 On plasma coss-sction sal chains of islands can xist E.D.Volko t al W fo simpl cas consid influnc of on poloidal chain on sha fomation. W consid ational sufac with small numbs, bcaus impotant popty of this sufac is appad, whn plasma is hatd sufficintly that its lctons pfom sal otation aound tooidal sufac duing f ( hot) pass tim π to ν < V th 8
29 ( hot) At sufficint plasma lcton hating π to ν < Vth na ational sufac lcton tanspot though island changs fom slow collisional to quick on collisionlss. Quick tanspot is alizd by such way that lctons miss island. 9
30 Elcton mos along with V ( E o + p 0 n )( ν f + ν ) c 0 = m Whn lcton achs island, it popagats collisionally though island in cas ( hot) π to ν >> Vth But in cas ( hot) π to ν << Vth ( hot) lcton without collision quickly, duing tim π to V th gt on scond bounday of island. Aft that lcton again can slow popagat with in diction of lag. V 0 30
31 Pat of tappd lctons la island with locity ν +ν ( ) Δ f V l Δ V = E = mc 0 (),t 0 31
32 Island missing by lctons and tappd lctons laing th island lad to appaanc of uncompnsatd ion olum chag δn<<n 0 in island and to sha. E 0 E δ 0 +Δ 0 0 +δ with stong tubulnc on > 0 + Δ 3
33 Using appoximation of poloidal chain of naow magntic islands as azimuth symmtical naow lay w ha E 0 Na, 0 0 π N a 0 δn 0, 0 + δ ( ) 0, δ small plasma polaization + δ ion olum ch ag 33
34 E 0 0 at = 0 +δ, δ<δ. Δ is island width. w ha Δ N a δn 0 Dnsity of uncompnsatd ion olum chag N 0 << δn << n 0 L is width of gion with ssntial E 0. Island can b naow >> Δ > δ fo ssntial sha fomation 0 (Δφ/T i )( di /Lδ sp )<1 Lt us stimat sha S E ( E ) without Th sha is lag fo gion of naow magntic islands 0 TB 0 + δ S ( )( ) N N δ a 0 0 sp S >>1 34
35 Sha of angl locity S θ0 θ0 θ 0 = V θ0 θ0 without TB θ 0 V without θ0 TB = = m p 1 H N H n 0 0 E 0 n p 0 0 S = ( N N ) 1 a 0 0 δ sp>> 35
36 Elctons la island with Elctons should shift on small adial distanc Tim of sha fomation ( ν +ν ) (),t 0 f V l = V = 0 +Δ V = 0 Δ Δ E0 0 = mc δ Δ δn n 0 Sha is fomd duing shot tim fo not y naow islands τ TB 1 ( ) ( ν + ν )( Δ) f c p 0 36
37 Conditions of sha fomation by chain of magntic islands in cossd filds That in island uncompnsatd ion olum chag appas it is ncssay Δ > ρc. Naow islands Δ << R, though poid fast lcton momnt though Δ, stongly suppss tanspot in boad thi nighbohood. Uncompnsatd ion olum chag has appad at n is tooidal numb. ( Δ) D > ( πn ) D to Lt duing f pass tim lcton has tim to mak q otations aound th tous. Thn max{ ρ c nρ, q c 1+ ν ν f i } < Δ 37
38 Condition of anomalous tanspot damping by sha J.W. Conno t al. 004; R.C.Wolf. 003; A. Fujisawa L > γ θ0 Δϕ πn 0 L Δϕ T i ci ρ Lδ > γ ci Sha can damp instabilitis with gowth at γ < ci 38
39 W di lati sha S. θ0 θ0 without TB But absolut sha can b incasd. In sal xpimnts stong localization of gion with V 0 θ 0 has bn obsd. Radial width Δ sh of aa V 0 localization is obsd. Sha ( V θ 0 Δ sh = 1cm 0θ ) ap can b incasd in compaison with smooth cas V ( ) R V0θ smooth 0θ stongly ( V0θ ) V0θ Δsh ( V0θ ) R Δsh ap smooth 39
40 ITB as a localizd dop of ion and lcton thmal conductiitis. Thy dcas by factos of 10 to 0 within 5 cm. Also shown is th calculatd noclassical ion hat conductiity. J.W. Conno t al
41 Anoth scnaio of sha fomation, whn in gion tb th is dns plasma with fqunt collisions ν. Hnc p0( ) ν V 0 is sufficintly lag and E 0 0 at. n tb m c If tubulnc and anomalous tanspot at is stong, again E is small at 0 tb + Δ tb tb + Δ tb If tubulnc and anomalous tanspot at a stongly dampd, and plasma lctons h a collisionlss, 0 tb tb + Δ slf-consistnt stong sha is fomd du to localizd lctic fild E fomation at + Δ as a doubl-lay-kind stuctu. tb tb tb tb 41
GRAVITATION 4) R. max. 2 ..(1) ...(2)
GAVITATION PVIOUS AMCT QUSTIONS NGINING. A body is pojctd vtically upwads fom th sufac of th ath with a vlocity qual to half th scap vlocity. If is th adius of th ath, maximum hight attaind by th body
More informationGRAVITATION. (d) If a spring balance having frequency f is taken on moon (having g = g / 6) it will have a frequency of (a) 6f (b) f / 6
GVITTION 1. Two satllits and o ound a plant P in cicula obits havin adii 4 and spctivly. If th spd of th satllit is V, th spd of th satllit will b 1 V 6 V 4V V. Th scap vlocity on th sufac of th ath is
More informationSTATISTICAL MECHANICS OF DIATOMIC GASES
Pof. D. I. ass Phys54 7 -Ma-8 Diatomic_Gas (Ashly H. Cat chapt 5) SAISICAL MECHAICS OF DIAOMIC GASES - Fo monatomic gas whos molculs hav th dgs of fdom of tanslatoy motion th intnal u 3 ngy and th spcific
More informationHydrogen atom. Energy levels and wave functions Orbital momentum, electron spin and nuclear spin Fine and hyperfine interaction Hydrogen orbitals
Hydogn atom Engy lvls and wav functions Obital momntum, lcton spin and nucla spin Fin and hypfin intaction Hydogn obitals Hydogn atom A finmnt of th Rydbg constant: R ~ 109 737.3156841 cm -1 A hydogn mas
More informationE F. and H v. or A r and F r are dual of each other.
A Duality Thom: Consid th following quations as an xampl = A = F μ ε H A E A = jωa j ωμε A + β A = μ J μ A x y, z = J, y, z 4π E F ( A = jω F j ( F j β H F ωμε F + β F = ε M jβ ε F x, y, z = M, y, z 4π
More informationCollective Focusing of a Neutralized Intense Ion Beam Propagating Along a Weak Solenodial Magnetic Field
Havy Ion Fusion Scinc Vitual National Laoatoy Collctiv Focusing of a Nutalizd Intns Ion Bam Popagating Along a Wak Solnodial Magntic Fild M. Dof (LLNL) In collaoation with I. Kaganovich, E. Statsv, and
More informationII.3. DETERMINATION OF THE ELECTRON SPECIFIC CHARGE BY MEANS OF THE MAGNETRON METHOD
II.3. DETEMINTION OF THE ELETON SPEIFI HGE Y MENS OF THE MGNETON METHOD. Wok pupos Th wok pupos is to dtin th atio btwn th absolut alu of th lcton chag and its ass, /, using a dic calld agnton. In this
More information8 - GRAVITATION Page 1
8 GAVITATION Pag 1 Intoduction Ptolmy, in scond cntuy, gav gocntic thoy of plantay motion in which th Eath is considd stationay at th cnt of th univs and all th stas and th plants including th Sun volving
More informationSolid state physics. Lecture 3: chemical bonding. Prof. Dr. U. Pietsch
Solid stat physics Lctu 3: chmical bonding Pof. D. U. Pitsch Elcton chag dnsity distibution fom -ay diffaction data F kp ik dk h k l i Fi H p H; H hkl V a h k l Elctonic chag dnsity of silicon Valnc chag
More informationMolecules and electronic, vibrational and rotational structure
Molculs and ctonic, ational and otational stuctu Max on ob 954 obt Oppnhim Ghad Hzbg ob 97 Lctu ots Stuctu of Matt: toms and Molculs; W. Ubachs Hamiltonian fo a molcul h h H i m M i V i fs to ctons, to
More informationSUPPLEMENTARY INFORMATION
SUPPLMNTARY INFORMATION. Dtmin th gat inducd bgap cai concntation. Th fild inducd bgap cai concntation in bilay gaphn a indpndntly vaid by contolling th both th top bottom displacmnt lctical filds D t
More informationAakash. For Class XII Studying / Passed Students. Physics, Chemistry & Mathematics
Aakash A UNIQUE PPRTUNITY T HELP YU FULFIL YUR DREAMS Fo Class XII Studying / Passd Studnts Physics, Chmisty & Mathmatics Rgistd ffic: Aakash Tow, 8, Pusa Road, Nw Dlhi-0005. Ph.: (0) 4763456 Fax: (0)
More informationPhysics 202, Lecture 5. Today s Topics. Announcements: Homework #3 on WebAssign by tonight Due (with Homework #2) on 9/24, 10 PM
Physics 0, Lctu 5 Today s Topics nnouncmnts: Homwok #3 on Wbssign by tonight Du (with Homwok #) on 9/4, 10 PM Rviw: (Ch. 5Pat I) Elctic Potntial Engy, Elctic Potntial Elctic Potntial (Ch. 5Pat II) Elctic
More information3.46 PHOTONIC MATERIALS AND DEVICES Lecture 10: LEDs and Optical Amplifiers
3.46 PHOTONIC MATERIALS AND DEVICES Lctu 0: LEDs and Optical Amplifis Lctu Rfncs:. Salh, M. Tich, Photonics, (John-Wily, Chapts 5-6. This lctu will viw how lctons and hols combin in smiconductos and nat
More informationThe angle between L and the z-axis is found from
Poblm 6 This is not a ifficult poblm but it is a al pain to tansf it fom pap into Mathca I won't giv it to you on th quiz, but know how to o it fo th xam Poblm 6 S Figu 6 Th magnitu of L is L an th z-componnt
More information5.61 Fall 2007 Lecture #2 page 1. The DEMISE of CLASSICAL PHYSICS
5.61 Fall 2007 Lctu #2 pag 1 Th DEMISE of CLASSICAL PHYSICS (a) Discovy of th Elcton In 1897 J.J. Thomson discovs th lcton and masus ( m ) (and inadvtntly invnts th cathod ay (TV) tub) Faaday (1860 s 1870
More informationCHAPTER 5 CIRCULAR MOTION
CHAPTER 5 CIRCULAR MOTION and GRAVITATION 5.1 CENTRIPETAL FORCE It is known that if a paticl mos with constant spd in a cicula path of adius, it acquis a cntiptal acclation du to th chang in th diction
More informationChapter Six Free Electron Fermi Gas
Chapt Six Elcton mi Gas What dtmins if th cystal will b a mtal, an insulato, o a smiconducto? E Band stuctus of solids mpty stats filld stats mpty stats filld stats E g mpty stats filld stats E g Conduction
More informationCollisionless Hall-MHD Modeling Near a Magnetic Null. D. J. Strozzi J. J. Ramos MIT Plasma Science and Fusion Center
Collisionlss Hall-MHD Modling Na a Magntic Null D. J. Stoi J. J. Ramos MIT Plasma Scinc and Fusion Cnt Collisionlss Magntic Rconnction Magntic connction fs to changs in th stuctu of magntic filds, bought
More informationPROBLEM SET #3A. A = Ω 2r 2 2 Ω 1r 2 1 r2 2 r2 1
PROBLEM SET #3A AST242 Figue 1. Two concentic co-axial cylindes each otating at a diffeent angula otation ate. A viscous fluid lies between the two cylindes. 1. Couette Flow A viscous fluid lies in the
More informationQ Q N, V, e, Quantum Statistics for Ideal Gas and Black Body Radiation. The Canonical Ensemble
Quantum Statistics fo Idal Gas and Black Body Radiation Physics 436 Lctu #0 Th Canonical Ensmbl Ei Q Q N V p i 1 Q E i i Bos-Einstin Statistics Paticls with intg valu of spin... qi... q j...... q j...
More informationStudy on the Classification and Stability of Industry-University- Research Symbiosis Phenomenon: Based on the Logistic Model
Jounal of Emging Tnds in Economics and Managmnt Scincs (JETEMS 3 (1: 116-1 Scholalink sach Institut Jounals, 1 (ISS: 141-74 Jounal jtms.scholalinksach.og of Emging Tnds Economics and Managmnt Scincs (JETEMS
More informationGAUSS PLANETARY EQUATIONS IN A NON-SINGULAR GRAVITATIONAL POTENTIAL
GAUSS PLANETARY EQUATIONS IN A NON-SINGULAR GRAVITATIONAL POTENTIAL Ioannis Iaklis Haanas * and Michal Hany# * Dpatmnt of Physics and Astonomy, Yok Univsity 34 A Pti Scinc Building Noth Yok, Ontaio, M3J-P3,
More informationChapter 1 The Dawn of Quantum Theory
Chapt 1 Th Dawn of Quantum Thoy * By th Lat 18 s - Chmists had -- gnatd a mthod fo dtmining atomic masss -- gnatd th piodic tabl basd on mpiical obsvations -- solvd th stuctu of bnzn -- lucidatd th fundamntals
More informationPhysics 111. Lecture 38 (Walker: ) Phase Change Latent Heat. May 6, The Three Basic Phases of Matter. Solid Liquid Gas
Physics 111 Lctu 38 (Walk: 17.4-5) Phas Chang May 6, 2009 Lctu 38 1/26 Th Th Basic Phass of Matt Solid Liquid Gas Squnc of incasing molcul motion (and ngy) Lctu 38 2/26 If a liquid is put into a sald contain
More informationQ Q N, V, e, Quantum Statistics for Ideal Gas. The Canonical Ensemble 10/12/2009. Physics 4362, Lecture #19. Dr. Peter Kroll
Quantum Statistics fo Idal Gas Physics 436 Lctu #9 D. Pt Koll Assistant Pofsso Dpatmnt of Chmisty & Biochmisty Univsity of Txas Alington Will psnt a lctu ntitld: Squzing Matt and Pdicting w Compounds:
More informationSchool of Electrical Engineering. Lecture 2: Wire Antennas
School of lctical ngining Lctu : Wi Antnnas Wi antnna It is an antnna which mak us of mtallic wis to poduc a adiation. KT School of lctical ngining www..kth.s Dipol λ/ Th most common adiato: λ Dipol 3λ/
More informationThe theory of electromagnetic field motion. 6. Electron
Th thoy of lctomagntic fild motion. 6. Elcton L.N. Voytshovich Th aticl shows that in a otating fam of fnc th magntic dipol has an lctic chag with th valu dpnding on th dipol magntic momnt and otational
More informationPhysics 240: Worksheet 15 Name
Physics 40: Woksht 15 Nam Each of ths poblms inol physics in an acclatd fam of fnc Althouh you mind wants to ty to foc you to wok ths poblms insid th acclatd fnc fam (i.. th so-calld "won way" by som popl),
More informationCollision Frequency of Adsorbed Particles
Bulg. J. Phys. 40 (2013) 214 218 Collision Fequency of Adsobed Paticles N.S. Peev Geogi Nadjakov Institute of Solid State Physics, Bulgaian Academy of Sciences, 72 Tzaigadsko Chaussee Blvd., 1784 Sofia,
More informationExtinction Ratio and Power Penalty
Application Not: HFAN-.. Rv.; 4/8 Extinction Ratio and ow nalty AVALABLE Backgound Extinction atio is an impotant paamt includd in th spcifications of most fib-optic tanscivs. h pupos of this application
More informationSpatial channeling of energy and momentum of energetic ions by destabilized Alfvén eigenmodes
Spatial channling of nrgy and momntum of nrgtic ions by dstabilizd Alfvén ignmods Ya.I. Kolsnichnko 1,V.V. Lutsnko 1, R.B. Whit, Yu.V. Yakovnko 1 1 Institut for Nuclar Rsarch, Kyiv, Ukrain Princton Plasma
More informationMagnetic Fluctuation-Induced Particle Transport. and Zonal Flow Generation in MST
Magnetic Fluctuation-Induced Paticle Tanspot and Zonal Flow Geneation in MST D.L. Bowe Weixing Ding, B.H. Deng Univesity of Califonia, Los Angeles, USA D. Caig, G. Fiksel, V. Minov, S.C. Page, J. Saff
More informationElectron spin resonance
Elcton sonanc 00 Rlatd topics Zman ffct, ngy quantum, quantum numb, sonanc, g-facto, Landé facto. Pincipl With lcton sonanc (ESR) spctoscopy compounds having unpaid lctons can b studid. Th physical backgound
More informationPHYS 272H Spring 2011 FINAL FORM B. Duration: 2 hours
PHYS 7H Sing 11 FINAL Duation: hous All a multil-choic oblms with total oints. Each oblm has on and only on coct answ. All xam ags a doubl-sidd. Th Answ-sht is th last ag. Ta it off to tun in aft you finish.
More informationPHYS 272H Spring 2011 FINAL FORM A. Duration: 2 hours
PHYS 7H Sing 11 FINAL Duation: hous All a multil-choic oblms with total oints. Each oblm has on and only on coct answ. All xam ags a doubl-sidd. Th Answ-sht is th last ag. Ta it off to tun in aft you finish.
More informationPH672 WINTER Problem Set #1. Hint: The tight-binding band function for an fcc crystal is [ ] (a) The tight-binding Hamiltonian (8.
PH67 WINTER 5 Poblm St # Mad, hapt, poblm # 6 Hint: Th tight-binding band function fo an fcc cstal is ( U t cos( a / cos( a / cos( a / cos( a / cos( a / cos( a / ε [ ] (a Th tight-binding Hamiltonian (85
More information6.Optical and electronic properties of Low
6.Optical and lctonic poptis of Low dinsional atials (I). Concpt of Engy Band. Bonding foation in H Molculs Lina cobination of atoic obital (LCAO) Schoding quation:(- i VionV) E find a,a s.t. E is in a
More informationCDS 101/110: Lecture 7.1 Loop Analysis of Feedback Systems
CDS 11/11: Lctu 7.1 Loop Analysis of Fdback Systms Novmb 7 216 Goals: Intoduc concpt of loop analysis Show how to comput closd loop stability fom opn loop poptis Dscib th Nyquist stability cition fo stability
More informationDIELECTRICS MICROSCOPIC VIEW
HYS22 M_ DILCTRICS MICROSCOIC VIW DILCTRIC MATRIALS Th tm dilctic coms fom th Gk dia lctic, wh dia mans though, thus dilctic matials a thos in which a stady lctic fild can st up without causing an appcial
More informationTakuya Ohtani (Osaka University Theoretical Astrophysics Group D2) Collaborator: Toru Tsuribe(Osaka Univ.)
Simultaneous Gowth of a Potosta and a Young Cicumstella Disk in the Ealy Phase of Disk Fomation * Takuya Ohtani (Osaka Univesity Theoetical Astophysics Goup D2) Collaboato: Tou Tsuibe(Osaka Univ.) 1 Abstact
More informationFrictional effects, vortex spin-down
Chapt 4 Fictional ffcts, votx spin-down To undstand spin-up of a topical cyclon it is instuctiv to consid fist th spin-down poblm, which quis a considation of fictional ffcts. W xamin fist th ssntial dynamics
More information4.4 Linear Dielectrics F
4.4 Lina Dilctics F stal F stal θ magntic dipol imag dipol supconducto 4.4.1 Suscptiility, mitivility, Dilctic Constant I is not too stong, th polaization is popotional to th ild. χ (sinc D, D is lctic
More information(, ) which is a positively sloping curve showing (Y,r) for which the money market is in equilibrium. The P = (1.4)
ots lctu Th IS/LM modl fo an opn conomy is basd on a fixd pic lvl (vy sticky pics) and consists of a goods makt and a mony makt. Th goods makt is Y C+ I + G+ X εq (.) E SEK wh ε = is th al xchang at, E
More informationV7: Diffusional association of proteins and Brownian dynamics simulations
V7: Diffusional association of poteins and Bownian dynamics simulations Bownian motion The paticle movement was discoveed by Robet Bown in 1827 and was intepeted coectly fist by W. Ramsay in 1876. Exact
More informationFourier transforms (Chapter 15) Fourier integrals are generalizations of Fourier series. The series representation
Pof. D. I. Nass Phys57 (T-3) Sptmb 8, 03 Foui_Tansf_phys57_T3 Foui tansfoms (Chapt 5) Foui intgals a gnalizations of Foui sis. Th sis psntation a0 nπx nπx f ( x) = + [ an cos + bn sin ] n = of a function
More informationSeven years of Hall thruster modeling: An European collaboration between Bari and Greifswald
Svn yas of Hall thust modling: An Euopan collaboation btwn ai and Gifswald IEPC-7- Psntd at th 3 th Intnational Elctic Populsion Confnc, Flonc, Italy F. accogna *, S. Longo and M. Capitlli Dip. Di Chimica,
More informationFree carriers in materials
Lctu / F cais in matials Mtals n ~ cm -3 Smiconductos n ~ 8... 9 cm -3 Insulatos n < 8 cm -3 φ isolatd atoms a >> a B a B.59-8 cm 3 ϕ ( Zq) q atom spacing a Lctu / "Two atoms two lvls" φ a T splitting
More informationProgress of HMGC Nonlinear Simulation
Pogess of HMGC Nonlinea Simulation Andeas Biewage [andeas@biewage.de] ENEA - Fascati Italy GSEP Wokshop 29 This wok is suppoted by SciDAC GSEP. Andeas Biewage (ENEA - Fascati) Pogess of HMGC Nonlinea Simulation
More information1. Radiation from an infinitesimal dipole (current element).
LECTURE 3: Radiation fom Infinitsimal (Elmntay) Soucs (Radiation fom an infinitsimal dipol. Duality in Maxwll s quations. Radiation fom an infinitsimal loop. Radiation zons.). Radiation fom an infinitsimal
More informationProfile Formation and Sustainment of Autonomous Tokamak Plasma with Current Hole Configuration
TH/- Pofile Fomation and Sustainment of Autonomous Tokamak Plasma with Cuent Hole Configuation N. Hayashi, T. Takizuka and T. Ozeki Naka JAERI, JAPAN Intoduction [MA/m] [kev] Cuent hole (CH) with nealy
More informationSolutions to Supplementary Problems
Solution to Supplmntay Poblm Chapt Solution. Fomula (.4): g d G + g : E ping th void atio: G d 2.7 9.8 0.56 (56%) 7 mg Fomula (.6): S Fomula (.40): g d E ping at contnt: S m G 0.56 0.5 0. (%) 2.7 + m E
More informationMon. Tues. 6.2 Field of a Magnetized Object 6.3, 6.4 Auxiliary Field & Linear Media HW9
Fi. on. Tus. 6. Fild of a agntid Ojct 6.3, 6.4 uxiliay Fild & Lina dia HW9 Dipol t fo a loop Osvation location x y agntic Dipol ont Ia... ) ( 4 o I I... ) ( 4 I o... sin 4 I o Sa diction as cunt B 3 3
More information22.615, MHD Theory of Fusion Systems Prof. Freidberg Lecture 4: Toroidal Equilibrium and Radial Pressure Balance
.615, MHD Theoy of Fusion Systems Pof. Feidbeg Lectue 4: Tooidal Equilibium and Radial Pessue Balance Basic Poblem of Tooidal Equilibium 1. Radial pessue balance. Tooidal foce balance Radial Pessue Balance
More informationThe Source of the Quantum Vacuum
Januay, 9 PROGRESS IN PHYSICS Volum Th Souc of th Quantum Vacuum William C. Daywitt National Institut fo Standads and Tchnology (tid), Bould, Coloado, USA E-mail: wcdaywitt@athlin.nt Th quantum vacuum
More informationCollisions between electrons and ions
DRAFT 1 Collisions btwn lctrons and ions Flix I. Parra Rudolf Pirls Cntr for Thortical Physics, Unirsity of Oxford, Oxford OX1 NP, UK This rsion is of 8 May 217 1. Introduction Th Fokkr-Planck collision
More informationEE243 Advanced Electromagnetic Theory Lec # 22 Scattering and Diffraction. Reading: Jackson Chapter 10.1, 10.3, lite on both 10.2 and 10.
Appid M Fa 6, Nuuth Lctu # V //6 43 Advancd ctomagntic Thoy Lc # Scatting and Diffaction Scatting Fom Sma Obcts Scatting by Sma Dictic and Mtaic Sphs Coction of Scatts Sphica Wav xpansions Scaa Vcto Rading:
More information217Plus TM Integrated Circuit Failure Rate Models
T h I AC 27Plu s T M i n t g at d c i c u i t a n d i n d u c to Fa i lu at M o d l s David Nicholls, IAC (Quantion Solutions Incoatd) In a pvious issu o th IAC Jounal [nc ], w povidd a highlvl intoduction
More informationAcoustics and electroacoustics
coustics and lctoacoustics Chapt : Sound soucs and adiation ELEN78 - Chapt - 3 Quantitis units and smbols: f Hz : fqunc of an acoustical wav pu ton T s : piod = /f m : wavlngth= c/f Sound pssu a : pzt
More informationCONDITION OF DAMPING OF ANOMALOUS RADIAL TRANSPORT, DETERMINED BY ORDERED CONVECTIVE ELECTRON DYNAMICS
CONDITION OF DAMPING OF ANOMALOUS RADIAL TRANSPORT DETERMINED BY ORDERED CONVECTIVE ELECTRON DYNAMICS VIMaslv SVBachuk VILapshin YuVMlnsv* EDVlkv NSC Khakv Insiu f Physics and Tchnlgy Khakv 608 Ukain *Kaain
More informationDiscrimination of Modes of Double- and Single- Negative Grounded Slab
Wold Acadm of Scinc, Engining and Tchnolog Intnational Jounal of Elctonics and Communication Engining Vol:, No:5, 7 Discimination of Mods of Doubl- and Singl- Ngativ Goundd Slab R. Boghol, T. Aguili Intnational
More informationRydberg-Rydberg Interactions
Rydbeg-Rydbeg Inteactions F. Robicheaux Aubun Univesity Rydbeg gas goes to plasma Dipole blockade Coheent pocesses in fozen Rydbeg gases (expts) Theoetical investigation of an excitation hopping though
More informationUGC POINT LEADING INSTITUE FOR CSIR-JRF/NET, GATE & JAM. are the polar coordinates of P, then. 2 sec sec tan. m 2a m m r. f r.
UGC POINT LEADING INSTITUE FOR CSIR-JRF/NET, GATE & JAM Solution (TEST SERIES ST PAPER) Dat: No 5. Lt a b th adius of cicl, dscibd by th aticl P in fig. if, a th ola coodinats of P, thn acos Diffntial
More informationHomework 7 Solutions
Homewok 7 olutions Phys 4 Octobe 3, 208. Let s talk about a space monkey. As the space monkey is oiginally obiting in a cicula obit and is massive, its tajectoy satisfies m mon 2 G m mon + L 2 2m mon 2
More informationCh. 6 Free Electron Fermi Gas
Ch. 6 lcto i Gas Coductio lctos i a tal ov fl without scattig b io cos so it ca b cosidd as if walitactig o f paticls followig idiac statistics. hfo th coductio lctos a fqutl calld as f lcto i gas. Coductio
More informationEstimation of a Random Variable
Estimation of a andom Vaiabl Obsv and stimat. ˆ is an stimat of. ζ : outcom Estimation ul ˆ Sampl Spac Eampl: : Pson s Hight, : Wight. : Ailin Company s Stock Pic, : Cud Oil Pic. Cost of Estimation Eo
More informationREPORT DOCUMENTATION PAGE
REPORT DOCUMENTATION PAGE Fom Appovd OMB No. 0704-0188 Public poting bud fo this collction of infomation is stibatd to avag 1 hou p spons, including th tim fo viwing instuctions, saching xisting data soucs,
More information2 E. on each of these two surfaces. r r r r. Q E E ε. 2 2 Qencl encl right left 0
Ch : 4, 9,, 9,,, 4, 9,, 4, 8 4 (a) Fom the diagam in the textbook, we see that the flux outwad though the hemispheical suface is the same as the flux inwad though the cicula suface base of the hemisphee
More informationSection 11. Timescales Radiation transport in stars
Section 11 Timescales 11.1 Radiation tanspot in stas Deep inside stas the adiation eld is vey close to black body. Fo a black-body distibution the photon numbe density at tempeatue T is given by n = 2
More informationBrushless Doubly-Fed Induction Machines: Torque Ripple
Bushlss Doubly-Fd Induction Machins: Toqu Rippl Tim. D. Stous, Xuzhou Wang, Hn Polind, Snio Mmb, IEEE, and J. A. (Bam Fia, Fllow, IEEE Abstact-- Th Bushlss DFIM without its bush-ga and slip-ings loos pomising
More informationOverview. 1 Recall: continuous-time Markov chains. 2 Transient distribution. 3 Uniformization. 4 Strong and weak bisimulation
Rcall: continuous-tim Makov chains Modling and Vification of Pobabilistic Systms Joost-Pit Katon Lhstuhl fü Infomatik 2 Softwa Modling and Vification Goup http://movs.wth-aachn.d/taching/ws-89/movp8/ Dcmb
More informationDerivation of Electron-Electron Interaction Terms in the Multi-Electron Hamiltonian
Drivation of Elctron-Elctron Intraction Trms in th Multi-Elctron Hamiltonian Erica Smith Octobr 1, 010 1 Introduction Th Hamiltonian for a multi-lctron atom with n lctrons is drivd by Itoh (1965) by accounting
More informationRadial Inflow Experiment:GFD III
Radial Inflow Expeiment:GFD III John Mashall Febuay 6, 003 Abstact We otate a cylinde about its vetical axis: the cylinde has a cicula dain hole in the cente of its bottom. Wate entes at a constant ate
More informationNUMERICAL STUDY OF A DC ELECTROMAGNETIC LIQUID METAL PUMP: LIMITS OF THE MODEL
NUMERICAL SUDY OF A DC ELECROMAGNEIC LIQUID MEAL PUMP: LIMIS OF HE MODEL Ndltcho Kandv Institut d chch d'hydo-qubc (IREQ) Qubc, Canada 600, av d la Montagn, Shawinigan, Qubc, G9N 7N5, Canada kandv.ndltcho@iq.ca
More informationCHAPTER 5 CIRCULAR MOTION AND GRAVITATION
84 CHAPTER 5 CIRCULAR MOTION AND GRAVITATION CHAPTER 5 CIRCULAR MOTION AND GRAVITATION 85 In th pious chapt w discussd Nwton's laws of motion and its application in simpl dynamics poblms. In this chapt
More informationA Most Useful Device of Studying Electrode Processes: The Rotating Disk Electrode
A Most Useful Device of Studying Electode Pocesses: The Rotating Disk Electode the theoetical basis Soma Vesztegom Laboatoy of Electochemisty & Electoanalytical Chemisty Eötvös Loánd Univesity of Budapest
More informationPath (space curve) Osculating plane
Fo th cuilin motion of pticl in spc th fomuls did fo pln cuilin motion still lid. But th my b n infinit numb of nomls fo tngnt dwn to spc cu. Whn th t nd t ' unit ctos mod to sm oigin by kping thi ointtions
More informationMONTE CARLO SIMULATION OF FLUID FLOW
MONTE CARLO SIMULATION OF FLUID FLOW M. Ragheb 3/7/3 INTRODUCTION We conside the situation of Fee Molecula Collisionless and Reflective Flow. Collisionless flows occu in the field of aefied gas dynamics.
More informationThe geometric construction of Ewald sphere and Bragg condition:
The geometic constuction of Ewald sphee and Bagg condition: The constuction of Ewald sphee must be done such that the Bagg condition is satisfied. This can be done as follows: i) Daw a wave vecto k in
More informationChapter 7 Dynamic stability analysis I Equations of motion and estimation of stability derivatives - 4 Lecture 25 Topics
Chapt 7 Dynamic stability analysis I Equations of motion an stimation of stability ivativs - 4 ctu 5 opics 7.8 Expssions fo changs in aoynamic an populsiv focs an momnts 7.8.1 Simplifi xpssions fo changs
More informationEAcos θ, where θ is the angle between the electric field and
8.4. Modl: Th lctric flux flows out of a closd surfac around a rgion of spac containing a nt positiv charg and into a closd surfac surrounding a nt ngativ charg. Visualiz: Plas rfr to Figur EX8.4. Lt A
More informationUsing the Hubble Telescope to Determine the Split of a Cosmological Object s Redshift into its Gravitational and Distance Parts
Apion, Vol. 8, No. 2, Apil 2001 84 Using th Hubbl Tlscop to Dtmin th Split of a Cosmological Objct s dshift into its Gavitational and Distanc Pats Phais E. Williams Engtic Matials sach and Tsting Cnt 801
More information06 - ROTATIONAL MOTION Page 1 ( Answers at the end of all questions )
06 - ROTATIONAL MOTION Page ) A body A of mass M while falling vetically downwads unde gavity beaks into two pats, a body B of mass ( / ) M and a body C of mass ( / ) M. The cente of mass of bodies B and
More informationMagnetohydrodynamics (MHD) I
Magnetohydodynamics (MHD) I Yong-Su Na National Fusion Reseach Cente POSTECH, Koea, 8-10 May, 006 Contents 1. Review Confinement & Single Paticle Motion. Plasmas as Fluids Fluid Equations 3. MHD Equations
More informationMicro-bunching: Longitudinal Bunch Profile Measurements at TTF
Shot Pulses in Rings Mico-bunching: Longitudinal Bunch Pofile Measuements at TTF ) The time vaying fields in a tansvese mode cavity kick the font of a bunch up, and the back of the bunch don. ) A betaton
More information0WAVE PROPAGATION IN MATERIAL SPACE
0WAVE PROPAGATION IN MATERIAL SPACE All forms of EM nrgy shar thr fundamntal charactristics: 1) thy all tral at high locity 2) In traling, thy assum th proprtis of was 3) Thy radiat outward from a sourc
More informationAdvanced School on Synchrotron and Free Electron Laser Sources and their Multidisciplinary Applications
96- Advancd School on Synchoton and F Elcton Las Soucs and thi Multidisciplinay Applications 7-5 Apil 8 Small angl x-ay scatting (Basic Aspcts) Aldo Caivich Univsity d Sao Paulo Bazil Small-Angl X ay Scatting
More informationII. FORMULATION OF THE PROBLEM
Intnational Jounal of Engining Scinc Invntion ISSN (Onlin): 39 6734 ISSN (Pint): 39 676 www.ijsi.og Volum 6 Issu 9 Sptmb 7 PP. - Study of Unstady Magntohydodynamic Flow of n Incompssibl Viscous Elctically
More informationCh. 24 Molecular Reaction Dynamics 1. Collision Theory
Ch. 4 Molcular Raction Dynamics 1. Collision Thory Lctur 16. Diffusion-Controlld Raction 3. Th Matrial Balanc Equation 4. Transition Stat Thory: Th Eyring Equation 5. Transition Stat Thory: Thrmodynamic
More informationDiffraction. Diffraction: general Fresnel vs. Fraunhofer diffraction Several coherent oscillators Single-slit diffraction. Phys 322 Lecture 28
Chapt 10 Phys 3 Lctu 8 Dffacton Dffacton: gnal Fsnl vs. Faunhof dffacton Sval cohnt oscllatos Sngl-slt dffacton Dffacton Gmald, 1600s: dffacto, dvaton of lght fom lna popagaton Dffacton s a consqunc of
More informationGet Solution of These Packages & Learn by Video Tutorials on GRAVITATION
FEE Download Study Packag fom wbsit: www.tkoclasss.com & www.mathsbysuhag.com Gt Solution of Ths Packags & an by Vido Tutoials on www.mathsbysuhag.com. INTODUCTION Th motion of clstial bodis such as th
More informationand integrated over all, the result is f ( 0) ] //Fourier transform ] //inverse Fourier transform
NANO 70-Nots Chapt -Diactd bams Dlta uctio W d som mathmatical tools to dvlop a physical thoy o lcto diactio. Idal cystals a iiit this, so th will b som iiitis lii about. Usually, th iiit quatity oly ists
More informationLoad Equations. So let s look at a single machine connected to an infinite bus, as illustrated in Fig. 1 below.
oa Euatons Thoughout all of chapt 4, ou focus s on th machn tslf, thfo w wll only pfom a y smpl tatmnt of th ntwok n o to s a complt mol. W o that h, but alz that w wll tun to ths ssu n Chapt 9. So lt
More informationAnalytical calculation of the power dissipated in the LHC liner. Stefano De Santis - LBNL and Andrea Mostacci - CERN
Analytical calculation of the powe dissipated in the LHC line Stefano De Santis - LBNL and Andea Mostacci - CERN Contents What is the Modified Bethe s Diffaction Theoy? Some inteesting consequences of
More informationDo not turn over until you are told to do so by the Invigilator.
UNIVERSITY OF EAST ANGLIA School of Mathematics Main Seies UG Examination 2015 16 FLUID DYNAMICS WITH ADVANCED TOPICS MTH-MD59 Time allowed: 3 Hous Attempt QUESTIONS 1 and 2, and THREE othe questions.
More informationCollisionless anisotropic electron heating and turbulent transport in coronal flare loops
Collisionlss anisotropic lctron hating and turbulnt transport in coronal flar loops K.-W. L and J. Büchnr 5 April 2011 Outlin: 1. HXR obsrvation and standard flar modl 2. Linar stability analysis (multi-fluid
More informationNEWTON S THEORY OF GRAVITY
NEWTON S THEOY OF GAVITY 3 Concptual Qustions 3.. Nwton s thid law tlls us that th focs a qual. Thy a also claly qual whn Nwton s law of gavity is xamind: F / = Gm m has th sam valu whth m = Eath and m
More informationMagnetic phase transition and confinement regimes
Magnetic phase tansition and confinement egimes Emilia R. Solano 1,2, Richad D. Hazeltine 3 1 Laboatoio Nacional de Fusión, CIEMAT, Madid, Spain 2 JET EFDA CSU 3 Institute fo Fusion Studies, Univ. of Texas
More informationDiffraction. Diffraction: general Fresnel vs. Fraunhofer diffraction Several coherent oscillators Single-slit diffraction. Phys 322 Lecture 28
Chapt 10 Phys 3 Lctu 8 Dffacton Dffacton: gnal Fsnl vs. Faunhof dffacton Sval cohnt oscllatos Sngl-slt dffacton Dffacton Gmald, 1600s: dffacto, dvaton of lght fom lna popagaton Dffacton s a consqunc of
More information/6/4 5 Stuctue-Induced Sediment Scou ef: Eosion and Sedimentation, P.Y. Julien, 998 The Mechanics of Scou in the Maine Envionment, B.M. Sume and J. Fedsoe, Evaluating Scou at Bidges (HEC-8), E.. ichadson
More information