Thomas BMT Spin Or Algebra - UNT Digital Library
BNL 66455April 19,1999Editors:M. Tigner, Cornel1A. Chao, SLACPublisher: World ScientificSections written by Thomas Roser, BNL:-2.7.1 - Thomas BMT equation2.2.2 - Spin or Algebra2.7.3 - Spin Rotators and Siberian Snakes2.7.4 - Ring with Spin Rotator and Siberian Snakes2.7.5 Depolarizing Resonances and Spin Flippers&7.6.2 Proton Beam Polarimeters-
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Handbook of A c c e l e r a t o r Physics and EngineeringBy A. Chao (SLAC) ; M. Tigner (Cornell) WorldS c i e n t i f i c , sections(2.7.1-2.7.5and 7.6,2.Iintroducing a large number of background beam-2.7 POLARIZATIONscheme has moved beyond the conceptual stage,to date.2.7.1 Thomas-BMT equationZ Roser; BNLion events, No indirect beam-beam compensationBetatron phase cancelation A single set ofbeam-beam resonances may be eliminated by adjusting the phase advance between neighboringIPS in a storage ring [18]. For example, if t5ephase advance between two Ips is A& A& 2n(p/N q) (p, q, N integers, p odd), then allbeam-beam resonances of order N are canceled.This scheme, which has not been fried in practice,relies on the collision points being clustered - notsmoothly distributed around the circumference.Other resonances, tune shifts, and tune spreads areleft uncompensated.BNL- 664 5 5Precession of polarization vector F of a particlewith mass m and charge Z e [l,2,3,4], P‘ is defined in the particle rest ftame, 2 and Bin the laboratory *e.B’ 2-1 Bll, Zil (v’. B)v’/v2.In the ftame rotating with v’ given by theLorentz force equation and assume Ell 0, d,xadp- fixp’atReferencesYK Batygin, T. Katayama, RTKEN-AF-AC-3,1997JE. Augustin et al, p.113, Vol. 2, Proc. 7th Int.Conf. H. E. Acc. (1969)G. Arzelia et a p.150, Roc. 8th Int. Conf. H. E.Acc. (1971)H. Zyngier, AD? Proc. 57 (1979) p.136YaS. Derbenev, 3rd All Union Conf. on Acc.(1972); INP 70-72 (1972); SLAC TRANS 151.(1973)E. Keil, Proc. 3rd ICFA Beam Dyn. Wkshp.(1989); ERN-LEI?-lW89-37 (1989)Orsay SR Group, EEE Trans. Nucl. Sci. NS-26,No.3 (1979) 3559R. Chehab et al, Proc. 1lth Int. Conf. High EnergyAcc. (1980)VE. Balakin, NA. Solyak, Proc 13th Int. Conf.High Energy ACC.(1986)[lo] N Soly&-INP 884,Novosibirsk (1988)[113 D. Whittum, R. Siemann, PAC 971121 Y. Chin, DESY 87-011 (1987)1131 JB. Rosenzweig et al, hoc. Lake ArrowheadWkshp., AD? Press (1989) p.3241141 R. Talman, unpublished (1976)[15j E. Tsyganov et al, SSCL-519, (1993); JINR-Eg964, Dubna (1996)[16] V. Shiltsev, D. Finley, FERMILAB-TM-2008(1997)[17J D. Whittum et al, LBL-25759 (1988)[18] S. Peggs, Proc. Wkshp. on AP Issues for SSC,UM HE 84-1 (1984) p.58dv’dt9 is the anomalous magnetic moment;25 is the pqyrom eticratio (Landau fac-G g G0.001159650.00116592p1.79285p-0.142562d3He 4.19144eI3H 47401I
One-turn matrix Mo (0):Mo (e) M,:References[l] B.W.Montague, Phys. Rep. 113 (1984)1[2] L.H. Thomas,Phil.Mag. 3 (1927)1[3] V. Bargmann, L. Michel, V.L. Telegdi, PRL 2(1 959)435[4] S.Y.Lee, World Scientific (1996)2.7.2(11)where 8 is the starting (and ending) azimuth. The spin tune uw and the spin closed orbit f i (alsocalled A0 axis or stable spin direction) are1(12)cos (7rvw) -tr2 (Mo (e))Spinor Algebra2: Rose BNLindependent of 8Coordinate frame symbols and indices: (1,2,3) (radial outward, longitudinal forward, verticalup) (2,-5, 9). Pauli matrices:a' (61,a2, a3)0 11 01 O)'(0 -1)] [((T1q8 a2a2 a3a3 I"Spin Rotators" rotate P' without changing G.Examples of Spin Rotators:(1)(2)3( 4)( 4) 2.73 Spin Rotators and Siberian SnakesiT Rosel; BNLii)( -0103 ia21(cyclic perm.)tr(ai) 0, det(ai) -1 1. Wien Filter: Transverse E,, B, with condiE x i 7 - 1B'tion- (3)(iq iz. (zxc)Spinor representation of normalized vector F:IY(4)MwienF ?pa 2. SolenoidCOScpcp- ia3 sin -22Ze(l G)mcPYc p Thomas-BMTequation in spinor or unitary representation:- - M2M1J iidscpcp cos - - 202 sin (2)22Example: cp 90" and p 1 GeV/c requires J BIIds 1.88 T-m for protons andJ BIIds 5.23 T-m for elecuons.kf&le.oid-d p f i x Fdt3. Dipole:ordt2solution for constant fi : xis A, 161 w):(7), ( t ) M (%4, (0) 3 or(a - P (t)) M ( , w t (a) - F ( 0 ) ) Mt (fi,wt)Rotation operation M by angle cp w t aroundaxis nI'[cosInverse operation:2(i) i (Z - ii)sin (g)n Ai2 sin0:-. 4. Full twist helical dipole withB ( s ) BO ( s i n y , O , c o s T ) , AM(fi,cp) exp - i ( - . i z ) -cpcpcos - io3 sin -(3)22Example: cp 90" and /3 x 1 requires J Byds 2.74 T-m for protons andJ Byds 2.31 T-m for electrons.MDipole(9)tr ( Ad)(3)103 s cpcpM cos - i(a2 xa3) sin -2ZeG BOXx ( 1 -G' r) mc 27r2(4)
5. A "Full Siberian Snake" rotates P' by 180"(9 n) around an axis in the horizontalplane with angle Q fkom 2 (Snake axis angle) Ill:M s n & -i (a1cosa2 sin or) (5)5. Ring with N pairs of full Siberian snakeswith axis angles or; and or; at 0; and g6:Mo(8) (-)NexP(-ic3x) Nx c(or;-a:)i lNote:(i) MDipoleMSnakeMDipole MSnake(ii) Type 1 snake: snake axis is longitudinal (or CE,( -Q6EEl (or; - or:).[l] YaS. Derbenev, A.M. Kondratenko, PA 8 (1978)and SiberianSnakesT.Rose BNLMO(8) exp (-iu3nG )(1)Note: usp G7.2. Ring with solenoid (partial type 1 Siberiansnake) at 80 0 [11:cp COS ( X G )M (e) cos -2cp sin ((n- 8) G7)- iul sin 2cp- iu2 sin - cos ((n- 8) G7)2cp- iu3 cos sin (nG7)(2)2 cos 5 cos (nGy).3. Ring with full Siberian snake with axis anglea at 00 0:MO(0) Note: usp - 0)GT)sin(a! - (n- 8)Gn/)] (3)--i[01 COS(CY - (T02for all 8; 8 nri.cosa Bsina n; then usp References[l] T.Roser, ROC.Workshop on Siberian Snakes andDepolarizing Techniques (1989) p.14421. Ideal ring without spin rotators or Siberiansnakes:Note: cos(nv,)MO is energy independent forNote:References2*704 Ring With SpinNi lgoo)(iii) Type 2 snake: snake axis is radial (or 0")115(5)- .720 2.7.5Depolarizing Resonances and SpinFlippersI: Roser, BNLThomas-BMT equation with azimuthal coordi-nate 8 as independent variable and the fields expressed in terms of the particle coordinates:(1 G7)g' - p ( 1 G)where p is bending radius. Resonance strength is111EK -f t e x p (-iK8) d62nK kP t uy : intrinsic resonance from verticalbetatron motion, P is the super periodicityK k : imperfection resonance from verticalclosed orbit distortions.For isolated resonance: E K exp (iK8).In frame rotating around jj with tune K , K exp ( m3)11,4. Ring with two full Siberian snakes with axisangles CY, and ab at Bu and 8b :Mo (8) -exp(-iu3x)(4)Under adiabatic conditions:x E - 4- (n- 66 4- &)G7Note: MO is energy independent for18, n;then usp ;;(ab- cra).Ob(2)-PY 104(G7 - K )d(G7 - Kl2 K 2I(4)
Passage through an isolated resonance, FroissartStora Equation [2]:-PfinalEnitialwithCY- 2exp(- )n IEKI-1(5)depolarizingresonances were not too strong in theweak focusing ZGS; thus it only required careful orbit control and fast betatron tune jumps tomaintain the polarization while crossing the resonances [l].c4GY) dB(crossing speed). Fast passage- PfinalM Pinitiai.-Pinitial 4 spin flip.Slow passage- PfinalM. Artificial resonance from local oscillating field (wLinac applied frequency, wo revolution frequency):BII on Source\2GQSllCOS(Wt)MeVPohrmler(7)Spin flip by ramping artificial resonance throughresonance condition with speed CY:Kend - KstartCY (8)2nNwhere N is number of turns during ramp. Formore than 99% spin flip:4)III a ring with Snakes (vsp additionalhigher order 'Snake' resonances [3] occur at ener-gies close to intrinsic resonances of the ring with-out Snakes when the fractional vertical betatrontune2k - 1AvY 2(21- 1)With vertical closed orbit distortions Snake resonances also occur whenReferences[l) ED.Courant, R.Ruth, BNL-51270(1980)[2] M.Froissart, R.Stora, NIM 7 (1960)297[3] S.Y. Lee, S . Tepikian, PRL 56 (1986)16352.7.6Polarized Proton Beams and SiberianSnakesA.D.Krisch, U.MichiganIn 1973, the first polarized proton beam was successfully accelerated in the Argonne ZGS.TheFigure 1: The complex individual depolarizing resonance correction hardware installed in the AGS [21.In 1984, polarized protons were first accelerated at the Brookhaven AGS. Maintaining the po-larization was much more difficult, because thestrong-focusing AGS has strong depolarizing resonances. As shown in Rg.1, the AGS requiredcomplex hardware modifications for this difficultjob. Moreover, 45 resonances needed to be corrected individuallyto maintain the polarization upto 22 GeV. A typical AGS resonance correctioncurve is shown in Fig2 [Z]. The polarized beamtune-up required 7 weeks of dedicated AGS operation. Clearly this individual resonance correctiontechnique was impractical for a much higher energy, since the number of imperfection resonancesto be crossed is E / (0.52 GeV). Thus, it becameclear [3] that Siberian snakes (41 (Sec.2.7.34)were needed to accelerate polarized protons above30 GeV.Many Siberian snake experiments have beenperformed at the 500-MeV IUCF Cooler Ring.The snake was a 2 T-msuperconducting solenoidinstalled in a 6-m straight section, as shown in105
Dr. T. RoserAGS DeptBroohaven National LabUpton, NY 11973-5000May 16,1998Dear Dr. Roser,Enclosed you will find type set proofs of your article for the Handbook of AcceleratorPhysics and Engineering for your correction before final editing and publication. Eventhough time is very short, it is being sent to you by post so that you can see, with goodresolution, how it will appear in the book.While the type setting process is largely automated, some needed format changes andequations require human intervention, thereby creating opportunity for errors. For thisreason it is extremely important for you to check every aspect PARTICULARLYEQUATIONS AND REFERENCES.Please mark the corrections clearly and fax them back to me at 607 254 4552 as soon aspossible. If you are unable to do it immediately, please note that it will be very difficult toinclude any corrections received after July 15 so if we have not heard from you by then wewill assume that you have no corrections to submit.Your expert and patient participation in this enterprise is very deeply appreciated indeed andwe hope that you will have your copy of the finished book in hand early in 1999.I?
(max for 90" scattering):All (7 cos2 8') sin28'(3 cos2 8/127I9(22)The polarized electron targets in Moller polarimeters typically consist of thin ferromagneticfoils exposed to a 100 gauss external magneticfield oriented with a given angle to the foil axis.A 8.3% maximum polarization of the target electrons (2 external out of 26 electrons per iron atom)has been achieved. The target polarization is measured to 1.5 - 2.0% precision (1.7% at SLAC).The full beam polarization vector is determined by varying the foil orientation relative tothe beam.The analyzing power of Mraller polarimetersneed corrections due to orbital motion of innershell target electrons [141 (momenta comparable-to e* rest mass).Fig3 shows the SLAC E-154 Mdler Polarimeter [U, 161Bend PlaneMoller. . Target,[2] DB. Gustavson et al,NIM 165 (1979) 177.[3] F.W. Lipps, HA. Toelhoek, Physica, XX (1954)85 and 395[4] HA. Toelhoek, Rev. Mod. Phys. 28 (1956) 277[5] 0. Klein, Y. Nishina, Z . Phys. 52 (1929) 853[6] U.Fano, J. Opt.SOC.Am., 39 (1949) 859171 M. Woods, Proc. Workshop on High Energy Polarimeters, NIKHEF (1996)[8] A. Most, Proc. Workshop on High Energy Polarimeters, NIKHEF (1996); PhD Thesis (1996)[9] M. Placidi, R. Rossmanith, NIM A274 (1989) 79[103 B .Dehning, Dissertation der Facultiit fijr Physik(1995)[I 13 L. Arnaudon et al, Z . Phys. C66 (1995) 45[12] K. Abe et al, PRL 78 (1997) 2075[13] C. Maller ,Ann. Phys. (Leipzig) 14 (1932) 532;J. Arrington et al, NIM A3 11 (1992) 39[14] L.G. Levchuk, NTM A345 (1994) 496[15] HR. Band, AIP Proc. 343 (1994) p245[161 H.R. Band et al, SLAC-PUB-7370 (1997)7.63 Proton Beam PolarimetersT Roser; BNLBeam polarization is typically measured using anuclear reaction in a plane that is perpendicular tothe polarization direction. The polarization P andits statistical error A P (for P A 1)are calculated as:Mask,vvSecondary MaskScattering PlaneA: Analyzing power of nuclear scatteringor reactionNL(NR):Number of particles observed to the left(right) of the beam.If the beam polarization is alternated between(along the stable spin direction n) and - (opposite to the stable spin direction n) the polarizationcan be measured with much less sensitivity to systematic errors: See Tab. 1.Figure 3: The SLAC M0ller Polarimeter."drvL NR N; N;References[l] W. Haeberli et al, NIM 163 (1979) 403[2] H. Spinka et al, NIM 21 1 (1983) 239References[3] S.Kat0 et al, NIM 169 (1980) 589[4] M. W. McNaughton et al, NIM A241 (1985)435[5] DL. Adams et al, Phys. Lett. B264 (1991)462[l] VN. Baier and V.A. Khoze, Sov. J. Nucl. Phys. 9(1969)238178
Table 1: Typical nuclear reactions used for proton beam polarimeters.Energy 0.1 GeV0.1. .1 GeV1. .20 GeV 2OGeVReactionp ” C - ) p 12 Cp ’” C p Xp p p pp p p pZI 12 C T (-) X7.7 CONTROLS A N D TIMINGK. Rehlich, DESYChange in computer hardware and software isKinematic region6 x 50’6 x 15”t -0.15 (GeV/c)2t -0.0001 (GeV/c)2vt0.5GeV/c:x x 0.5Anal. powerA 0.8. . -0.9A x 0.2. .0.6A 0.7GeV/cPT,ahA x 0.04A x 0.15Client programs often need information froma group of devices or need to operate on such agroup. A middle layer server should provide suchcollective reports and controls. Likewise, the mid-Architecture As shown in Fig.1, the overall architectureconsists of three layers of computers. Adle layer should supply frequently requested dataof all its front-end computers in a single blocktransfer. Proxy services may also be added sincethe middle layer servers can be faster than thefront-end computers. But, a direct access to frontends (and not just for debugging purposes) is stillnecessary. In general, the middle layer implements higher services and improves the performance of the system.Data bases, file servers, simulation serversand other kind of servers without direct deviceconnections should be placed in the middle layeralso. Subsystems of the machine use their ownsubnet with front-end computers. The front-endsare distriiuted and close to the devices of the machine. Some hardware is directly connected to thedevice servers, other equipment use field bussesto connect the front-end electronics to the deviceservers. Fieldbus electronics introduce a furtherlevel of computers in the system. Programmableend layer with device servers and UO and a middle layer with powerful group servers. The upperlayer is the interface to the operators. These upperservices should be available to the consoles in thecontrol room, the experts working at the machineand the specialists in their offices. All of themshould be able to use the same programs. Only thelevel of det‘ails presented should be different, butnonetheless available to all levels of users. Modifications of device data must be protected withaccess rights.Since a lot of users and client programs accessa lot of data from the front-end and the middlelayer, a fast network is necessary to decouple thedisplay stations. A net switch that routes packets from the clients to their servers provides theimportant bandwidth.are examples of such stand-alone processors.All group servers and most fi-ont-end serversare equipped with disk drives. The other deviceservers mount their N e systems from the corresponding group server. If a front-end has torun stand-alone in case of a network problem, itshould have a direct connected disk or must havethe program and data files in memory. Archivingof all data fiom the equipment can consume a highportion of the network bandwidth if the storage isnot in a local disk.Front-end computer Most of the device inputand output channels connect via VME modulesor fieldbus electronics to the device servers. TheVME system is designed for a reliable industrialelectronic environment. Almost any computer,analog or digital input/output module and field-rapid on the scale of accelerator constructionschedules. Nevertheless software developmentmust begin early to be ready in time. Most ofthe investment in a control system goes into thesoftware and front-end electronics. For front endcomponents the use of industrial standards is nowquite safe as systems such as VME have shown along lifetime.Softwaredevelopment should be based on thenew industrial methods. Object oriented toolshave proven to be very powerN for control system design. In addition to object orientation, implementation on more than one platform leadsto better design and helps to prepare for the inevitable evolution of computer systems during theproject lifetime. Below we discuss the general architectureof a system and argu for a clear modulardesign of hardware and software together.top level with display or client programs, a fi-ont-Logic Controller (PLC) and “intelligent” devices179
Editors: M. Tigner, Cornel1 A. Chao, SLAC Publisher: World Scientific BNL 66455 April 19,1999 Sections written by Thomas Roser, BNL: 2.7.1 - Thomas - BMT equation 2.2.2 - Spin or Algebra 2.7.3 - Spin Rotators and Siberian Snakes 2.7.4 - Ring with Spin Rotator and Siberian Snakes 2.7.5 - Depolarizing Resonances and
Boxed Studs - Screw Fixing only required if studs are unlined. Fig. 1 Spliced Studs – Back to Back Screw through at maximum 500mm centres. Spliced Studs 0.75 BMT - 150mm studs 1.15 BMT - 64, 76, 92, 150mm studs Spliced Studs 0.50 BMT - 51, 64mm studs 0.55 BMT - 76, 92mm studs 0.75 BMT - 51, 64, 76, 92mm
the Department of National Budget, MoF has developed the Budget Monitoring Tool (BMT). The BMT will facilitate the budgetary bodies and MoF to monitor the financial and physical progress of the approved budgeted activities through a real time monitoring system. In addition to the video tutorial on BMT, The Department of National Budget has .
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Low spin-orbit coupling is good for spin transport Graphene exhibits spin transport at room temperature with spin diffusion lengths up to tens of microns Picture of W. Han, RKK, M. Gmitra, J. Fabian, Nature Nano. 9, 794–807 (2014) Overview: Spin-Orbit Coupling in 2D Materials
Spin current operator is normally defined as: Issues with this definition: 1. Spin is not conserved so the spin current does not satisfy the continuity equation 2. Spin current can occur in equilibrium 3. Spin currents also can exist in insulators 4. Spin current cannot
Chapter 5 Many-Electron Atoms 5-1 Total Angular Momentum Spin magnetic quantum number: ms 2 1 because electrons have two spin types. Quantum number of spin angular momentum: s 2 1 Spin angular momentum: S s s ( 1) h h 2 3 Spin magnetic moment: μs -eS/m The z-component of spin angular momentum: Sz ms h 2 1 h
First course (on tables) Breads/rolls of many types (white, sour, rye, sesame, olive/caper, Italian season) Flavoured butters (honey, garlic, italian others .) Preserves (apple, pear, blackberry, salal) Two scalded milk cheese, one sweet, one savory Stout/Portwine cheese fondue Then: Soups/Stews - one beef/barley, one borshch and one bean pottage 2nd course Salmon Pie (head table gets .
