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Spin Polarization as a Tool for Precision Experiments

Lecture. Erhard Steffens Univ. of Erlangen-Nürnberg, Germany steffens@physik.uni-erlangen.de. Spin Polarization as a Tool for Precision Experiments. Spin in Nuclear and Particle Physics Basics of Storage Rings Spin Precession in Storage Rings Spin Tools for Experiments

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Spin Polarization as a Tool for Precision Experiments

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  1. Lecture Erhard Steffens Univ. of Erlangen-Nürnberg, Germany steffens@physik.uni-erlangen.de Spin Polarization as a Tool for Precision Experiments Spin in Nuclear and Particle Physics Basics of Storage Rings Spin Precession in Storage Rings Spin Tools for Experiments Measurement of Nuclear Moments by Spin Precession in Storage Rings E. Steffens - Univ. of Erlangen- N. - Lecture GGSWBS'16

  2. Spin Polarization as a Tool for Precision Experiments Spin in Nuclear and Particle Physics Basics of Storage Rings Spin Precession in Storage Rings Spin Tools for Experiments Measurement of Nuclear Moments by Spin Precession in Storage Rings E. Steffens - Univ. of Erlangen- N. - Lecture GGSWBS'16

  3. The role of Spin Spin s: intrinsic angular momentum of elementary particles (e, q, g,..). Later applied to composite particles, too, like nucleons (p, n), nuclei (4He, 6Li, 12C,…) and other hadrons (p, K, r, L, S, X,...). Half-integer spin (1/2, 3/2,…): Fermions, e.g. e, q, p, n, 3H, 7Li. They obey Fermi-Dirac statistics – fundamental for the electron structure of atoms and solids! Integer spin (0, 1,..): Bosons, e.g. p, d, a, 6Li,.., g, g (gluon), Z0, W±. They obey Bose-Einstein statistics – fundamental for Super-conductivity and BE condensation. Spin Polarization P: assume Nup particles with spin up, and Ndown with spin down, then P = [Nup - Ndown] / [Nup + Ndown] (-1 ≤ P ≤ +1) E. Steffens - Univ. of Erlangen- N. - Lecture GGSWBS'16

  4. Scattering of a polarized hadron beam (p,d,...) (y-axis up) Scattering normal n Scattering to the left: n up, … to the right: n down LR asymmetry eLR: A() = Analyzing power For Parity-conserving forces (strong interaction): Ax = Az = 0! E. Steffens - Univ. of Erlangen- N. - Lecture GGSWBS'16

  5. Polarization by scattering Elastic scattering, in CM system (Lab→ CM): Compare 1. vector analyzing power Ay() 2. polarization Py´() of outgoing p Time Reversal Invariance (TRI): Py´ = Ay (same ) → Method to create (1st scattering) and calibrate (2nd scatt.) a polarized (proton) beam by “Double Scattering”: historically the 1st method [M. Heusinkfeld and G. Freier (1952): determination of the sign of Vls in the Shell Model of nuclei in p+4He scattering – the p3/2 level in 5He was above the p1/2 , in contrast to Atomic Physics!] . E. Steffens - Univ. of Erlangen- N. - Lecture GGSWBS'16

  6. Spin as a tool The spin s of charged elementary particles (leptons, quarks) is accompanied by a magnetic moment m. For pointlike spin-1/2 particles (no internal structure) the strength of m can be calculated from the Dirac equation (g = 2) and QED (corrections). For particles composed from quarks and gluons (mesons and baryons) and for nuclei composed of nucleons (p, n) there is no such ‘simple’ connection. The spins of particles with magnetic moment can be manipulated by external fields, e.g. a magnetic holding field or a time-dependent rf-field. The spin and its related magnetic moment may be used as a tool, e.g. polarized muons slowed down in solids, indicate their spin direction by its decay distribution m→ e + 2n. By measuring the time dependence of “muon spin rotation” internal fields in the solid under study can be deduced. Using a precisely known external B-field, this effect can be employed to measure the g-factor of the muon. Spin tools are used to manipulate the spins of particles or ensembles of particles, like beams or targets. These could be (i) polarized electron or ion sources, (ii) polarized solid or gas targets, (iii) spin-transparent storage rings conserving spin polarization, (iv) polarimeters to measure the polarization of beams or targets, (v) spin rotators, Siberian snakes etc. E. Steffens - Univ. of Erlangen- N. - Lecture GGSWBS'16

  7. ...precision measurement of moments - magnetic or electric – and comparison with theory might indicate new physics... How to study moments (m,d) of particles with high precision? • No universal rule! But very successful recipe: • ISOLATED LOCATION • LONG OBSERVATION TIMES • Could be realized using a • Trap – e.g. a penning trap for charged particles to study single electrons or protons and compare them with their anti-particle, or optical traps for neutrals • Storage Ring – e.g. a muon storage ring (CERN, BNL) or the light-ion storage ring COSY at FZ Jülich with its powerful Spin Tools E. Steffens - Univ. of Erlangen- N. - Lecture GGSWBS'16

  8. Beams of different polarization states prepared by a source could be injected, e.g. • protons (s = ½) with vertical, radial or longitudinal vector polarization (Py, Px, Ps) • deuterons (s = 1) with vector or 2nd rank tensor polarization (Pi, Pkl) Additional benefit from Storage Rings • An internal (polarized) ultra-thin* gas target could be used to study the beam-target cross section by • detecting the scattered particles (standard method) • detecting the change in time of the circulating current: see TRIC experiment *) 1014 H /cm2 0.2 ng /cm2 = 2∙10-10 g /cm2 Let us have a closer look on storage rings... E. Steffens - Univ. of Erlangen- N. - Lecture GGSWBS'16

  9. Spin Polarization as a Tool for Precision Experiments Spin in Nuclear and Particle Physics Basics of Storage Rings Spin Precession in Storage Rings Spin Tools for Experiments Measurement of Nuclear Moments by Spin Precession in Storage Rings E. Steffens - Univ. of Erlangen- N. - Lecture GGSWBS'16

  10. Elements of a storage ring Lattice of bending and focusing magnets for keeping the beam of charged particles ‘on track’; Vacuum system providing a low pressure for a sufficient beam life time (e.g. UHV system at ≈ 10-9 mbar); Injection system for injection of ion beams at suitable energies, spin-polarized or unpolarized; Acceleration cavities for changing the momentum of stored beams; Diagnostic system to measure non-destructively the beam parameters, e.g. revolution frequency (→ momentum p), beam current, position , emittance, and beam polarization; Cooling system to achieve a low phase space volume and to counteract blow up of the beam by scattering, e.g. Electron Cooling or Stochastic Cooling; Experimental straight sections ; Spin handling system, etc E. Steffens - Univ. of Erlangen- N. - Lecture GGSWBS'16

  11. Low energy ion storage ring:TSR (MPI Heidelberg) Heavy ion storage ring – no shielding required, in contrast to COSY E. Steffens - Univ. of Erlangen- N. - Lecture GGSWBS'16

  12. p, d with momenta up to 3.7 GeV/c • internal experiments – • with circulating beam • external experiments – • with extracted beam Cooler Synchrotron COSY (FZJ) E. Steffens - Univ. of Erlangen- N. - Lecture GGSWBS'16

  13. wc(t) HF Model of a Synchrotron ! Particle dynamics in a circular machine p B(t) • Particles (m = g m0, q) on a circular orbit with R = const. and homogeneous B • field B(t):and |p| = q B R (momentum). • 2. Synchroneous acceleration: with n = harmonic number. • The momentum p rises prop. to B (t), the frequency wHF rises prop. to b and • approaches a limit at b≈ 1. E. Steffens - Univ. of Erlangen- N. - Lecture GGSWBS'16

  14. Particle dynamics in a circular machine Focusing elements (quadrupole magnets) required for stable motion near design orbit → focusing or betatron oscillations in the horizontal (x) and vertical (y) direction. Number of betatron oscillations per turn: Qx (hor.), Qy (vert.). The betatron tune Qx, Qymust not be integer! Otherwise Orbit Resonances are excited → beam losses! E. Steffens - Univ. of Erlangen- N. - Lecture GGSWBS'16

  15. Spin Polarization as a Tool for Precision Experiments Spin in Nuclear and Particle Physics Basics of Storage Rings Spin Precession in Storage Rings Spin Tools for Experiments Measurement of Nuclear Moments by Spin Precession in Storage Rings E. Steffens - Univ. of Erlangen- N. - Lecture GGSWBS'16

  16. = spin component ┴ to , i.e. in the orbit plane aprecession = angle (tangent, ) Precession frequency wp : g = Lorentz factor a = anomaly (g-2)/2 Note: a << 1 for true (pointlike) Dirac particles, like electron and muon (aexp ≠ 0 explained by QED). Reminder: proton has spin component sz = ± ½ and magnetic moment mz = ± ½ gp e /2mp with gp = 5.586 ( i.e. no Dirac particle – proton has internal structure) → proton anomaly ap = 1.793 Spin precession on a circular orbit aprec E. Steffens - Univ. of Erlangen- N. - Lecture GGSWBS'16

  17. Proton energy Ep = gm0c2: wprec. = g ∙ 1.793 ∙ wcycl. • → the hor. spin component precesses about 1.8 x g per turn! We call the number of spin precessions per turn the spin tune ns. • COSY: gmax = 3.67 → nsmax = 6.58 • RHIC: gmax = 267 → nsmax = 479 • Note: the precession angle is always defined relative to the local beam direction, i.e. wp refers to a frame rotating with wc! • During acceleration (“ramping”) ns increases with time and crosses integer values: for ns = n at a certain orbit position z0 the horizontal component has always (i.e. after 1 turn, 2 turns,..., many turns) the same direction → kicks on • by field errors add up coherently → resonant depolarization! • ns = n “imperfection resonance” Spin precession of protons on a circular orbit E. Steffens - Univ. of Erlangen- N. - Lecture GGSWBS'16

  18. Imperfection resonances (ga = n): • proper spin-flip induced with enhanced resonance strength (corr. dipoles); sign changed, but magnitude is conserved! Acceleration of polarized protonsat COSY (B. Lorentz et al, Proc. Spin2010) 6 intrinsic and 10 intrinsic resonances at COSY • Intrinsic resonances ( ga = kQy + m ) • Fast crossing of resonances by tune-jumping (induced by a fast quadrupole magnet) → negligible polarization losses! E. Steffens - Univ. of Erlangen- N. - Lecture GGSWBS'16

  19. Injector with source of polarized particles (ions, electrons) and a pre-accelerator • Flexible scheme, e.g. sign of P might vary from bunch-to-bunch; • but: P must be conserved (to a high degree) during acceleration • Build-up of polarization in a stored beam • of ions or electrons • spin-filtering for polarizing anti-protons ( ) Sokolov-Ternov effect, applied at HERA • see PAX exp. and Parallel Session 8 on Thursday e.g. for the HERMES experiment at DESY • Storage ring must conserve polarization, but resonant depol. is avoided; • Note: Build-up may take a long time (1h for HERA-e, many hours for ‘s) Methods to produce a polarized beam stored in a ring E. Steffens - Univ. of Erlangen- N. - Lecture GGSWBS'16

  20. Polarized source of H- and D- negative ions • Acceleration by AVF Cyclotron to 45 MeV H- and 75 MeV D- ions • Stripping injection into COSY cooler synchrotron • Cooling near injection energy (45 MeV p) by Electron Cooler • Acceleration to pmax = 3.7 GeV/c • Cooling at high energies by Stochastic Cooling in order to improve beam life time and quality Polarized p, d beams at COSY E. Steffens - Univ. of Erlangen- N. - Lecture GGSWBS'16

  21. Principle of polarized ion (proton) sources *) CEX = charge exchange on Alkali vapor E. Steffens - Univ. of Erlangen- N. - Lecture GGSWBS'16

  22. Charge exchange reaction H0(D0) + Cs0 H-(D-) + Cs+ Ref.: Haeberli , NIM 62(1968) COSY Colliding-Beam polarized ion source fast Cs0 beam cold pol. H0↑ atoms E. Steffens - Univ. of Erlangen- N. - Lecture GGSWBS'16

  23. Gas Target in a Storage Ring Detector The basic principle of storage ring experiment is shown schematically. In order to minimize Coulomb losses at the target, it is placed at the center of a low-beta section, where the acceptance angle is high. Electron Cooling (or Stochastic Cooling) may be used in order to compensate for the energy loss and beam blow-up by the target. In this way, storage times of several hours can be accomplished. E. Steffens - Univ. of Erlangen- N. - Lecture GGSWBS'16

  24. Beam cooling to compensate for heating by the target • - Ion rings: Cooling device necessary (Electron cooling, Stochastic cooling) • - Electron rings: usually damping of betatron oscillations due to SR sufficient! Requirements for experiments with internal (pol.) targets • Sufficient acceptance A at the target position (IP) A = ring acceptance • - main losses in Ion Rings: ‚single scattering losses‘ prop. to Z2/ qacc2 • - qacc=(A / b)1/2low-beta values at IP required ! • - for A = 30mm mrad and qacc =10mrad : b = 0.3m E. Steffens - Univ. of Erlangen- N. - Lecture GGSWBS'16

  25. Polarized atoms from source • Storage Cell proposed by W. Haeberli • Proc. Pol. Symp. Karlsruhe 1965, p. 64 • see Review E. Steffens & W. Haeberli, Polarized Gas Targets, Rep. Progr. Phys. 66 (2003) 1887 Storage Cells for density enhancement of polarized jets Density gain compared to Jet of same intensity can be up to several hundred! Target areal density given by t = L rowith ro = It / Ctot and Ctot = S Ci Note:Conductance of tube proportional to d3/L E. Steffens - Univ. of Erlangen- N. - Lecture GGSWBS'16

  26. Minimum aperture allowed by machine optics for high density: t ~ 1/r3e.g. r = x,y = 15sx,y + 1mm Maximum length compatible with tracking detector e.g. 2L = 400mm (HERMES) Thin walls with coating for minimum recombination and depolarization e.g.Teflon, Drifilm Cooling of cell wall? -density enhancement - compensation of cell heating - frozen layer of water helps to prevent recombination Storage Cell Design: Requirements FILTEX target for TSR test experiment (1992) E. Steffens - Univ. of Erlangen- N. - Lecture GGSWBS'16

  27. p, d with momenta up to 3.7 GeV/c • Internal experiments with • polarized gas target: • ANKE (dismantled) • PAX Cooler Synchrotron COSY (FZJ) E. Steffens - Univ. of Erlangen- N. - Lecture GGSWBS'16

  28. PAX polarized H&D targetTarget cell & low-b section Cell walls made up by very thin teflon foils. Movable to provide large cell opening during beam injection! Top right: b-function in the target region (blue: horizontal, red: vertical) Right: Arrangement of quadru-pole lenses (yellow) and special low-bquadrupoles (blue) E. Steffens - Univ. of Erlangen- N. - Lecture GGSWBS'16

  29. Erhard Steffens Univ. of Erlangen-Nürnberg, Germany steffens@physik.uni-erlangen.de Spin as a Tool for Storage Ring Experiments Spin in Nuclear and Particle Physics Basics of Storage Rings Spin Precession in Storage Rings Spin Tools for Experiments Measurement of Nuclear Moments by Spin Precession in Storage Rings E. Steffens - Univ. of Erlangen- N. - Lecture GGSWBS'16

  30. Magnetic moment of a particle with spin s: m = g s mBohr • Leptons: point-like “Dirac” particles ; theory: g = 2→ for s = ½: m = mB • Small corrections to g = 2 described by Anomaly a: a = (g-2)/2 = g/2 -1 • Reminder: spin tunens = g a → anomaly a could be measured via ns ! • QED: ae = ½ (a/p) + C2 (a/p)2 + C3(a/p)3 + C4(a/p)4 + ... with a fine structure const. (1/137) • in 1st order: ns (e, m) ≈ 1.162∙10-3 ∙ g • Theor. predictions for ae and am (with add. QCD corrections) up to 4th order exist (T. Kinoshita et al.) – extremely elaborate calculations! Anomalous magnetic momentof charged leptons (e, m) E. Steffens - Univ. of Erlangen- N. - Lecture GGSWBS'16

  31. from Lecture HC Schmitz-Coulon, KIP Heidelberg Cyclotron frequency implies that the angle between spin and tangent stays constant: ns = 0 E. Steffens - Univ. of Erlangen- N. - Lecture GGSWBS'16

  32. Basic idea for measuring anomaly Relativistic: wa /wc = g a → measure spin tune! E. Steffens - Univ. of Erlangen- N. - Lecture GGSWBS'16

  33. Most precise measurement of ae Resolve Cyclotron and Spin levels: vertical oscillations nz coupled to Cyclotron and Larmor frequency nc and ns→ Observe Quantum jumps by discrete changes of nz (Nickel rings) ! E. Steffens - Univ. of Erlangen- N. - Lecture GGSWBS'16

  34. 0.07 ppb or 7 ∙10-11 (ge–2) result of the Harvard group Unfortunately, Muons can not be trapped in a Penning trap →USE A STORAGE RING ! E. Steffens - Univ. of Erlangen- N. - Lecture GGSWBS'16

  35. Muon (g-2) measurementsat AGS (Brookhaven) E. Steffens - Univ. of Erlangen- N. - Lecture GGSWBS'16

  36. Muon (g-2) measurement at BNL E. Steffens - Univ. of Erlangen- N. - Lecture GGSWBS'16

  37. huge SC magnet with high homogeneity; vertically defocusing! Muon (g-2) measurement at BNL another story... /c E. Steffens - Univ. of Erlangen- N. - Lecture GGSWBS'16

  38. BNL (g-2) ring (open) E. Steffens - Univ. of Erlangen- N. - Lecture GGSWBS'16

  39. G.W. Bennett, et. al.,Phys. Rev. Lett. 89, 101804 (2002) Muon (g-2) measurement E. Steffens - Univ. of Erlangen- N. - Lecture GGSWBS'16

  40. For comparison CERN result: J. Bailey et al., Nucl. Phys. B150, 1 (1979) Muon (g-2) measurement E. Steffens - Univ. of Erlangen- N. - Lecture GGSWBS'16

  41. Muon (g-2) result BNL exp. 0.5 ppm or 5∙ 10-7 E. Steffens - Univ. of Erlangen- N. - Lecture GGSWBS'16

  42. see talk Hans Stroeher at Plenary this morning, and session 5 on EDM searches tomorrow Future Challenge: EDM of Ions • Spin of hadrons might be, apart from m, accompanied by a very small Electric Dipole Moment d, indicating new physics. By observing spin precession in B and E fields of different combinations (↑↑, ↑↓), d can be separated in principle. • Present state: search for EDM limited to trapped neutral systems (neutrons or high-Z atoms). Up to now upper limits only of the order 10-25e∙cm. Proton limit derived from datoms in the same order of magnitude. • New attempt to employ storage ring techniques for a first direct measurement of EDM’s of charged particles and, hopefully, for setting lower limits or even detect a non-zero value! E. Steffens - Univ. of Erlangen- N. - Lecture GGSWBS'16

  43. Arrange particles in a ring with spin fixed parallel to momentum (Frozen spin condition) • Search for time development of vertical polarization! EDM in a storage ring: basic procedure E. Steffens - Univ. of Erlangen- N. - Lecture GGSWBS'16

  44. note: G = a (anomaly) Spin motion is governed by Thomas-BMT equation: Frozen Spin method d: electric dipole moment m: magnetic dipole moment Two options to get rid of terms G (magic condition): 1. Pure E ring (works only for G>0, e.g proton): 2. Combined ExB ring (works also for G<0, e.g deuteron) E. Steffens - Univ. of Erlangen- N. - Lecture GGSWBS'16

  45. JEDI approachJülich Electric Dipole Initiative • Combined ExB ring optimized for deuteron EDM • Feasibility studies already on the existing COSY machine: Spin Coherence Time (SCT) - >103s required and achieved! - , polarimetry, beam diagnostics, studies with Spin tracking program and comparison to machine studies, partly presented here at this workshop • Cooperation with other Labs working on EDM of charged particles (e.g. KAIST-South Korea) see session#5 tomorrow E. Steffens - Univ. of Erlangen- N. - Lecture GGSWBS'16

  46. The spin of particles stored in a ring provides a handle for experiments of extreme precision; • A variety of tools exist to produce stored spin-polarized beams and to manipulate its spins; • By sharpening the available Spin tools or developing new tools which we don’t know at this moment, we will succeed in surmounting the enormous challenges involved! Summary Thank You! E. Steffens - Univ. of Erlangen- N. - Lecture GGSWBS'16

  47. n E. Steffens - Univ. of Erlangen- N. - Lecture GGSWBS'16

  48. N H C E. Steffens - Univ. of Erlangen- N. - Lecture GGSWBS'16

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