AFP – a fast & easy nuclear polarization reversal ?

1. Santa Fe Polarized Drell-Yan Physics Workshop October 31- November 1, 2010Santa Fe, NM 87501, USA AFP – a fast & easy nuclear polarization reversal ? P. Hautle Paul Scherrer Institut CH-5232 Villigen PSI Switzerland

2. Outline • Introduction • polarised targets = unique DNP systems • AFP Theory • thermodynamic of a nuclear spin system • classical picture - rotating frame • quantum statistical description – spin temperature • which effects set limits on the optimum efficiency • Overview of Experimental Data • overview of experimental data • some details / comments • Implementation • technical and physics constraints • what can be expected

3. PSI East Aare SwissFEL (p, m,mSR, SINQ, UCN) Accelerator Facilities PSI West SLS cw Proton accelerator (590 MeV, 2.2 mA)

4. Particle physics experiments on beams of pions, protons, neutrons….. 100 cm3 „Frozen Spin“ Polarised Target

5. “Ultra-thin” polarised solid target cell with two 500 nm thick Si3Ni4 windows 60 μm thick polystyrene foil cooled to 200 mK by a sub micron thick film of superfluid 4He [J.P Urrego Blanco et al., NIM B 261 (2007) 1112]

6. polarised nuclei in the scintillating detector itself H H C C n CH3 CH3 CH3 CH3 N · O N O coincident in situ detection of low energy recoil protons in the target itself suppress background scattering by TOF B. van den Brandt et al., NIM A 446 (2000) 592

7. Detector Beam neutron beam Observe DNP build up with small angle neutron scattering through spin contrast variation Europhys. Lett. 59 (2002)62 Eur. Phys. J. B 49 (2006) 157–165 J. Appl. Cryst. 40 (2007) s106-s110

8. B0=2.5T Pseudomagnetic precession of cold neutrons 6LiF 58 mm target holder 45 mm d-PS targetdoped with d-TEMPO Ø 5 mm x 1.2 mm [F. M. Piegsa et al., NIM A 611 (2009)231]

9. Dissolution DNP for MRI / NMR Polarize organic samples labeled with 13C, 6Li, 15N nuclei in solid state (1 K / 5T) Dissolve rapidly and inject into rat in imager (9.4 T) => image of brain metabolism Details and List of publications see: http//: sdnpi.epfl.ch

10. Nuclear Spin Thermodynamics

11. ~ few G Nuclearspinsystem (in a solid) in externalfield equation of motion External field ( ~ T) including rf field (~ G) “Local field” which spin i feels because of neighbours (averaged over all orientations and spin states) FWHM (Gaussian) Magnetization

12. Applied field Local field Energy Entropy constant Energy – Entropy – Isentropiccooling (spin energy / thermal energy) Curie Law Isentropic cooling Adiabatic demagnetization

13. H0 HL constant Isentropiccooling – Adiabaticdemagnetization precession about H0 H0 is decreased precession about HL Entropy transferred from polarization to spin-spin ordering Important change when H0@HL: Reversibility: change of H0 slow compared to equilibration time (w HL)-1

14. Adiabatic fast passage (AFP)

15. External field contains rf field static field: rf field: Larmor frequency: rf field - Rotating frame of reference [F. Bloch, Phys Rev 70 (1946) 460] H0 [A. Abragam, Principles of Nuclear Magnetism, 1961] H0 - ω/γ He rotating frame H1

16. H0 External field contains rf field static field: rf field: H0 - ω/γ He H1 Larmor frequency: rf field - Rotating frame of reference [F. Bloch, Phys Rev 70 (1946) 460] [A. Abragam, Principles of Nuclear Magnetism, 1961] rotating frame He can be rotated by 180° sweeping H0 or ω through resonance

17. Adiabatic Theorem What happens to the magnetization ? For any vector satisfying a similar equation of motion the angle between and remains constant provided the change of direction of in time is sufficiently slow equation of motion Possible to reverse the magnetization Adiabaticity: Faster than relaxation:

18. What happens to the magnetization ? For any vector satisfying a similar equation of motion the angle between and remains constant provided the change of direction of in time is sufficiently slow constant Adiabtic demagnetization in the rotating frame (ADRF) Isentropic passage Adiabatic Theorem equation of motion Possible to reverse the magnetization Adiabaticity: Faster than relaxation: Thermodynmics in solid sample Entropy transferred from polarization to spin-spin ordering (Zeeman to dipolar ordering) Important change when He@HLR:

19. Estimatethelosses -AFP in thespintemperature model Mixing rate: [M. Goldman et al., Phys Rev 168 (1968) 301] Provotorov equations describe mixing between Zeeman and spin-spin subsystem: Evolution of inverse spin temperatures a and b to common value Conditions: High temperatures Low nuclear polarizations AFP: variation of D very small during time T2 ~ D -1

20. Sweepoffield / frequencythroughtheresonance Sudden to adiabatic transition Quasiadiabatic part Relaxation Fast sweep – in time much shorter than mixing time W-1 H1 Slightly saturating passage Quasiadiabatic fast passage – in time much longer than mixing time W-1 ~ 5 – 8 % loss, almost independant of Spin-lattice relaxation of the spin-spin (dipolar) interactions

21. Theoretical prediction Spin-lattice relaxation in the rotating frame = Spin-lattice relaxation of the spin-spin system narrow line width long relaxation time in RF Sample temperature & dopant concentration !!

22. Experimental results I - Protons effect of sample temperature

23. Experimental results II – 7LiH

24. Experimental results III Deuteratedalcoholsare a different story: • large quadrupolar coupling • small dipolar coupling • 1 and ½ sweep to reverse the polarization of the spin 1 system

25. Experiment & Theory Data fitted with spin temperature model

26. Sample temparature / dopantconcentration d-butanol + EHBA(CrV)-d22 increase sweep rate for higher temperatures

27. FWHM (Gaussian) Line width / Polarization d= 50 kHz => HLR = 2.9 G

28. FWHM (Gaussian) Line width / Polarization d= 50 kHz => HLR = 2.9 G

29. Two nuclear spin species Coupling of the nuclear spin systems through electron non-Zeeman system [Cox, Bouffard, Goldman, J Phys C 6 (1973) L100] heat capacity ! start microwaves polarization of both nuclear spin systems should be reversed

30. In practice: polarizationreversal AFP vs DNP DNP reversal AFP reversal T =80 mK / B = 2.5 T gain can be dramatic in certain cases (especially at low temperatures) AFP efficiency <-> DNP build up time

31. Technical aspects I requirements e.g. typical AFP parameters for protons: • B1 = 0.3 G perpendicular to static field B0 • homogeneityD B1/B1 ~ 0.5 • dB/dt = 10 – 20 G/sor40 – 80 kHz/s • frequency sweep width= 400 kHz – 1 MHz • produce the required B1amplitude • do not excessively heat the sample challanges solutions tune and match the rf coil ? radiation damping asymmetry of efficiency superradiance potential pitfalls

32. Technical aspects II radiation damping -> superradiance Two coupled systems: resonance circuit < - > rotating magnetization damping time constant [S. Bloom, J Appl Phys 28 (1957) 800] electromagnetic energy provided by the spins compensates losses in the circuit auto-oscillation threshold [M. Odehnal, V. Petricek, Physica 67 (1973) 377] AFP gets asymmetric superradiance superradiant polarization reversal - 90 % -> + 60 % [Yu. F. Kiselev et al., JETP 67 (1988) 413] [L.A. Reichertz et al., NIM A 340 (1994) 278] (NH3, V =6.5 cm3 ; Q = 33)

33. G/A Technical aspects III Example design of a rf irradiation system polarized target system 5 T / 1 K system (S. Pentilla) magnetic to be rotated to have vertical field sample size cylinder of 8 cm length/ 1.5 cm diameter sample ammonia / 6LiD reversal every 2 h rf structure (coil) B1 ~ 0.3 – 0.5 G @ 212 MHz solenoid large sample tuning notpossible (superradiance) match to 50 Ohm rf power ~ 10 W or more -> heat load !!

34. t180 = 5 ms B1 =11.7 G AFP <-> 180° pulse (pulsed NMR) apply strong pulse: H1 > HL need to excite ~ 100 kHz superradiance !! AFP used by the Standford group [F. Bloch, W.W. Hansen, M Packard, Phys Rev 70 (1946) 474]

35. low temperature, T 1 K • low concentration of paramagnetic centers Conclusion “Strategy“ to get a high AFP efficiency ?? local field HL sample properties line width d (dipolar relaxation time T1D ) dipolar relaxation time T1D experimental conditions one „free“ parameter : relaxation time in the rotating frame Whatcanbeexpected (conservativeguess) • 6LiD 5 T / 1K dP >-0.5 2.5 T / 80 mK dP ~-0.9 • Ammonia 5 T / 1K dP <-0.5 2.5 T / 80 mK dP ~-0.7 Trade off between AFP efficiency and DNP build up time