AFP – a fast & easy nuclear polarization reversal ?

P. Hautle, Santa Fe Polarized Drell-Yan Physics Workshop, Nov 2010

AFP – a fast & easy AFP – a fast & easy nuclear polarization nuclear polarization

reversal ?reversal ?P. Hautle

Paul Scherrer InstitutCH-5232 Villigen PSI

Switzerland

Santa Fe Polarized Drell-Yan Physics WorkshopOctober 31- November 1, 2010

Santa Fe, NM 87501, USA


OutlineOutline

Introduction polarised targets = unique DNP systems

Overview of Experimental Data overview of experimental data

some details / comments

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

Implementation technical and physics constraints

what can be expected


PSI East

PSI West

Aare

SLS

cw Proton accelerator (590 MeV, 2.2 mA)

(, , SR SINQ, UCN)

SwissFEL

Accelerator Facilities


100 cm100 cm33

„„Frozen Spin“ Frozen Spin“ Polarised Polarised

TargetTarget

Particle physics experimentson beams of pions, protons, neutrons…..


60 μm thick polystyrene foil cooled to 200 mK by a sub micron thick film of superfluid 4He

cell with two 500 nm thick Si3Ni4 windows

“Ultra-thin” polarised solid target

[J.P Urrego Blanco et al., NIM B 261 (2007) 1112]


suppress background suppress background scattering by TOFscattering by TOF

coincident coincident in situin situ detection of low detection of low energy recoil protons energy recoil protons in the target itselfin the target itself

polarisedpolarised nuclei in nuclei in the the scintillatingscintillating detector itselfdetector itself

O

N

HC

HC

n

CH3

O

CH3

CH3

CH3

N·B. van den Brandt B. van den Brandt et al.,et al., NIM A 446 (2000) 592 NIM A 446 (2000) 592


BeamBeamDetector

neutron beamneutron beam

Observe DNP build up with Observe DNP build up with

small angle neutron scatteringsmall angle neutron scatteringthrough spin contrast variation

Europhys. Lett. 59 (2002) 62 Eur. Phys. J. B 49 (2006) 157–165J. Appl. Cryst. 40 (2007) s106-s110


BB00=2.5T=2.5T

58

mm

58

mm

d-PS targetd-PS targetdoped with d-TEMPOdoped with d-TEMPO

Ø Ø 5 mm x 1.2 mm5 mm x 1.2 mm

66LiFLiF

targettargetholderholder

45 mm45 mm

Pseudomagnetic precession of cold Pseudomagnetic precession of cold neutronsneutrons

[F. M. Piegsa et al., NIM A 611 (2009) 231]


Dissolution DNP for MRI / NMRDissolution 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 metabolismimage of brain metabolism

Details and List of publications see: http//: sdnpi.epfl.ch


Nuclear Spin Nuclear Spin ThermodynamicThermodynamic

ss


Frequency [MHz]149.0 149.2 149.4 149.6 149.8 150.0

ii i

dH h

dt

equation of motion

H

ih

External field ( ~ T) including rf field (~ G)

“Local field” which spin i feels because of neighbours 3 5

3j iji j ij

j ij ij

rh r

r r

2 212L iH h (averaged over all orientations and spin states)

~ few GLH

Nuclear spin system (in a solid) in external Nuclear spin system (in a solid) in external fieldfield

ii

M

I H

FWHM (Gaussian)

2 523LH M

22 2ln 2 M

Magnetization


Energy – Entropy – Isentropic coolingEnergy – Entropy – Isentropic cooling

0 / SM CH T

2 / 3C N kCurie Law

0ZE M H 1

2S i ii

E h

2 /S L SE CH T20 /Z SE CH T

Energy

Entropy 2 2/ 2 / 2S S S L SS E T CH T 2 20/ 2 / 2Z Z S SS E T CH T

Applied field Local field

2 2 212 0 /Z S L SS S C H H TS constantconstantIsentropic coolingIsentropic cooling

Adiabatic demagnetizationAdiabatic demagnetization

0 /M H kT

(spin energy / thermal energy)


Isentropic cooling –Isentropic cooling –Adiabatic demagnetizationAdiabatic demagnetization

2 2 212 0 /Z S L SS S C H H TS constantconstant

HL

H0

precession about H0

HH00 is decreased is decreased

precession about HL

Important change when H0

HL :

Entropy transferred from polarizationpolarization to spin-spin orderingspin-spin ordering

Reversibility:Reversibility: change of H0 slow compared to equilibration time (HL)1


Adiabatic fast Adiabatic fast passage (AFP)passage (AFP)


rf field - Rotating frame of referencerf field - Rotating frame of reference[F. Bloch, Phys Rev 70 (1946) 460]

[A. Abragam, Principles of Nuclear Magnetism, 1961]

rotating framerotating frame

0 1 1ˆ ˆcos( ) sin( )ˆH H z H t x H t y

External field H

contains rf fieldrf field

0 1 ˆ( ) ˆ re rH z HH x

1 1

0 0

tan( )

H

H

0 0H Larmor frequency:

0zH H 12 cos( )xH H tstatic field: rf field:

H1

He

H0 ω/γ

H0rz z

rx

M

M


rf field - Rotating frame of referencerf field - Rotating frame of reference[F. Bloch, Phys Rev 70 (1946) 460]

[A. Abragam, Principles of Nuclear Magnetism, 1961]

rotating framerotating frame

0 1 1ˆ ˆcos( ) sin( )ˆH H z H t x H t y

External field H

contains rf fieldrf field

0 1 ˆ( ) ˆ re rH z HH x

1 1

0 0

tan( )

H

H

0 0H Larmor frequency:

0zH H 12 cos( )xH H tstatic field: rf field:

H1

He

H0 ω/γ

H0rz z

rx

M

M

HHee can be rotated by 180° can be rotated by 180°

sweeping sweeping HH00 or or ω ω through through resonance resonance


Adiabatic TheoremAdiabatic Theoremd

Hdt

equation of motion

For any vector satisfying a similar equation of motion the angle For any vector satisfying a similar equation of motion the angle between and remains constant provided the change of between and remains constant provided the change of direction of in time is sufficiently slowdirection of in time is sufficiently slow

H H

Possible to reverse the magnetization

What happens to the magnetization ? M

21

dHH

dtAdiabaticAdiabaticity: FastFaster than relaxation: 1

1H


Adiabatic TheoremAdiabatic Theoremd

Hdt

equation of motion

For any vector satisfying a similar equation of motion the angle For any vector satisfying a similar equation of motion the angle between and remains constant provided the change of between and remains constant provided the change of direction of in time is sufficiently slowdirection of in time is sufficiently slow

H H

Possible to reverse the magnetization

2 2 212 /e LR SS C H H T constantconstant

What happens to the magnetization ? M

Thermodynmics in Thermodynmics in solidsolid sample sample

Adiabtic demagnetization in the rotating frame (ADRF) Isentropic passageIsentropic passage

Important change when He

HLR :

Entropy transferred from polarizationpolarization to spin-spin orderingspin-spin ordering

((Zeeman Zeeman toto dipolar ordering dipolar ordering))

21

dHH

dtAdiabaticAdiabaticity: FastFaster than relaxation: 1

1H


Frequency [MHz]149.0 149.2 149.4 149.6 149.8 150.0

( )g

Estimate the losses -Estimate the losses -AFP in the spin temperature modelAFP in the spin temperature model

[M. Goldman et al., Phys Rev 168 (1968) 301]

1 LH H

( ) 1g d

Provotorov equations describe mixing between Zeeman and spin-spin subsystem:

0H

Conditions:

High temperatures

Low nuclear polarizations

2 21( ) ( )W H g Mixing rate:Mixing rate:

AFPAFP:: variation of very small during time T2 D

12

W T

2 2

/ ( )

/ ( / )( )

d dt W

d dt W D

Evolution of inverse spin temperatures and to common value


Frequency [MHz]149.0 149.2 149.4 149.6 149.8 150.0

( )g

Sweep of field / frequency through the Sweep of field / frequency through the resonanceresonance

121expfinal

initial

PP H dH dt

P

Fast sweepFast sweep – in time much shortershorter than mixing time W1

21

3exp

4 LR

P H dH dtH

1

exp L

D

R

T

HP

dH dt

Slightly saturating passageSlightly saturating passage H1

Quasiadiabatic fast passageQuasiadiabatic fast passage – in time much longerlonger than mixing time W1

Quasiadiabatic partQuasiadiabatic part

RelaxationRelaxation

Sudden to adiabatic transitionSudden to adiabatic transition~ 5 – 8 % loss, almost independant of 21H dH dt

1DT Spin-lattice relaxation of the spin-spin (dipolar) interactions

2 21( ) ( )W H g


A = H12/(dH/dt)

1 10 100

Effi

cien

cy

P [P

F/P

I]

-1.0

-0.8

-0.6

-0.4

-0.2

0.0

H1 = 0.25 G

quasiadiabtic relaxation

= 10 kHz, T1D = 1 s = 25 kHz, T1D = 1 s

= 50 kHz, T1D = 1 s

= 50 kHz, T1D = 10 s

21 1

1 1 2 2LR

DLR

HT T

H

Spin-lattice relaxation in the rotating frame

Theoretical predictionTheoretical prediction

Sample temperature & dopant concentration !!

narrow line widthnarrow line width long relaxation time in RF long relaxation time in RF

= Spin-lattice relaxation of the spin-spin system


A = H12/(dH/dt)

0.01 0.1 1 10 100 1000

Effi

cien

cy

P [P

F/P

I]

-1.0

-0.5

0.0

0.5

1.0

n-butanol + 4 x 1019 e /cm3

porphyrexideT = 0.5 K / B = 2.5 T

EHBA(CrV)T ~ 80 mK / B = 2.5 T

Experimental results I - ProtonsExperimental results I - Protons

effect of sample temperatureeffect of sample temperature


A = H12/(dH/dt)

0.01 0.1 1 10 100 1000

Effi

cien

cy

P [P

F/P

I]

-1.0

-0.5

0.0

0.5

1.0

7LiH irradiated

T ~ 80 mK / B = 2.5 T

Experimental results II – Experimental results II – 77LiHLiH


Experimental results IIIExperimental results III

substance nucleu

sdopant

e- conc.[spins/g]

T[K]

P max

1-butanol 1H porphyrexide 4.0 x 1019 0.5 0.36

1-butanol 1H CrV EHBA 4.0 x 1019 0.08 0.76

7LiH7Li

irrad low ? 0.08 0.88

1H 0.92

8-fluoro-pentanol

19FTEMPO 2.0 x 1020 0.08

0.37

1H 0.40

d-butanol

2H

CrV EDBA 6.35 x 1019

1 0.75

2H 0.5 0.85

2H 0.08 0.90

d-butanol 2H CrV EDBA 2.36 x 1019 0.08 0.92

Deuterated alcohols are a different storyDeuterated alcohols are a different story::

large quadrupolar coupling

small dipolar coupling

1 and ½ sweep to reverse the polarization of the spin 1 system


Experiment & TheoryExperiment & Theory

Data fitted with spin temperature model


e concentration [x 10 19]

2 3 4 5 6 7

Effi

cien

cy

P [P

F/P

I]

-0.96

-0.92

-0.88

-0.84

-0.80

-0.76

-0.72

Col 1 vs Col 2 Col 1 vs Col 3 Col 1 vs Col 4 Col 1 vs Col 5 Col 1 vs Col 6

T = 0.08 K

T = 0.5 K

T = 1 K

Sample temparature / dopant concentrationSample temparature / dopant concentration

d-butanol + EHBA(CrV)-d22

increase sweep rate for higher temperaturesincrease sweep rate for higher temperatures


1

6ln 2LRH

22 2( ) (0) 1M P M P

Line width / PolarizationLine width / Polarization

Frequency [MHz]149.0 149.2 149.4 149.6 149.8 150.0

FWHM (Gaussian)

22 2ln 2 M

50 kHz HLR = 2.9 G

Proton AFP efficiency vs line widthT ~ 80 mK and B = 2.5 T

FWHM NMR line width [kHz]

44 46 48 50 52 54 56 58

AF

P e

ffici

en

cy

P

-0.94

-0.92

-0.90

-0.88

-0.86

-0.84

-0.82

positive polarizationnegative polarization


7Li AFP efficiency vs polarizationT ~ 80 mK and B = 2.5 T

7Li nuclear polarization [%]

10 20 30 40 50

AF

P e

ffici

ency

P

-0.90

-0.88

-0.86

-0.84

-0.82

-0.80

-0.78

1

6ln 2LRH

22 2( ) (0) 1M P M P

Line width / PolarizationLine width / Polarization

Frequency [MHz]149.0 149.2 149.4 149.6 149.8 150.0

FWHM (Gaussian)

22 2ln 2 M

50 kHz HLR = 2.9 G


Two nuclear spin speciesTwo nuclear spin species

Time [sec]0 200 400 600 800 1000

Deu

tero

n po

lariz

atio

n [a

.u.]

0.75

0.80

0.85

0.90

0.95

1.00

1.05

1.10

without proton AFP

with proton AFP (P ~ 0.5)

99.4 % deuterated without proton AFP(6.35 x 1019spins/g)

98 % deuterated (4 x 1019spins/g)

Coupling of the nuclear spin systems through electron non-Zeeman system

start microwaves

[Cox, Bouffard, Goldman, J Phys C 6 (1973) L100]

polarization of both nuclear spin systems should be reversedpolarization of both nuclear spin systems should be reversed

heat capacity !heat capacity !


In practice: polarization reversal AFP vs DNPIn practice: polarization reversal AFP vs DNP

T =80 mK / B = 2.5 T

gain can be dramatic in certain cases gain can be dramatic in certain cases (especially at low temperatures)(especially at low temperatures)

DNP reversalDNP reversal

AFP reversalAFP reversal

AFP efficiency <-> DNP build up timeAFP efficiency <-> DNP build up time


radiation damping

asymmetry of efficiency

superradiance

e.g. typical AFP parameters for protons:

Technical aspects ITechnical aspects I

requirementsrequirements

challangeschallanges

solutionssolutions tune and match the rf coil ?

B1 = 0.3 G perpendicular to static field B0

homogeneity B1/B1 ~ 0.5

dB/dt = 10 – 20 G/s or 40 – 80 kHz/s

frequency sweep width = 400 kHz – 1 MHz

produce the required B1 amplitude

do not excessively heat the sample

potential pitfalls


Technical aspects IITechnical aspects II

radiation damping -> superradianceradiation damping -> superradiance

2R T

12 / ZQM H

threshold

210

0.1

electromagnetic energy provided by the spins compensates losses in the circuit

auto-oscillationauto-oscillation

12 ZM NP

Two coupled systems: resonance circuit < - > rotating magnetization

102

R Q M damping time constant [S. Bloom, J Appl Phys 28 (1957) 800]

[M. Odehnal, V. Petricek, Physica 67 (1973) 377]

[Yu. F. Kiselev et al., JETP 67 (1988) 413]

AFP gets asymmetric

superradiance

superradiant polarization reversalsuperradiant polarization reversal

[L.A. Reichertz et al., NIM A 340 (1994) 278] (NH3, V = 6.5 cm3 ; Q = 33)


Technical aspects IIITechnical aspects III

Example Example design of a rf irradiation system

5 T / 1 K system (S. Pentilla) magnetic to be rotated to have vertical field

sample sizesample size

polarized target systempolarized target system

samplesample

cylinder of 8 cm length/ 1.5 cm diameter

ammonia / 6LiD

reversalreversal every 2 h

rf rf structurestructure (coil) B1 ~ 0.3 – 0.5 G @ 212 MHz

01 2 2

1

2

nB

a g

1 ~ 0.12B n G/A

212 cP I R

large sample tuning not possible (superradiance)

solenoid

match to 50 Ohm

rf power ~ 10 W or more -> heat load !!


AFP used by the Standford group

1 180 B

AFP <-> 180° pulse (pulsed NMR)AFP <-> 180° pulse (pulsed NMR)

Frequency [MHz]149.0 149.2 149.4 149.6 149.8 150.0

50 kHz need to excite ~ 100 kHz

apply strong pulse: H1 > HL

1 1 2 100 B kHz

5 s

B1 11.7 G

[F. Bloch, W.W. Hansen, M Packard, Phys Rev 70 (1946) 474]

superradiance !!


ConclusionConclusion

low temperature, T 1 K

low concentration of paramagnetic centers

experimental conditions

sample properties

one „free“ parameter : relaxation time in the rotating frame

local field HL

line width

(dipolar relaxation time T1D )

dipolar relaxation time T1D

““Strategy“ to get a high AFP efficiency ??Strategy“ to get a high AFP efficiency ??

What can be expected (conservative guess)What can be expected (conservative guess)

6LiD 5 T / 1K P > 0.5 2.5 T / 80 mKP ~ 0.9

Ammonia 5 T / 1K P < 0.5 2.5 T / 80 mKP ~ 0.7

Trade off between AFP efficiency and DNP build up time


Documents

AFP – a fast & easy nuclear polarization reversal ?