Frozen Spin Targets In a Nutshell Version 2.0 Chris Keith
Dynamic Nuclear Polarization (the simple model) Use Low Temperature + High Field to polarize free electrons (aka paramagnetic centers) in the target material. Use microwaves to transer this polarization to nuclei. ωe + ωp ωe - ωp 140 GHz B=5 T 210 MHz e e p Zeeman energy levels of a hydrogen-like atom Positive polarization Negative polarization
Dynamic Nuclear Polarization (the abstract model) ESR { e e E k TL E k T ss Spins in equilibrium with lattice P = PTE t2 spin-spin relaxation time constant e E k T ss Spins colder than lattice P > PTE e E k T ss Spins at negative temperature P<0
Equipment List for Dynamically Polarized Target Polarizing Magnet: 5 Tesla, DB/B ~ 10-5 Microwaves: 20 mw/g @ 140 GHz Polarizing Refrigerator: Q 20 mw @ T 1 K NMR: 212 MHz Target: free protons (or deuterons) w/ paramagnetic centers Disadvantage: Large magnet restricts aperture for scattered particles to about ± 50 Solution: Polarize with a smaller magnet Or: Use a Frozen Spin Target
Four Easy Steps to a Frozen Spin Target Step 1. Polarize the Target via DNP Step 2. Freeze the Polarization at a Very Low Temperature (and modest magnetic field) Step 3. Take Physics Data while the Polarization (slowly) Decays Polarization Step 4. Go to Step 1 Days
Ch. Bradtke PhD Thesis, Univ. Bonn, 1999
Equipment List for Frozen Spin Target Polarizing Magnet: 5 Tesla Microwaves: 1-2 mw/g @ 140 GHz Polarizing Refrigerator: Q 20 mw @ T 0.5K NMR: 212 MHz Holding Magnet: 0.5 Tesla internal solenoid Holding Refrigerator: Q 10 mw @ T 0.05 K NMR: 21 MHz Target: Ø15 mm 50 mm butanol (C4H9OH)
Polarizing Magnet Max. Field: 5.1 T B/B: < 3 10-5 Bore: Ø127 mm Cryomagnetics, Inc. Oak Ridge, TN, USA A. Dzyubak, priv. comm..
Holding Magnet, Longitudinal Wire: Ø.1 mm multifilament NbTi, three layers Dimensions: Ø 50 110 Max. Field: 0.42 Tesla Homogeneity: B/B ~ 3 10-3
Holding Magnet, Transverse (Prototype) Wire: Ø.1 mm multifilament NbTi, three layers Dimensions: Ø 40 355 mm Max. Field: 0.27 Tesla Homogeneity: B/B ~ 5 10-3
Refrigeration Techniques below 1 Kelvin 1. Evaporative cooling of liquid Helium Q T = n L L V P n = evaporation rate L = Latent heat constant V = pump speed constant 1/T P = vapor pressure e Vapor Pressure (and therefore cooling power) decreases exponentially
Refrigeration Techniques below 1 Kelvin 2. 3He/4He Dilution Refrigeration Below 0.8 K, a 3He/4He mixture will separate into two phases Xd Note: Even at absolute zero, some 3He remains in the dilute phase (about 6.5%) Xc
Thermodynamics of Dilution Refrigeration At very low temperatures ³He behaves as a non-interacting gas of spin-½ particles (e.g. electrons in a metal) 2/3 2 Nmk T V 2/3 C = V T ℏ 3N Since Vd = Vc Vc x 0.065 Cd 6 Cc Experimentally, C d = 106 T [ J mol 1 K 1 ] C c = 22 T [ J mol 1 K 1 ] The specific heat of a 3He atom is higher in the lower, dilute phase than in the upper, concentrated phase! Therefore, 3He will absorb energy when it dissolves into the dilute phase. If 3He is removed from the lower part of the mixing chamber, 3He from the upper part will absorb heat from its surroundings in order to dissolve into the dilute phase and reestablish equilibrium. H. London, 1951
Cooling Power of Dilution Process Consider chemical potential m of ³He in the two phases: H = enthalpy S = entropy = H TS In equilibrium, d = c H d TSd = Hc TSc Re-arrange, Hd H c = T S d S c T C C = T d c dt T 0 T Latent heat of dilution T = T 106 22 dt 0 = 84 T 2 Ideal cooling power of the dilution process: Q = n [H d H c ] = 84 n T 2 Watt /mol K 2 Cooling power decreases as T-2
Practical Dilution Refrigeration 3 He is distilled from the lower, dilute phase of the mixing chamber After distillation, the 3He is recondensed in a LHe bath at ~1.5K and returned to the mixing chamber The cooling power and minimum temperature depend strongly on heat exchange between the concentrated (warm) and dilute (cold) fluid streams 2 2 Q T m = n [Hd T m Hc T c ] 2 2 = n [95T m 11T c ] Performance of HX determines T2c
Heat Exchange between 3Hed and 3Hec Heat Flow: 3 Hec HX walls 3 Hed At low temperatures, the main impediment to heat transfer is the thermal boundary (Kapitza) resistance Rk between the helium and the HX walls Only a small fraction of phonons from liquid will enter the HX walls 1 v 31 2 v 3 2 3 T AT = T Or a more familiar form: Q K = R Rk 5 10 A 4 4 Q K = [T 2 T 1 ] 2RK Heat transfer drops fast at low T!
Cooling Power with Ideal Heat Exchanger Cooling power, assuming 100% heat exchange is determined by molar flow rate and Rk/A of heat exchanger Q T m = n [94.5T 2m 12.5T 2c ] RkT 2 = n [94.5T m 625 n ] A (Giorgio Frossati, 1986) Build HX with low RkT OR, large Area Use sinter of ultra-fine silver or copper powder to provide several m2 of area
40 mesh copper powder sintered at 870 C 0.08 m2/g 50 m 1 micron silver powder sintered at 370 C 0.3 m2/g 2 m 150 nm silver powder sintered at 370 C 1.5 m2/g 2 m
Optimization of Heat Exchanger Geometry To optimize heat exchangers, must consider heat leaks due to both axial conduction and frictional heating Qcond D2 = T dt 4L =ad 2 Minimize Qcon + Qfric : 128L 2 n V 4 D = b D 4 Qfric = d 2 4 ad bd = 0 dd Dopt = (2b/a)1/6
Intrinsic heat leak as a function of tube diameter HX Length: 1.5 m Flow rate: 1 mmol/s Inlet temperature: 200 mk Outlet temperature: 20 mk
1 micron Ag powder Sinter at 250 oc 0.5 m2/g Outside (dilute): 15 g = 7.5 m2 Inside (concentrated): 8.5 g = 4.2 m2
An example of a commercial, vertical dilution refrigerator Leiden Cryogenics, BV Very nice, but it won't fit inside CLAS...
Horizontal Dilution Refrigerator for Frozen Spin Target T.O. Niinikoski, CERN 1971
Hall B Frozen Spin Target
The Frozen Spin Waltz Step 1: Polarizing - Target is fully retracted, magnet is lifted to beam height - Target is inserted into magnet, magnet energized, microwaves on Step 2: Beam On - Microwaves off, magnet off, holding coil on - Target is fully retracted, magnet is lowered -Target is fully insert into CLAS
Equipment List for Frozen Spin Target 1 microwave generator + power supply (140 GHz) + misc. waveguide components 1 power meter 1 frequency counter 1 RF generator (NMR) + RF voltmeter 2 NMR Q-meters 2 superconducting magnets + 2 power supplies 2 gas panels (4He & 3He/4He) 29 valves 13 pressure transducers 4 flow meters 2 storage tanks (3He + 4He) 18 vacuum pumps 6 vacuum transducers 1 Dilution Refrigerator 18 thermometers 2 8-channel temperature monitors 1 AC resistance bridge 2 superconducting level probes + readouts 1 capacitance level probe + bridge circuit 4 micro needle valves + actuators 2 heaters
Summary - A frozen spin polarized target for tagged photon experiments is under development at Jefferson Lab. - 5 Tesla polarizing magnet is in house. - Superconducting holding coils (~1mm thick), both longitudinal and transverse, are under development. - Horizontal dilution refrigerator is under construction. - Positioning system for Hall B is still in conceptual design stage.