Enhanced Tensor Polarization in Solid-State Targets
EEnhanced Tensor Polarization in Solid-State Targets
D. Keller, D. Crabb, D. Day
University of Virginia Physics Department, Charlottesville, Virginia 22901
Abstract
We report measurements of enhanced tensor polarization on solid-state targets. Theresults here represent an increase in tensor polarization over that previously achievedin high energy and nuclear scattering experiments that focused on the measurementof tensor polarized observables. Enhancement techniques are used which require RFproduced close to the Larmor frequency of the target spins and use selective semi-saturation resulting from two sources of irradiation, microwave for the DNP processand the additional RF used to manipulate the population of the energy levels in the tar-get material. The spin dynamics of the solid target are used to align the spins enhancingthe ensemble average to improve the figure of merit of the scattering experiment. Targetrotation at an optimized rate can lead to additional enhancement by applying selectivesemi-saturation in polycrystalline materials that possess a Pake doublet in their NMRsignal.
1. Introduction
Dynamic nuclear polarization (DNP) of targets using solid diamagnetic material,doped with paramagnetic radicals, provides a considerable advantage in interactionrate over gaseous targets when limited to ( ∼ × e/sec) equivalent beam intensity.For a 1 K and 5 T system, dynamically enhanced targets can be used in vector polar-ized proton and deuteron experiments near 98% and 50% respectively for this beamintensity range. These high cooling power DNP target systems have been used to reachluminosities up to 10 cm − s − . These systems contain a high powered microwavegenerator, a superconducting magnet ( ∼ Preprint submitted to NIM A August 24, 2020 a r X i v : . [ phy s i c s . i n s - d e t ] A ug igh cooling power evaporation refrigerator used to hold the target at 1 K despite theheat-load from the beam and microwaves [1].Polarization of spin-1 deuterons can be achieved using DNP with deuterated ma-terials like ND , C D OH, or LiD. In the spin-1 target, the deuterons have nonzeroquadrupole moments, and the structural arrangement of the nuclei in the solid generateelectric field gradients (EFG) which couple to the quadrupole moment. This results inan additional degree of freedom in polarization that the spin-1/2 nucleons do not pos-sess. The target spins in the ensemble can be aligned in both a vector ( P ) and a tensor( P zz ) polarization. Defined in terms of the relative occupation of the three magneticsubstates of the spin-1 system ( m = ± P = n + − n − N and P zz = n + − n + n − N , where n + , n , and n − being are the relative occupation of the magnetic substate m , andthe total population is N = n + + n + n − .Interest in tensor-polarized observables [2–11] has prompted a new research effortto develop a maximally enhanced solid-state tensor polarized target that can be usedunder continuous beam application. These observables are unique, allowing access toinformation not available using vector-polarized targets alone. There is still very littlescattering data on tensor-polarized observables from solid polarized target experimentsto date [12–16]. This is because it is necessary to maximize both the tensor polarizationand beam intensity to achieve sufficiently high precision. This requires a target systemthat can withstand the heat load of a high intensity beam, but also can produce and holdhigh tensor polarization.This article reports on a set of experimental measurements of enhanced tensor po-larization for a solid-state target in a 1 K and 5 T system using the method of selectivesemi-saturation. The details of the technique and measurement theory have been dis-cussed previously [17]. This article is organized as follows. In Section 2, a descriptionof the spin-1 NMR lineshape is given, along with the definitions of vector and tensorpolarizations and how they relate to the lineshape of the materials of interest. The2 − − − R m V ) E I ( C Figure 1: An example of the NMR lineshape of a spin-1 target with a non-cubic symmetry demonstratingthe two overlapping absorption lines. The two intensities of the signal I + and I − are shown in blue and pinkrespectively. tensor enhancement technique is discussed in Section 3. Section 4 provides the ex-perimental techniques used to obtain the NMR measurements. Section 5 contains theresults for two methods. The first method uses semi-saturating RF enhancement andother the second uses this same technique while rotating the target cell. There is also abrief discussion on other RF techniques in this section. Concluding remakes are givenin Section 6.
2. The Deuteron NMR Lineshape
The quadrupole moment of the spin-1 nuclei results from the nonspherically sym-metric charge distribution in the quadrupolar nucleus. For materials without cubicsymmetry (e.g. C D OH or ND ), the interaction of the quadrupole moment with theEFG breaks the degeneracy of the energy transitions, leading to two overlapping ab-sorption lines in the NMR spectra. The spin-1 NMR lineshape is shown in Fig. 1,demonstrating the two intensities I + (in blue) and I − (in pink). In terms of population, I + = C ( ρ + − ρ ) I − = C ( ρ − ρ − ) , where ρ x is the population density in the m = x energy level, and C is the calibrationconstant. The term intensity is used here to indicate both the height and area of thesetwo individual regions. The frequency is indicated by a dimensionless position in theNMR line R = ( ω − ω D ) / ω Q which spans the domain of the NMR signal, where ω Q is the quadrupolar coupling constant. In these units, R = ω D = .
679 MHz). The local electric field gradi-ents that couple to the quadrupole moments of the spin-1 system cause an asymmetricsplitting of the energy levels into two overlapping absorption lines. The energy levelsof the non-cubic symmetry spin-1 system can be expressed as, E m = − ¯ h ω D m + ¯ h ω Q ( θ − + η sin θ cos2 φ )( m − ) , where θ is the polar angle between the axis of the deuteron bond and the magneticfield, see Fig. 2. The azimuthal angle φ and parameter η are fixed parameters usedto characterize the electric field gradient with respect to the deuteron bond axis. Thedegree of axial symmetry and dependence on the polar angle can be understood fromthe basis lineshape for an isotropic rigid solid which is known as a Pake doublet [18].The polarization information can be extracted from a fit of the NMR data providing theareas of the two intensities [17, 19]. The peaks of the Pake doublet ( R ∼ ±
1) corre-spond to the principal axis of the coupling interaction being perpendicular ( θ = π / θ =
0) to the magnetic field, which has muchless statistical significance as indicated by the small relative height in the intensities ineach transition around ( R ∼ ∓ r = I + / I − ) can be used to extract the polarizations directly [19]. P = r − r + r + P zz = r − r + r + r + -1 =cos θ -10+1 /2 π = θ =0 θ D ω D ω Q ω +3 D ω Q ω -3 D ω Q ω +6 D ω Q ω -6 D ω Figure 2: The energy level diagram for deuterons in a magnetic field for three values of θ where ¯ h ω D is the deuteron Zeeman energy, and ¯ h ω Q is the quadrupole energy. The color indicates which transitioncorresponds to which peak shown in Fig. 1. or simply, P zz P = r − r + . (2)The extracted information from the fit also gives the sum of the two intensities whichprovides the vector polarization P = C ( I + + I − ) , while the difference provides the ten-sor polarization P zz = C ( I + − I − ) . It is important to note that these two expressionsremain true even if the system is not in thermodynamic equilibrium, unlike Eq. 1 and2. Once the calibration constant C is measured, these expressions can be used to ex-tract the averaged polarizations of the ensemble over the course of the HEP/Nuclearscattering experiment [20].
3. Tensor Polarization Enhancement
To manipulate the magnitude of tensor polarization during DNP pumping, a sepa-rate source of coil generated RF irradiation is used to selectively saturate some portionof the deuteron NMR line. By applying RF irradiation at a frequency or over a fre-quency range (hole burning [21, 22]), transitions are induced between the magnetic5ublevels within the frequency domain of the applied RF. A spin-diffusion rate that issmall compared to the effective nuclear relaxation rate allows for significant changesto the NMR line via the RF, which can be strategically applied to manipulate the spin-1tensor polarization. In the presented set of measurements, DNP microwaves were used,as well as an additional RF source that used semi-saturating RF (ss-RF) irradiation tomaximize the tensor polarization for the a 1 K and 5 T system [17]. A semi-saturatedsteady-state condition was used which manipulated and held the magnetic sublevels re-sponsible for polarization enhancement. The continuous wave NMR (CW-NMR) line-shape was measured and manipulated to maximize tensor polarization. The techniqueof ss-RF requires using a power profile that is sensitive to the intensity distributionswith the correct modulation time signature over the frequency domain to optimally en-hance. To be useful in a scattering experiment setting, the target ensemble averagedtensor polarization must be increased and held in a continuous mode for application atcontinuous beam facilities such as Jefferson Lab. Temporarily enhanced states duringbeam-target interactions are also possible for facilities that have a short beam spill percycle such as Fermilab.The source of ss-RF comes from a dedicated coil with a field B ν resulting in aninduced transition rate proportional to [17], ξ = π B ν a ν B δ ( ω D − ω ν ) , (3)where ω D is the Larmor frequency, ω ν is the ss-RF frequency, a ν is the coupling con-stant, and B is the strength of the holding field. The ss-RF can only play a role betweennuclear spin energy levels that differ by the spin of the mediating photon. The ss-RFdrives transitions that lead to equalization of the populations in the energy levels at theapplied frequencies. This implies that the change in intensities at the location R in theNMR line due to the ss-RF can be expressed as, I ± ( R ) dt = − ξ ω I ± ( R ) , (4) I ∓ ( − R ) dt = ξ ω I ± ( R ) . (5)6n other words, the rate at which any one of the intensities change due to ss-RF is onlydependent on the intensity level and the strength of the B ν field, or RF power. Here ω is the reciprocal of the electron longitudinal relaxation rate used to be consistent withprevious work [17]. The total polarization can only be decreased at the ss-RF locationin R , so strategic implementation is required to enhance the difference in the integrated I + and I − regions. Equation 4 describes the rate of change in the intensity driven by thess-RF for any region at R . The transitions driven by the ss-RF decrease the intensityat R . However, the coupling to Equation 5 indicates an increase in intensity in theopposing absorption line at − R at a rate that is half as fast as the decrease in intensityat R . This also implies that the region at − R increases in area by half of the lost area at R . Equations 4 and 5 affirm that materials with the same lineshape can be treatedexactly the same under ss-RF tensor enhancement. This expression does not changefor different materials relaxation rates. For many of our experimental results, we usedeuterated butanol (C D OD) (99% deuterated) rather than deuterated ammonia (ND )only because the paramagnetic complex of deuterated butanol is easier to optimize, butthe maximum total polarizations and lineshapes are very similar.
4. Experimental Techniques
All experimental results were taken at the University of Virginia’s Solid PolarizedTarget Lab. The experimental data was taken at 5 T and 1 K with an evaporationrefrigerator [1, 23] that had a cooling power of just over 1 W, and a DNP microwavesource generating approximately 0.3 W on the target. The nuclear spin polarizationwas measured with an CW-NMR coil and Liverpool Q-meter [24]. With this system,the RF susceptibility of the material was inductively coupled to the NMR coil, whichwas part of a series LCR Q-meter circuit that was tuned to the Larmor frequency of thenuclei of interest. The Q-meter based NMR provided a non-destructive polarizationprobe of the nuclear spin ensemble in the solid-state target.For the selective excitation using ss-RF, an additional coil around the target cup wasconnected to an RF-generator. The ss-RF coil consisted of 20 turns of silver covered7 igure 3: Drawing of the ss-RF cup and coil used for the set of experiments discussed. The NMR coil is alsoshown inside. copper clad non-magnetic steel with a diameter of ∼ , which held about 9 g of d-butanol. The ss-RF coil was fitted and fixed aroundthe diameter of the target cell. The ss-RF was modulated over the frequency domainof interest at the appropriate RF power to semi-saturate the NMR line to the intensitylevel of interest.Adequate power delivery to the material from the ss-RF source was critical. Evenwith the ss-RF coil matched and tuned, amplification was required as the SMT03 Rohde& Schwarz (R&S) RF generator used only delivered a maximum of 20 mW. We usedan inline RF amplifier from Minicircuits (model LZY-1+) at 50 Ω and with 50 Wamplification between 20 to 512 MHz. The power requirements at the coil was on the8rder of 10 mW.The software controlled power specifications and RF modulation were handled inLabView. The computer controlled R&S RF Generator could be made to change am-plitude and duration at each frequency step, enabling a highly selective degree of spinmanipulation as a function of time. In this initial study, we did not optimize this fea-ture. The distribution of the power profile delivered was also dependant on the coil. Ahigh quality factor and optimized tune in the ss-RF coil delivered a more precise andlocalized RF load in the signal domain. The power profile of the ss-RF in the CW-NMRwas characterized by the Voigt function [17].The target material used in these measurements was warm irradiated ( ∼
87 K) underliquid argon using 10 MeV electrons, with integrated fluxes of about 10 e − /cm atthe MIRF facility at NIST. The production of the paramagnetic complex in irradiatedC D OH conditioned the sample to polarize to about P =
50% at 5 T and 1 K. UnderBoltzmann equilibrium (no ss-RF), this resulted in a tensor polarization of, P zz = − (cid:112) − P = . . (6)Enhancement beyond this level requires application of selective excitation using the ss-RF to maximize the difference in the two intensities I + and I − such that P zz = C ( I + − I − ) is maximized.Figure 4 shows a plot of the NMR lineshape for a vector polarization of 50%. Thisplot represents the sum of I + ( R ) and I − (R) over the frequency domain in R . Similarly,a tensor polarization plot is shown in Figure 5 and represents the difference of I + ( R ) and I − ( R ) over the frequency domain in R . By selectively applying the ss-RF, it waspossible to reduce the regions in the P zz line that drop below the x-axis. When this wasdone simultaneously over all negative regions in the domain, the tensor polarizationwas enhanced.
5. Experimental Results
To optimize the enhancement, the ss-RF excitation had to minimize the negativetensor polarization for all R while minimizing the reduction to the overall area of the9 − − − − R m V ) E I ( C Vector Polarization
Figure 4: The NMR lineshape for a vector polar-ization of 50% which comes from the sum of theintensities I + ( R ) and I − ( R ) . − − − − R − − m V ) E I ( C Tensor Polarization
Figure 5: The tensor polarization shown from thedifference of the intensities I + ( R ) and I − ( R ) . NMR signal from the process. The two critical regions lie around R ∼ ∓ θ ≈ π / ± < R < ± θ ≈ I − . This can be thoughtof as minimizing the negative parts of the tensor polarization, shown in Fig. 5. In bothfigures, the y-axis would normally be millivolts scaled by a multiplicative factor C E which is sensitive to the characteristics of the NMR coil, such as inductance, geome-try, and orientation. We therefore leave these units generalized and provide a scale forrelative change when necessary. For negative vector polarization, the greatest enhance-ment came from the reduction of the transition area with intensity I + . Otherwise, thetreatment of both cases was identical, so it was convenient to focus on positive vectorand tensor polarization.The target had to first be polarized with DNP to achieve the highest vector polar-ization possible for that material. This maximized the signal area to be used in thess-RF manipulation. For C D OH, the polarization started to maximize at about 50%in about 35 minutes. For ND , the time to polarize would be significantly longer, but itcan reach the same maximum.The ss-RF was then applied as described. Because of the power amplification in thess-RF, damage to the Q-meter may result if these systems are running simultaneously.Cycling between RF manipulation and NMR measurement can result in additional un-10ertainty in the NMR measurement due to the delayed sampling and the evolution ofthe spin state in the ensemble over time. In the results presented, the Q-meter and ss-RF were run simultaneously near the end of the ss-RF cycle to acquire the best NMRmeasurements before the manipulated signal relaxed back to Boltzmann equilibrium.This still required considerable synchronicity between these two RF systems to makethe most of the limited NMR sweeps after the ss-RF was turned off and before thesignal lineshape changed from relaxation. The Q-meter NMR sampling rate was set toabout 15.4 Hz over the 500 steps in the domain where each bin represented one of the500 RF scan steps of the CW-NMR. For the sake of accurate measurement of the ss-RF enhancement to the signal, the material spin diffusion relaxation rate became veryrelevant. This relaxation rate was reduced as much as possible by maintaining low tem-perature ( ∼ I − ) could be brought to near saturationto optimize. Saturation occurred when the RF drove the population of the magneticsublevels to equalize. However, the peak was highly sensitive to power being higherin magnitude, and it was necessary to preserve as much of the larger intensity ( I + )underneath the I − peak as possible. Optimization required just the right amount of RFpower to reduce the area in I − without depleting I + .Figure 6 shows the NMR measurement right before ss-RF manipulation. The vectorpolarization was 49.8%. A fit to the data is also shown indicating the I + intensity inblue and the I − intensity in pink. Figure 7 shows the NMR measurement after the ss-RF had been applied to the two negative tensor regions in R . A fit to the data is shownwhich uses only the constraints from Eq. 4 and Eq. 5, resulting in a tensor polarizationmeasurement of 28.8%. Several iterations were made to optimize enhancement givenvariation in the set of RF parameters. After several trials, it was determined that thebest RF waveform was triangular with modulation at around 1 kHz. The duration ofthe step where the modulation was applied could also be a critical parameter, becausethe saturation level under DNP is sensitive to both power and time of modulation. Inthe following, we held the duration constant across the applied modulation to reduce11 − − − R m V ) E I ( C Figure 6: The NMR measurement for a deuteronpolarization at 49.8%, with the fit used to extractthe polarization measurement. − − − R m V ) E I ( C Figure 7: NMR measurement with fit result afterthe ss-RF has been applied to the two negativetensor regions. The tensor polarization from thisexample was 28.8%. the number of variables. We then waited for the system to reach a steady-state and thenrecorded the results. We present the parameters for the best measurements with thecleanest signal and best fit results in Table 1.ss-RF Enhanced MeasurementsPeak (MHz) Amp(mV) Pedestal (MHz) Amp(mV) P zz (%) Error(%)32.62(0.000) 20 32.85(0.015) 70 26.7 5.432.63(0.015) 30 32.85(0.020) 40 28.8 5.732.64(0.015) 30 32.84(0.025) 40 29.4 7.232.64(0.015) 25 32.83(0.035) 20 26.5 6.832.64(0.015) 20 32.85(0.035) 70 30.3 7.832.64(0.020) 20 32.85(0.025) 40 27.5 4.732.64(0.015) 40 32.88(0.055) 50 31.1 8.5 Table 1: NMR measurements for various trials of optimized tensor enhancement for different applied ss-RFamplitude and frequency location for both the pedestal and peak, and the corresponding modulation range.
For the set of measurements listed in Table 1, the amplitude (Amp) and modulationcenter frequency and range are given for the RF applied to the peak and pedestal. Theresulting tensor polarization was extracted after the data was taken and analyzed offline.12he listed errors were calculated from the systematic error from the fit and the standardNMR uncertainty measurements [20]. All the errors listed in the table are relativecontributions. For all of this data, the initial vector polarization was very close to 50%with an uncertainty of 3.2% relative. To minimize the uncertainty, multiple thermalequilibrium calibration measurements were performed at different temperatures whilecross checking with the standard intensity fitting procedure [17, 19]. The conclusiondeduced from this set of data is that optimal enhancement comes from the selectionof the appropriate frequencies and modulate range without applying any additionalunnecessary power. Ultimately, it is necessary to implement the ss-RF with a powerprofile that is sensitive to the lineshape over the frequency domain while minimizingthe overall RF-power load to the target.The same techniques that are used to enhance the tensor polarization can also beused to reduce it. This is done by applying the ss-RF to the larger peak and manipulat-ing the signal so that I − and I + are equal. We performed tests of this application andmeasured approximately 37% vector polarization with tensor polarization of 0.02 witha 3% relative error. The target was initially polarized to vector polarization of about50%. This approach is helpful for spin-1 observable extraction where tensor polarizedobservables can contaminate the measurement.There is still further opportunity to advance this approach by using NMR and ss-RFthat are optimally synchronized. Additionally, the power profile of the ss-RF shouldbe delivered across the domain as a function of the lineshape. In the results presented,this was only approximately achieved by eye and not computationally. Finer controland granularity could be achieved by automating this process to have greater ss-RFpower deposition at higher intensities and less at lower intensities while monitoring thetensor polarization enhancement under continuous DNP. Such improvements wouldalso reduce uncertainties by making the resulting modified lineshape more smooth.Effective optimization of the enhancement through selective semi-saturation in real-time depends greatly on the continuous knowledge of the overlapping absorption lines.Online monitoring and enhancement would be critical during scattering experi-ments where polarization decay occurs with the accumulation of dose due to changesin the paramagnetic complex. As the polarization decays, the amount of enhancement13er unit area increases so, like the microwave system, the ss-RF would have to becontinuously monitored and optimized. Hardware and software tools are under devel-opment at UVA to accommodate these needs for future experiments. For a given vector polarization of 50%, one can not achieve much over a 10%absolute gain in tensor polarization with ss-RF alone. This is because the smaller ofthe two intensities has a large portion of its absorption line completely inaccessibleto the application of ss-RF. Further, ss-RF manipulation of a broader domain wouldultimately deplete the overall enhancement.To access the spins in the overlapping region, it is possible to apply ss-RF in thenon-overlapping region close to θ ≈ θ ≈
0. If the ss-RF were to be appliedcontinuously in the non-overlapping region while rotating at a rate just faster than thespin diffusion rate under DNP, but slow with respect to the nuclear spin relaxation rate,then additional enhancement is possible. The enhancement condition is, ω σ d ( R ) < Ω ( t ) < ω λ , (7)where Ω ( t ) is the rate of rotation at time t and ω σ d is the spin-diffusion rate, with σ d being the diffusion constant at the manipulated position R and ω λ being the nuclearrelaxation rate.Slow rotation of the target revolves the target crystallites over all possible orien-tations relative to the holding field. In this way, the local spins with any given angle θ of the internuclear vector with respect to the holding field pass through every other θ in the spectrum. Rotation clockwise moves the spins oriented at θ = π / θ . Counter-clockwise rotation moves the spins at θ = θ = π / igure 8: The direction of spins moving through the absorption lines with counter-clockwise rotation. The type of diffusion that is most critical to rss-RF is the rotation driven spectraldiffusion. This process occurs when individual nuclear spins undergo continuous ex-change of energy, resulting in a transfer of polarization between spins of close proxim-ity and neighboring frequency. The mechanism has a cos θ dependence governing thefundamental rate of the flip-flop process. Spectral diffusion increases during rotationdue to the changes in spin θ orientation. Changes occur to the line after selective ex-citation when nuclear spin polarization transfers across the NMR spectrum effectivelyrefilling the depleted area to return to Boltzmann equilibrium across θ . The diffusionrate can be expressed as [25], ω σ d ( θ ) ∝ b I ( θ ) , (8) b = − w r (cid:0) θ − (cid:1) , (9)where w is the coupling constant and r is the internuclear distance between spins. Wenote that Eq. 8 is an approximation for the target rotation orientation used here of90 ◦ with respect to the holding field. This expression is valid for slow magic anglespinning (MAS) with the axis of rotation being 54.7356 ◦ from the holding field andfor frequencies much lower than the local field frequencies but higher than the spin-diffusion rate.Figure 9 shows an example plot that illustrates the direction of movement of a15 − − − R m V ) E I ( C Figure 9: A plot showing the direction of movement of a hole from ss-RF. Both the depleted portion and theenhanced portion in the other absorption line move inward under counter-clockwise rotation. hole from ss-RF. Both the depleted portion and the enhanced portion in the opposingabsorption line move inward under counter-clockwise rotation. Due to the rotationdriven spectral diffusion, the effect is difficult to pass through the θ = π / θ dependence. In this regard, rotation that is too fast depletesthe enhancement and can result in overall signal area reduction.We attempted many trials of rss-RF at different rotation rates Ω and different am-plitudes and ss-RF locations in the frequency domain. We express the rotation rate innumber of seconds in one full rotation of the target cup. We explored a range of Ω − be-tween 25 and 145 seconds per rotation. Table 2 presents the best results achieved fromthat study, showing the resulting tensor polarization NMR measurements for varioustrials given the different applied rotation rate, ss-RF amplitude and frequency locationfor both the pedestal and peak, and the corresponding modulation range. Again, thelisted errors were calculated from the systematic error from the fit and the standardNMR uncertainty measurements. The errors in the table are relative contributions. Forall of this data, the initial vector polarization was very close to 50% with an uncertaintyof 3.2% relative. The resulting vector polarization after the rss-RF was approximately43%.With ss-RF only applied to the edge ( R ∼
2) of the smaller intensity pedestal duringrotation, significant increase to the opposing absorption line could be seen, see Fig.16ss-RF Enhanced Measurements Ω − Peak (MHz) Amp(mV) Pedestal (MHz) Amp(mV) P zz (%) Error(%)50 32.65(0.010) 15 32.85(0.015) 45 35.7 8.444 32.66(0.000) 10 32.88(0.015) 40 36.5 9.740 32.65(0.000) 15 32.88(0.015) 40 36.3 9.3 Table 2: NMR measurements for various trials of optimized tensor enhancement for different applied ro-tation rate, ss-RF amplitude and frequency location for both the peak and pedestal, and the correspondingmodulation range.
10. The opposite pedestal grew and the enhanced region moved under the smallerpeak. This is the most optimization that was achieved with this single location of ss-RF while rotating continuously over the rotation rate that was studied. In this example, Ω − =
40 seconds and the resulting tensor polarization was approximately 33% (8%).For maximal enhancement during rotation, similar application of the ss-RF in thefrequency domain is required. The RF was frequency modulated to saturate the major-ity of the pedestal from R = . R = I − peakallowing rotation into the ss-RF region rather than away from. This provided a slightbenefit to enhancement during rotation. The power was also reduced at this positionas was very easy to destroy the enhancement gained by irradiating the other absorptionline underneath with too much RF. Figure 11 shows the results of this type of selectiverss-RF. The total tensor enhancement for this example was 36.5% (9.7%).With ss-RF applied to the two regions indicated during rotation, significant increaseto the opposing absorption line could be seen, see Fig. 11. The opposite pedestal grewand the enhanced region moved under the smaller peak. The opposing peak region alsogrew in response to the ss-RF. This is so far the best method for producing a maximum17 − − − R m V ) E I ( C Figure 10: NMR measurement of tensor en-hancement optimization that was achieved withsingle location of ss-RF while rotating continu-ously at a fixed rate. The resulting tensor polar-ization was approximately 33%. − − − R m V ) E I ( C Figure 11: NMR measurement of tensor en-hancement maximized by using two locations ofss-RF while rotating continuously at a fixed rate.The resulting tensor polarization was approxi-mately 36%. tensor polarization enhancement during continuous DNP and continuous rotation at aconstant rate. These results indicate that an absolute tensor polarization enhancementof around 15% given an initial 50% vector polarization is viable under the standardconditions of a scattering experiment. What we conclude from the analysis of the datafrom rotation is that it is necessary to implement the ss-RF with a power profile that issensitive to the lineshape as a function the ss-RF frequency, modulation range as well astarget rotation rate. The modulation range should be minimized while using rotation toreduce excess RF-power load to the target. Rotation can be used to effectively modulateeven when the ss-RF is fixed.There is additional measurement error when rotation is involved due to the timedependence of the spectral diffusion. This error can likely be reduced with furtherresearch and the development of online rss-RF optimization software and measurementtools. This work is also underway at UVA.Figure 12 shows a model of a rotating target which would be similar to what wouldbe used in a scattering experiment. The front and back of the cup would be made ofthin foil for the beam to pass through, and the cup would be made to rotate around by agear driven from the perimeter of the cup. The ss-RF coil would be fixed to the targetladder and not in contact with the rotating part of the cup, while the NMR coil would befixed on the inside of the ss-RF coil. The cup that was used to take the measurements18 igure 12: Drawing of a possible design for a rss-RF cup that would work in a scattering experiment. A thinfoil lid and bottom would be used directly in the beam path. The microwave horn and the rotation drive arealso visible. presented here is similar to this design.
The MAS technique is standard in solid-state NMR frequently used in NMR spec-troscopy to suppress dipolar broadening [26]. The local field produced at an observedspin has components with symmetry like those of second rank spherical harmonics.When the sample is spun, local fields orthogonal to the spinning axis are rendered timedependent and modulate the NMR signal at multiples of the spin rate. The resultingNMR signal contains a set of side bands at multiples of the spin rate and a center bandwhose width is determined by the distribution of local fields along the rotation axis.For dipolar fields, the component along a spinning axis oriented at angle β with re-spect to the holding field is reduced by a factor of P ( cos β ) . For MAS, P ( cos β ) =
6. Conclusion
To achieve the highest figure-of-merit (FOM) in scattering experiments which re-quire a solid-state tensor polarized target, it is necessary to maximize the tensor polar-ization throughout the beam target interaction time. Optimization of the tensor polar-ization of the spin-1 target ensemble can be achieved by applying ss-RF irradiation atselect frequencies with the necessary power. Experimental results are provided demon-strating the degree of enhancement using the ss-RF technique to manipulate and mea-sure the CW-NMR signal. Optimization is achieved using a critical RF decay constantthat is controlled by the amplitude of the RF. The RF partially saturates the overlappingregions of the Pake doublet corresponding to P zz ( R ) < Acknowledgement
The authors thank Chris Keith of the Jefferson Lab Target Group for thoroughlyreading this manuscript. We also thank Mikhail Yurov for his contributions to thesemeasurements and the development of the initial software used to perform ss-RF andrss-RF. His commitment to good scientific practice must be acknowledged. Figure 3and 12 were produced by Carlos Ramirez using SolidWorks. All NMR data presentedhere was taken at the University of Virginia Solid Polarized Target Lab. This work wassupported by DOE contract DE-FG02-96ER40950.
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