Perspectives on microwave coupling into cylindrical and spherical rotors with dielectric lenses for magic angle spinning dynamic nuclear polarization

Continuous wave dynamic nuclear polarization (DNP) increases the sensitivity of NMR, yet intense microwave fields are required to transition magic angle spinning (MAS) DNP to the time domain. Here we describe and analyze Teflon lenses for cylindrical and spherical MAS rotors that focus microwave power and increase the electron Rabi frequency, ν_1s. Using a commercial simulation package, we solve the Maxwell equations and determine the propagation and focusing of millimeter waves (198 GHz). We then calculate the microwave intensity in a time-independent fashion to compute the ν_1s. With a nominal microwave power input of 5 W, the average ν_1s is 0.38 MHz within a 22 μL sample volume in a 3.2 mm outer diameter (OD) cylindrical rotor without a Teflon lens. Decreasing the sample volume to 3 μL and focusing the microwave beam with a Teflon lens increases the ν_1s to 1.5 MHz. Microwave polarization and intensity perturbations associated with diffraction through the radiofrequency coil, losses from penetration through the rotor wall, and mechanical limitations of the separation between the lens and sample are significant challenges to improving microwave coupling in MAS DNP instrumentation. To overcome these issues, we introduce a novel focusing strategy using dielectric microwave lenses installed within spinning rotors. One such 9.5 mm OD cylindrical rotor assembly implements a Teflon focusing lens to increase the ν_1s to 2.7 MHz within a 2 μL sample. Further, to access high spinning frequencies while also increasing ν_1s, we analyze microwave coupling into MAS spheres. For 9.5 mm OD spherical rotors, we compute a ν_1s of 0.36 MHz within a sample volume of 161 μL, and 2.5 MHz within a 3 μL sample placed at the focal point of a novel double lens insert. We conclude with an analysis and discussion of sub-millimeter diamond spherical rotors for time domain DNP at spinning frequencies >100 kHz. Sub-millimeter spherical rotors better overlap a tightly focused microwave beam, resulting in a ν_1s of 2.2 MHz. Lastly, we propose that sub-millimeter dielectric spherical microwave resonators will provide a means to substantially improve electron spin control in the future.

A versatile custom cryostat for dynamic nuclear polarization supports multiple cryogenic magic angle spinning transmission line probes

Dynamic nuclear polarization (DNP) with cryogenic magic angle spinning (MAS) provides significant improvements in NMR sensitivity, yet presents unique technical challenges. Here we describe a custom cryostat and suite of NMR probes capable of manipulating nuclear spins with multi-resonant radiofrequency circuits, cryogenic spinning below 6 K, sample exchange, and microwave coupling for DNP. The corrugated waveguide and six transfer lines needed for DNP and cryogenic spinning functionality are coupled to the probe from the top of the magnet. Transfer lines are vacuum-jacketed and provide bearing and drive gas, variable temperature fluid, two exhaust pathways, and a sample ejection port. The cryostat thermally isolates the magnet bore, thereby protecting the magnet and increasing cryogen efficiency. This novel design supports cryogenic MAS-DNP performance over an array of probes without altering DNP functionality. We present three MAS probes (two supporting 3.2 mm rotors and one supporting 9.5 mm rotors) interfacing with the single cryostat. Mechanical details, transmission line radio frequency design, and performance of the cryostat and three probes are described.

Electron decoupling with cross polarization and dynamic nuclear polarization below 6 K

Dynamic nuclear polarization (DNP) can improve nuclear magnetic resonance (NMR) sensitivity by orders of magnitude. Polarizing agents containing unpaired electrons required for DNP can broaden nuclear resonances in the presence of appreciable hyperfine couplings. Here we present the first cross polarization experiments implemented with electron decoupling, which attenuates detrimental hyperfine couplings. We also demonstrate magic angle spinning (MAS) DNP experiments below 6 K, producing unprecedented nuclear spin polarization in rotating solids. ¹³C correlation spectra were collected with MAS DNP below 6 K for the first time. Polarization build-up times with MAS DNP (T_{1DNP, 1H}) of urea in a frozen glassy matrix below 6 K were measured for both the solid effect and the cross effect. Trityl radicals exhibit a T_1DNP (¹H) of 18.7 s and the T_1DNP (¹H) of samples doped with 20 mM AMUPol is only 1.3 s. MAS below 6 K with DNP and electron decoupling is an effective strategy to increase NMR signal-to-noise ratios per transient while retaining short polarization periods.

Frequency-agile gyrotron for electron decoupling and pulsed dynamic nuclear polarization

We describe a frequency-agile gyrotron which can generate frequency-chirped microwave pulses. An arbitrary waveform generator (AWG) within the NMR spectrometer controls the microwave frequency, enabling synchronized pulsed control of both electron and nuclear spins. We demonstrate that the acceleration of emitted electrons, and thus the microwave frequency, can be quickly changed by varying the anode voltage. This strategy results in much faster frequency response than can be achieved by changing the potential of the electron emitter, and does not require a custom triode electron gun. The gyrotron frequency can be swept with a rate of 20 MHz/μs over a 670 MHz bandwidth in a static magnetic field. We have already implemented time-domain electron decoupling with dynamic nuclear polarization (DNP) magic angle spinning (MAS) with this device. In this contribution, we show frequency-swept DNP enhancement profiles recorded without changing the NMR magnet or probe. The profile of endofullerenes exhibits a DNP profile with a <10 MHz linewidth, indicating that the device also has sufficient frequency stability, and therefore phase stability, to implement pulsed DNP mechanisms such as the frequency-swept solid effect. We describe schematics of the mechanical and vacuum construction of the device which includes a novel flanged sapphire window assembly. Finally, we discuss how commercially available continuous-wave gyrotrons can potentially be converted into similar frequency-agile high-power microwave sources.

Magic angle spinning NMR below 6 K with a computational fluid dynamics analysis of fluid flow and temperature gradients

We report magic angle spinning (MAS) up to 8.5 kHz with a sample temperature below 6 K using liquid helium as a variable temperature fluid. Cross polarization ¹³C NMR spectra exhibit exquisite sensitivity with a single transient. Remarkably, ¹H saturation recovery experiments show a ¹H T₁ of 21 s with MAS below 6 K in the presence of trityl radicals in a glassy matrix. Leveraging the thermal spin polarization available at 4.2 K versus 298 K should result in 71 times higher signal intensity. Taking the ¹H longitudinal relaxation into account, signal averaging times are therefore predicted to be expedited by a factor of >500. Computer assisted design (CAD) and finite element analysis were employed in both the design and diagnostic stages of this cryogenic MAS technology development. Computational fluid dynamics (CFD) models describing temperature gradients and fluid flow are presented. The CFD models bearing and drive gas maintained at 100 K, while a colder helium variable temperature fluid stream cools the center of a zirconia rotor. Results from the CFD were used to optimize the helium exhaust path and determine the sample temperature. This novel cryogenic experimental platform will be integrated with pulsed dynamic nuclear polarization and electron decoupling to interrogate biomolecular structure within intact human cells.

Instrumentation for cryogenic magic angle spinning dynamic nuclear polarization using 90L of liquid nitrogen per day

Cryogenic sample temperatures can enhance NMR sensitivity by extending spin relaxation times to improve dynamic nuclear polarization (DNP) and by increasing Boltzmann spin polarization. We have developed an efficient heat exchanger with a liquid nitrogen consumption rate of only 90L per day to perform magic-angle spinning (MAS) DNP experiments below 85K. In this heat exchanger implementation, cold exhaust gas from the NMR probe is returned to the outer portion of a counterflow coil within an intermediate cooling stage to improve cooling efficiency of the spinning and variable temperature gases. The heat exchange within the counterflow coil is calculated with computational fluid dynamics to optimize the heat transfer. Experimental results using the novel counterflow heat exchanger demonstrate MAS DNP signal enhancements of 328±3 at 81±2K, and 276±4 at 105±2K.

Frequency swept microwaves for hyperfine decoupling and time domain dynamic nuclear polarization

Hyperfine decoupling and pulsed dynamic nuclear polarization (DNP) are promising techniques to improve high field DNP NMR. We explore experimental and theoretical considerations to implement them with magic angle spinning (MAS). Microwave field simulations using the high frequency structural simulator (HFSS) software suite are performed to characterize the inhomogeneous phase independent microwave field throughout a 198GHz MAS DNP probe. Our calculations show that a microwave power input of 17W is required to generate an average EPR nutation frequency of 0.84MHz. We also present a detailed calculation of microwave heating from the HFSS parameters and find that 7.1% of the incident microwave power contributes to dielectric sample heating. Voltage tunable gyrotron oscillators are proposed as a class of frequency agile microwave sources to generate microwave frequency sweeps required for the frequency modulated cross effect, electron spin inversions, and hyperfine decoupling. Electron spin inversions of stable organic radicals are simulated with SPINEVOLUTION using the inhomogeneous microwave fields calculated by HFSS. We calculate an electron spin inversion efficiency of 56% at a spinning frequency of 5kHz. Finally, we demonstrate gyrotron acceleration potentials required to generate swept microwave frequency profiles for the frequency modulated cross effect and electron spin inversions.