Abstract
We present a calculation of the microwave field distribution in a magic angle spinning (MAS) probe utilized in dynamic nuclear polarization (DNP) experiments. The microwave magnetic field (B(1S)) profile was obtained from simulations performed with the High Frequency Structure Simulator (HFSS) software suite, using a model that includes the launching antenna, the outer Kel-F stator housing coated with Ag, the RF coil, and the 4mm diameter sapphire rotor containing the sample. The predicted average B(1S) field is 13μT/W(1/2), where S denotes the electron spin. For a routinely achievable input power of 5W the corresponding value is γ(S)B(1S)=0.84MHz. The calculations provide insights into the coupling of the microwave power to the sample, including reflections from the RF coil and diffraction of the power transmitted through the coil. The variation of enhancement with rotor wall thickness was also successfully simulated. A second, simplified calculation was performed using a single pass model based on Gaussian beam propagation and Fresnel diffraction. This model provided additional physical insight and was in good agreement with the full HFSS simulation. These calculations indicate approaches to increasing the coupling of the microwave power to the sample, including the use of a converging lens and fine adjustment of the spacing of the windings of the RF coil. The present results should prove useful in optimizing the coupling of microwave power to the sample in future DNP experiments. Finally, the results of the simulation were used to predict the cross effect DNP enhancement (ϵ) vs. ω(1S)/(2π) for a sample of (13)C-urea dissolved in a 60:40 glycerol/water mixture containing the polarizing agent TOTAPOL; very good agreement was obtained between theory and experiment.