Simulation of pulsed dynamic nuclear polarization in the steady state

TL;DR

This paper develops and compares algorithms to simulate the steady state of pulsed DNP, providing insights into optimizing pulse sequences and matching experimental results at various magnetic fields.

Contribution

It introduces and evaluates three algorithms for steady-state simulation of pulsed DNP, identifying the most efficient method and enhancing understanding of pulse sequence dynamics.

Findings

Algorithms (1) and (3) are stable; (3) is most efficient.

Simulations agree well with experimental results at multiple fields.

Trajectory during pulse differs from steady state, affecting sequence design.

Abstract

In pulsed dynamic nuclear polarization (DNP), enhancement of the polarization of bulk nuclei requires the repeated application of a microwave pulse sequence. So far, analysis of a one-time transfer of electron spin polarization to a dipolar-coupled nuclear spin has guided the design of DNP pulse sequences. This has obvious shortcomings, such as an inability to predict the optimal repetition time. In an actual pulsed DNP experiment, a balance is reached between the polarization arriving from the unpaired electrons and nuclear relaxation. In this article, we explore three algorithms to compute this stroboscopic steady state: (1) explicit time evolution by propagator squaring, (2) generation of an effective propagator using the matrix logarithm, and (3) direct calculation of the steady state with the Newton-Raphson method. Algorithm (2) is numerically unstable for this purpose. Algorithm (1) and (3) are both stable; algorithm (3) is the most efficient. We compare the steady-state simulations to existing experimental results at 0.34 T and 1.2 T and to the first experimental observation of X-inverse-X (XiX) DNP at 3.4 T: agreement is good, and improves further when electron-proton distance and electron Rabi frequency distributions are accounted for. We demonstrate that the trajectory of the spin system during one-time application of a microwave pulse sequence differs from the steady orbit. This has implications for DNP pulse sequence design.