We report proton NMR measurements of the effect of very high magnetic fields up to 44.7 T
(1.9 GHz) on the spin density wave (SDW) transition of the organic conductor TMTSF2PF6.
Up to 1.8 GHz, no effect of critical slowing close to the transition is seen on the proton
relaxation rate (1/T1), which is determined by the SDW fluctuations associated with the phase
transition at the NMR frequency. Thus, the correlation time for such fluctuations is less than
$1O^{-10}$s. A possible explanation for the absence of longer correlation times is that the transition
is weakly first order, so that the full critical divergence is never achieved. The measurements
also show a dependence of the transition temperature on the orientation of the magnetic field
and a quadratic dependence on its magnitude that agrees with earlier transport measurements
at lower fields. The UCLA part of this work was supported by NSF Grant DMR-0072524.