Placing high permittivity, low conductivity materials (HPM) between the radiofrequency (RF) coil and the sample has been proposed as a method for reshaping B₁⁺ fields, independent of RF shimming or parallel transmission^1,2,3. HPMs have also been shown to improve both receive sensitivity^2,4 and transmit efficiency^2,5,6 of RF coils. L-curves analysis has been employed to optimize the relative permittivity of an encircling layer of HPM surrounding the imaging sample⁷. Specifically, the optimal tradeoff between global SAR and profile fidelity was investigated for different HPMs using Ultimate Intrinsic SAR (UISAR) as a performance reference for a SAR-minimizing RF shimming algorithm⁸. However, the algorithm constrains the target excitation profile to have flat amplitude and phase throughout the excitation plane, whereas phase-relaxed RF shimming approaches are much more common, and can allow for larger SAR reduction. Relaxing the phase constraint in the algorithm would make SAR minimization a non-convex optimization. Therefore, to investigate the effects that the phase of the target excitation profile has on the optimal relative permittivity of the HPM, we generated L-curves for realistic phase distributions.Simulations for a closely-packed 48-coil array geometry⁹ were performed with a full-wave simulation tool based on dyadic Green’s functions¹⁰. The array elements were placed at a 1 cm distance from a uniform spherical phantom (radius_sphere = 8.4cm) (Figure 1) with electrical properties of average brain tissue¹¹ (ε_R = 63, σ = 0.46S/m) at 7 Tesla. The space between the coil and the phantom was filled with HPM, for which conductivity was kept to zero and relative permittivity was varied between 1 and 300. UISAR and global SAR of the array were calculated for three target excitation profiles with uniform amplitude and: flat phase, Gaussian phase, and a CP-like phase (Figure 2). The Gaussian phase distribution was chosen to match a low-field phase profile, while the CP-like phase distribution was chosen to match phase-unconstrained excitation profiles¹². All excitations were for a transverse plane through the center of the sphere. The SAR of the array was normalized by the UISAR and plotted as a function of the root mean square error (RMSE) of the achieved excitation profile for various degrees of regularization (i.e., L-curve plots). For each case, the optimal relative permittivity for the HPM layer was chosen based on the proximity of the corresponding L-curve to the origin, and results were compared to the case without HPM.UISAR for a near perfect excitation (RMSE < .001) was constant for the three phase profiles. UISAR values varied for different phase profiles only for large RMSE (Figure 3). The phase distribution of the target excitation profile did not affect the optimal relative permittivity for the HPM layer, which was ε_R = 100 for the cases of Gaussian, CP-like, and flat phase (Figure 4). L-curves for optimal HPM show similar performance benefits when compared to the case without HPM for all three phase distributions (Figure 5).Similar coil performance was found for the realistic profile phase distributions and the original flat-phase excitation. Some performance benefit was seen under a case of poor excitation uniformity for the Gaussian phase distribution, similar to what may be expected at lower field strength. However, performance loss was seen under the same conditions for the CP-like phase distribution, which may be explained by a misalignment of the CP-like phase profile with the coil geometry. This and previous work⁷ suggest that, for a given field strength, the optimal relative permittivity depends mainly on the array geometry. However, since previous work has shown that lower global SAR can be achieved by relaxing the phase constraint¹³, another explanation could be that the spatial distribution of the phase in a target excitation profile has a smaller effect on coil performance than the constraint of the phase in the RF shimming algorithm. In all cases the target profile amplitude was uniform to investigate the effect of the phases. Future work will include combining realistic phase with smoother distributions of the profile amplitude, which are known to improve coil performance⁸, and could result in different optimal HPM properties. In addition, to confirm that the choice of the target profile has a minor effect, phase-unconstrained RF shimming optimization will be explored in future work.