At the subsequent iterations, the higher order PO currents are given by;
:<math> \mathbf{J^{(n)}(r)} = (1+\alpha)\mathbf{\hat{n}} \times \left\lbrace \begin{align} & - jk_0 \iint_{S_J} \left( 1 - \frac{j}{k_0 R} \right) (\mathbf{ \hat{R} \times J^{(n-1)}(r') }) \frac{e^{-jk_0 R}}{4\pi R} \,ds' \\ & -j k_0 Y_0 \iint_{S_M} \left[ \left( 1 - \frac{j}{k_0 R} - \frac{1}{(k_0 R)^2} \right) \mathbf{M^{(n-1)}(r')} - \left( 1-\frac{3j}{k_0 R}-\frac{3}{(k_0 R)^2} \right) \mathbf{ (\hat{R} \cdot M^{(n-1)}(r')) \hat{R} } \right] \frac{e^{-jk_0 R}}{4\pi R} \,ds' \end{align} \right\rbrace </math>
:<math> \mathbf{M^{(n)}(r)} = -(1-\alpha)\mathbf{\hat{n}} \times \left\lbrace \begin{align} & jk_0 \iint_{S_M} \left( 1 - \frac{j}{k_0 R} \right) (\mathbf{ \hat{R} \times M^{(n-1)}(r') }) \frac{e^{-jk_0 R}}{4\pi R} \,ds' \\ & -j k_0 Z_0 \iint_{S_J} \left[ \left( 1 - \frac{j}{k_0 R} - \frac{1}{(k_0 R)^2} \right) \mathbf{J^{(n-1)}(r')} - \left( 1-\frac{3j}{k_0 R}-\frac{3}{(k_0 R)^2} \right) \mathbf{ (\hat{R} \cdot J^{(n-1)}(r')) \hat{R} } \right] \frac{e^{-jk_0 R}}{4\pi R} \,ds' \end{align} \right\rbrace </math>
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