4 Contract your selection by 4 (Selections>Modify>Contract). Fill the the area of the smaller circle with Sunburst Gradient Fill
Fill Style = Sunburst Gradient
Match Mode = None
Tolerance = 100
Opacity = 100
Sample Merge = NOT checked
Under the Flood Fill Options Tab
Gradient = Foreground-Background
Repeats = 0
Vertical and Horizontal Offset = 30

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