Based on the restraining effect that spatial filtering has on the frequency spectrum of a beam, from the small-scale focusing theory of Bespalov and Talanov (B-T theory) we derive an expression for the pinhole diameter of the spatial filter corresponding to the fastest growing frequency. Then, compared with the theoretical pinhole diameter of the spatial filter, the restraining effect of the spatial filter on a hot image with different pinhole diameters is numerically investigated. The numerical results show that, if the pinhole diameter is larger than the theoretical one, the hot-image intensity will remain steady; once the pinhole diameter becomes smaller than the theoretical one, the hot-image intensity will begin to decrease. Moreover, as the pinhole diameter decreases, a more prominent restraining effect can be obtained. But reducing the diameter of the spatial filter would lead to greater beam energy loss. The parameters of the spatial filter must be chosen to guarantee that the scheme fulfills the demand for low beam energy loss and a satisfactory restraining effect simultaneously.
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