Recovery of particle distribution function in four-dimensional phase space from measurements with pepper-pot method
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The possibility of recovering the particle distribution function at any point of the four-dimensional transverse phase volume “x, x′, y, y′” using the results of measurements with the pepper-pot method is demonstrated. The proposed method for processing experimental data is based on the assumption that the one-to-one correspondence between holes in the mask and their images on the screen is established. Such a preliminary calibration should be experimentally performed on the measured ion beam. The method of moments is used for the recovery of the distribution function. Using Legendre polynomials for processing experimental results reduces the problem to a sequence of recurrence relations. A numerical simulation of the measurement process demonstrated that the recovery accuracy of the particle distribution function is about ±10%.
KeywordsNucleus Letter Legendre Polynomial Recurrence Formula Particle Distribution Function Dimensional Phase Space
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