Physics of Particles and Nuclei Letters

, Volume 7, Issue 2, pp 145–151 | Cite as

Recovery of particle distribution function in four-dimensional phase space from measurements with pepper-pot method

  • N. Yu. Kazarinov
  • V. I. Kazacha
Methods of Physical Experiment


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%.


Nucleus Letter Legendre Polynomial Recurrence Formula Particle Distribution Function Dimensional Phase Space 
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  1. 1.
    A. Van Steenbergen, “Evaluation of Particle Beam Phase Space Measurement Techniques,” Nucl. Instrum. Methods Phys. Res. 51, 245–253 (1967).CrossRefADSGoogle Scholar
  2. 2.
    C. Le Jeune and J. Aubert, Emittance and Brightness Definitions and Measurements (Academic, New York, 1980).Google Scholar
  3. 3.
    Y. Yamazaki et al., “High-Precision Pepper-Pot Technique Or a Low-Emittance Electron Beam,” KEK Preprint No. 92-59 A (1992).Google Scholar
  4. 4.
    H. R. Kremers et al., “The KVI-4D Emittance Meter,” in Proc. of ECRIS08 (Chicago, IL, USA, 2008), pp. 204–207Google Scholar

Copyright information

© Pleiades Publishing, Ltd. 2010

Authors and Affiliations

  • N. Yu. Kazarinov
    • 1
  • V. I. Kazacha
    • 1
  1. 1.Joint Institute for Nuclear ResearchDubnaRussia

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