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Chinese Physics C> 2007, Vol. 31> Issue(S1) : 201-205 

Elementary Theory for Optimum Extraction of Space-Charge-Dominated Ion Beams from Plasma Boundaries

  •  Oak Ridge National Laboratory, Oak Ridge, TN 37831-6372, USA

  • The problem of extracting space-charge-limited ion beams from spherical emission boundaries is analyzed for simple, two electrode, parallel-plate and spherical sector electrode systems by application of Langmuir-Blodgett theory with account taken for the divergent lens effect caused by the aperture in the extraction electrode. Results derived from simulation studies for the three electrode system, designed for use with the Oak Ridge National Laboratory ECR ion source, complement predictions made from elementary analytical theory with or without magnetic field in the extraction region of the source. Under minimum half-angular divergence (minimum emittance) conditions, the plasma emission boundary has an optimum curvature and the perveance, P, (i.e, current density, j+ and extraction gap, d), has an optimum value for a given charge-state. From these studies, we find that the optimum perveance for any electrode system can be determined from the Child-Langmuir relation for the parallel-plate electrode system multiplied by a factor, F with value 0.49≤F≤1.
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    [1] . Langmuir I, Blodgett K R. Phys. Rev., 1923, 22: 3472. Langmuir I, Blodgett K R. Phys. Rev., 1924, 24: 493. Langmuir I, Compton K. Rev. Mod. Phys., 1931, 13: 1914. Harrison E R. J. Appl. Phys., 1958, 29: 9095. Thompson E. Particle Accelerators, 1972, 4: 696. Coupland J R, Green T S, Hammond D P et al. Rev. Sci.Instrum., 1973, 44: 12587. Davisson C J, Calbick C J. Phys. Rev., 1931, 38: 5858. Brewer G. High Intensity Electron Guns, in Focusing of Charged Particles, Volume II. Edited by Septier A, Academic Press (1967) New York, Ch. 3.2, pp. 23-729. Child C. Phys. Rev., 1911, 32: 49210. Langmuir I. Phys. Rev., 1913, 2: 45011. Raiko V I. Kernenergie, 1967, 10: 8912. Chavet I, Bernas R. Nucl. Instrum. and Meth., 1967, 47:77

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G.D.Alton and H.Bilheux. Elementary Theory for Optimum Extraction of Space-Charge-Dominated Ion Beams from Plasma Boundaries[J]. Chinese Physics C, 2007, 31(S1): 201-205.
G.D.Alton and H.Bilheux. Elementary Theory for Optimum Extraction of Space-Charge-Dominated Ion Beams from Plasma Boundaries[J]. Chinese Physics C, 2007, 31(S1): 201-205. shu
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Received: 2007-05-30
Revised: 1900-01-01
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Elementary Theory for Optimum Extraction of Space-Charge-Dominated Ion Beams from Plasma Boundaries

    Corresponding author: G.D.Alton,
  • Oak Ridge National Laboratory, Oak Ridge, TN 37831-6372, USA
  • Received Date: 2007-05-30
  • Accepted Date: 1900-01-01
  • Available Online: 2007-01-03

Abstract: The problem of extracting space-charge-limited ion beams from spherical emission boundaries is analyzed for simple, two electrode, parallel-plate and spherical sector electrode systems by application of Langmuir-Blodgett theory with account taken for the divergent lens effect caused by the aperture in the extraction electrode. Results derived from simulation studies for the three electrode system, designed for use with the Oak Ridge National Laboratory ECR ion source, complement predictions made from elementary analytical theory with or without magnetic field in the extraction region of the source. Under minimum half-angular divergence (minimum emittance) conditions, the plasma emission boundary has an optimum curvature and the perveance, P, (i.e, current density, j+ and extraction gap, d), has an optimum value for a given charge-state. From these studies, we find that the optimum perveance for any electrode system can be determined from the Child-Langmuir relation for the parallel-plate electrode system multiplied by a factor, F with value 0.49≤F≤1.

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