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1、1 31 ? Or. 2007 c 7 ?p U ? n ? ? ? n HIGHENERGYPHYSICSANDNUCLEARPHYSICSVol. 31, Supp. Jul., 2007Elementary Theory for Optimum Extraction ofSpace-Charge-Dominated Ion Beams from Plasma Boundaries*G. D. Alton1)H. Bilheux(Oak Ridge National Laboratory, Oak Ridge, TN 37831-6372, USA)AbstractThe problem
2、of extracting space-charge-limited ion beams from spherical emission boundariesis analyzed for simple, two electrode, parallel-plate and spherical sector electrode systems by application ofLangmuir-Blodgett theory with account taken for the divergent lens effect caused by the aperture in theextracti
3、on electrode. Results derived from simulation studies for the three electrode system, designed for usewith the Oak Ridge National Laboratory ECR ion source, complement predictions made from elementaryanalytical theory with or without magnetic field in the extraction region of the source. Under minim
4、um half-angular divergence (minimum emittance) conditions, the plasma emission boundary has an optimum curvatureand 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 electro
5、de system can be determinedfrom the Child-Langmuir relation for the parallel-plate electrode system multiplied by a factor, F with value0.496F 61.Key wordsspace-charge dominated beam extraction theory, ion beam extraction simulation, optimum per-veance, optimum angular divergence1IntroductionLangmui
6、r-Blodgett-Comptonformulationforelectron flow in curved electrode systems13af-ter correction for mass and charge, can be manip-ulated into analytical approximations useful in un-derstanding, on an elementary level, the ion opticsof space-charge-dominated ion beams extracted fromcylindrical and spher
7、ical-sector plasma boundariesand accelerated through simple electrode structures(see, for example, Refs. 46). In such analyses, theplasma emission boundary is treated as a curved fluidsurface, the radius of curvature, of which changesdue to changes in plasma density or extraction field.The extractio
8、n process is further complicated by thepresence of an aperture in the extraction electrode,necessary for ion extraction. The aperture effect canbe accounted for by application of the appropriateDavisson-Calbick relation7to account for opticaleffects, including space-charge influences on the di-verge
9、nces of beams4, 5, 8.2Elementary extraction optics theory(without magnetic field)2.1Langmuir-blodgett formalismSolutions to Poissons equation for space-charge-limited flow from spherical emission boundaries canbe derived from the Langmuir-Blodgett relation1, 2.The appropriate equation for space-char
10、ge-limitedflow of electrical current, I, of a beam of particles ofcharge-state q and mass M, in a spherical sector elec-Received 20 April 2007*Supported by the U.S. Department of Energy under contract DE-AC05-00OR22725 with UT-Battelle, LLC 1)E-mail:altongdornl.gov 201 205202p U ? n ? ? ? n( HEP q i
11、s the charge-state and Mthe mass of the extracted beam. After expansion ofEq. (3), to order d/rsfor d ? rs, the following ap-proximation is obtained:P =I/3/2ex=Ppp(11.6d/rs).(5)Tabulations of the function can be found in severalreferences, including Ref. 8. Further details of thesolution of Eq. (2),
12、 resulting in expressions appropri-ate for optimizing extraction of space-charge domi-nated beams from parallel-plate, spherical-sector andthe remotely positional three electrode system usedfor extracting beams from the ORNL ECR ion sourcewill be the subject of a forthcoming article.3Ion extraction
13、from spherical-sectorplasma boundariesThe Langmuir-Blodgett relation1, 2, representedby Eq. (3), can be manipulated to approximateextraction of space-charge-dominated beams fromspherical-sector plasma emitting diode structureswith appropriate corrections for the lens action onthe beam during passage
14、 from one electric field re-gion to another.3.1Electrode systemsFigures 13 respectively, schematically illustratetwo-electrode, parallel-plate (Fig. 1), two electrode,spherical sector (Fig. 2) and the ORNL three elec-trode system (Fig. 3) for extraction of convergent,space-charge limited positive io
15、n beams from concavespherical-sector plasma emission boundaries (spheri-cal radii: rs, and circular emission apertures: a) toextraction electrodes of aperture radii; b) Extractionis effected between the source at potential, and theextraction electrode, at potential, ex, separated bya distance z = d
16、= rsrex. For the three electrodesystem, g, is the potential of the ground electrode.In each of the respective Figures, is the half-angularconvergence of the beam at the emission boundary; is the half-angular convergence imparted to the beamby the electric field in the extraction aperture; isthe final angular divergence of the beam after passingthrough the electrode system.Fig. 1.Simplified parallel-plate electrode sys- tem, two-electrode for ion extraction fr
