Electrostatic Analyzers with Application to Electric Propulsion Testing

Electrostatic analyzers (ESAs) are used in electric propulsion to measure the energy per unit charge ⁄ distribution of ion and electron beams, in the downstream region of thrusters for example. This paper serves to give an overview of the most fundamental, yet most widely used, types of ESA designs. Analyzers are grouped into two classifications: (1) mirror-type analyzers and (2) deflector-type analyzers. Common mirror- type analyzers are the parallel-plate mirror analyzer (PMA) and the cylindrical mirror analyzer (CMA). For deflector type analyzers, a generalized toroidal type is first described and the commonly used cylindrical deflector (CDA) and spherical deflector (SDA) analyzers are discussed as special cases. The procedure for energy resolution calculations of ESAs is described, which is a common way of comparing analyzers. Finally, we present ion energy distributions from a SDA, comparing variations in particle energy, particle angle, entrance and exit geometry, and sector angle using both numerical calculation and particle simulation.

[1]  I. Powis,et al.  Parallel, multichannel energy and angle resolving electrostatic electron analyzer , 1995 .

[2]  D. Varga,et al.  A modified distorted field electrostatic analyzer , 1994 .

[3]  J. L. Powell,et al.  Electrostatic Analyzer for Selection of Homogeneous Ion Beam , 1947 .

[4]  C. Kuyatt,et al.  Electron Monochromator Design , 1967 .

[5]  D. Dubé,et al.  A generalized analytic approach for the determination of transmission functions of charged-particle energy analyzers , 1982 .

[6]  T. S. Green.  Space charge effects in plasma particle analyzers , 1970 .

[7]  M. Arnow.  Electrostatic cylindrical spectrometers , 1976 .

[8]  J. P. McFadden,et al.  Computer simulation in designing electrostatic optics for space plasma experiments , 1998 .

[9]  W. Mehlhorn,et al.  Parallel plate analyser with second order focusing property , 1972 .

[10]  P. Kruit,et al.  Resonantly enhanced multiphoton ionization of xenon: photoelectron enrgy analysis , 1980 .

[11]  H. Moestue.  The electric field and geometrical factor of an annular curved plate electrostatic analyzer , 1973 .

[12]  F. Paolini,et al.  The Angular Response of Spherical Plate Electrostatic Analyzers , 1969 .

[13]  H. Ewald,et al.  Der Astigmatismus des Toroidkondensators , 1955 .

[14]  D. Dubé,et al.  New approach to improve performances of electron spectrometers , 1981 .

[15]  G. Bosi.  Fringing Field of Electrostatic Analyzers , 1972 .

[16]  C. Kuyatt,et al.  Comparison of the Spherical Deflector and the Cylindrical Mirror Analyzers , 1968 .

[17]  J. F. Mckenzie,et al.  The solar wind ion composition spectrometer , 1992 .

[18]  M. Schulz,et al.  Energy spread and ion current measurements of several ion sources , 1994 .

[19]  W. Miyake,et al.  Transmission characteristics and fringing field effect of a 270° spherical electrostatic analyzer , 1986 .

[20]  D. Mccomas,et al.  Absolute detection efficiency of space-based ion mass spectrometers and neutral atom imagers , 2005 .

[21]  M. Yavor,et al.  Design of a versatile energy analyzer for photoelectron spectroscopy studies at synchrotron radiation sources , 2001 .

[22]  David T. Young,et al.  Diagnostics of space plasmas (invited) , 1986 .

[23]  Koh-ichiro Oyama,et al.  INACCURACIES IN ELECTRON DENSITY ESTIMATES DUE TO SURFACE CONTAMINATION OF LANGMUIR PROBES , 1976 .

[24]  Robert A. Meyers,et al.  Encyclopedia of physical science and technology , 1987 .

[25]  R. K. Haaland,et al.  Miniaturized electrostatic analyzer manufactured using photolithographic etching , 2003 .

[26]  R. Arnoldy,et al.  The Calibration of Electrostatic Analyzers and Channel Electron Multipliers Using Laboratory Simulated Omnidirectional Electron Beams , 1973 .

[27]  T. Zouros,et al.  Improving the energy resolution of a hemispherical spectrograph using a paracentric entry at a non-zero potential , 2000 .

[28]  S. N. Davydov,et al.  CONE ELECTROSTATIC ENERGY ANALYSER OF HIGH LUMINOSITY , 1998 .

[29]  C. Ruan,et al.  Optimization of spherical deflecting analyzer with finite-size effects , 1999 .

[30]  Christopher C. Davis,et al.  Building Scientific Apparatus , 1983 .

[31]  David T. Young,et al.  2π-Radian field-of-view toroidal electrostatic analyzer , 1988 .

[32]  T. L. Thomas,et al.  Effects of Contamination on Langmuir Probe Measurements in Glow Discharge Plasmas , 1970 .

[33]  J. Day,et al.  A mathematical model of the arc pioneer 6-7 plasma probe. , 1971, The Review of scientific instruments.

[34]  M. Jacka,et al.  A fast, parallel acquisition, electron energy analyzer: The hyperbolic field analyzer , 1999 .

[35]  D. Roy,et al.  Design of electron spectrometers , 1990 .

[36]  S. Höckh,et al.  A simple double-focusing electrostatic ion beam deflector. , 2010, The Review of scientific instruments.

[37]  F. R. Paolini,et al.  Charged Particle Transmission Through Spherical Plate Electrostatic Analyzers , 1967 .

[38]  A. Johnstone.  The geometric factor of a cylindrical plate electrostatic analyzer , 1972 .

[39]  M. Yavor,et al.  High-resolution energy analyzer for photoelectron diffraction studies , 2007 .

[40]  A. Mavretic,et al.  SWE, a comprehensive plasma instrument for the WIND spacecraft , 1995 .

[41]  H. Sar‐el.  Cylindrical Capacitor as an Analyzer I. Nonrelativistic Part , 1967 .

[42]  F. M. Quinn,et al.  TEARES: A toroidal energy- and angle-resolved electron spectrometer , 2004 .

[43]  K. Sevier.  Low energy electron spectrometry , 1972 .

[44]  A. D. Luisa,et al.  Design and test of a lens system for a high energy and high resolution electron spectrometer , 2005 .

[45]  J. Risley.  Magnetic Field Measurements Using an Electron Beam and an Electrostatic Analyzer , 1971 .

[46]  J. Vilppola,et al.  Optimization of hemispherical electrostatic analyzer manufacturing with respect to resolution requirements , 1993 .

[47]  F. Rogers.  On the Theory of the Electrostatic Beta‐Particle Analyzer. V , 1951 .

[48]  T. Matsuo.  Particle trajectories in a cylindrical condenser calculated in a third-order approximation , 1972 .

[49]  J. R. Shell,et al.  Optimizing the energy resolution of planar retarding potential analyzers , 1992 .

[50]  I. Katz,et al.  Fundamentals of Electric Propulsion: Ion and Hall Thrusters , 2008 .

[51]  M. J. Sablik,et al.  Computer simulation of a 360° field‐of‐view ‘‘top‐hat’’ electrostatic analyzer , 1988 .

[52]  H. Fellner-Feldegg,et al.  A new ESCA instrument with improved surface sensitivity, fast imaging properties and excellent energy resolution , 1990 .

[53]  Alec D. Gallimore,et al.  Top hat electrostatic analyzer for far-field electric propulsion plume diagnostics , 2006 .

[54]  R. Abiad,et al.  The THEMIS ESA Plasma Instrument and In-flight Calibration , 2008 .

[55]  J. Berthelier,et al.  The Thermal Ion Dynamics Experiment and Plasma Source Instrument , 1995 .

[56]  V. Formisano,et al.  The Giotto three-dimensional positive ion analyser , 1986 .

[57]  R. Compton,et al.  Apparatus for energy, angle, and mass analysis of products from alkali-molecule reactions , 1978 .

[58]  A. Ilyin.  New class of electrostatic energy analyzers with a cylindrical face-field , 2003 .

[59]  D. Young,et al.  Experimental tests of a toroidal electrostatic analyzer , 1987 .

[60]  J. H. Westbrook,et al.  Ion Beams with Applications to Ion Implantation , 1973 .

[61]  R. Imhof,et al.  Energy and time resolution of the 180 degrees hemispherical electrostatic analyser , 1976 .

[62]  Y. Jiang,et al.  The 3-D plasma distribution function analyzers with time-of-flight mass discrimination for Cluster, FAST, and Equator-S , 2013 .

[63]  H. Matsuda.  The influence of a toroidal electric fringing field on the trajectories of charged particles in a third order approximation , 1971 .

[64]  T. Zouros,et al.  Novel and traditional fringing field correction schemes for the hemispherical analyser: comparison of first-order focusing and energy resolution , 2007 .

[65]  Comparison between simulations and calibrations of a high resolution electrostatic analyzer , 2001 .

[66]  D. Kataria,et al.  On variable geometric factor systems for top-hat electrostatic space plasma analyzers , 2010 .

[67]  J. Nordholt,et al.  Plasma Experiment for Planetary Exploration (PEPE) , 2007 .

[68]  P. Marmet,et al.  AN IMPROVED ELECTROSTATIC ELECTRON SELECTOR , 1960 .

[69]  M. Gruntman.  Energetic neutral atom imaging of space plasmas , 1997 .

[70]  Cylindrical deflector focusing in two directions , 1995 .

[71]  R. Franchy,et al.  Numerical calculations of electron trajectories in the 127° analyzer using a position‐sensitive detector under conditions of fringing fields , 1983 .

[72]  K. L. Wang.  OPTIMUM TRANSPORT IN CHARGED PARTICLE ANALYSERS. , 1972 .

[73]  K. L. Man,et al.  The miniature cylindrical mirror analyzer: A new tool for surface analysis , 2001 .

[74]  W. M. Holber,et al.  Ion energetics in electron cyclotron resonance discharges , 1990 .

[75]  R. H. Ritchie,et al.  The Spherical Condenser As A High Transmission Particle Spectrometer , 1959 .

[76]  Daniel L. Brown,et al.  Remote Diagnostic Measurements of Hall Thruster Plumes , 2009 .

[77]  G. North,et al.  Study of Calibration, Resolution, and Transmission of Electrostatic Velocity Selector , 1971 .

[78]  T. S. Green,et al.  Minimum Image Size in a Parallel Plate Electrostatic Spectrograph , 1970 .

[79]  J. Risley.  Design Parameters for the Cylindrical Mirror Energy Analyzer , 1972 .

[80]  M. Gruntman,et al.  IBEX—Interstellar Boundary Explorer , 2009 .

[81]  K. Jost.  Novel design of a 'spherical' electron spectrometer , 1979 .

[82]  W. Feldman,et al.  Effects of a long entrance aperture upon the azimuthal response of spherical section electrostatic analyzers. , 1978, The Review of scientific instruments.

[83]  E. Blauth.  Zur Energieverteilung der von Protonen in Gasen ausgelösten Sekundärelektronen , 1957 .

[84]  U. Gliese,et al.  The geometric factor of electrostatic plasma analyzers: a case study from the Fast Plasma Investigation for the Magnetospheric Multiscale mission. , 2012, The Review of scientific instruments.

[85]  M. Aono,et al.  Optimum angle of deflection electrodes of a cylindrical electrostatic analyzer , 1985 .

[86]  J. Simpson,et al.  DESIGN OF RETARDING FIELD ENERGY ANALYZERS , 1961 .

[87]  J. Carette,et al.  Improvement of the Resolving Power and Transmission of Electrostatic Spectrometers , 1971 .

[88]  David T. Young,et al.  Space Plasma Particle Instrumentation and the New Paradigm: Faster, Cheaper, Better , 2013 .

[89]  G. Paschmann,et al.  An instrument for rapidly measuring plasma distribution functions with high resolution , 1982 .

[90]  H. Sar‐el.  More on the spherical condenser as an analyser I. Nonrelativistic part , 1966 .

[91]  T. S. Green,et al.  A Parallel Plate Electrostatic Spectrograph , 1970 .

[92]  K. Siegbahn,et al.  A high resolution and large transmission electron spectrometer , 1997 .

[93]  D. Hutchison.  Critical Ionization Potentials Using a Parallel‐Plate Energy Selector , 1956 .

[94]  T. Matsuo,et al.  Numerical calculation of fringing—field integrals for arbitrary electrode (magnetic pole) structures , 1982 .

[95]  H. Ibach.  Electron Spectroscopy for Surface Analysis , 1977 .

[96]  Alec D. Gallimore,et al.  Energy Analysis of a Hall Thruster Cluster , 2003 .

[98]  F. H. Read,et al.  The parallel cylindrical mirror analyzer: axis-to-axis configuration , 2004 .

[99]  Brian Eric Beal,et al.  Clustering of Hall effect thrusters for high -power electric propulsion applications. , 2004 .

[100]  Joseph E. Borovsky,et al.  Measurement techniques in space plasmas : particles , 1998 .

[101]  Allen L. Victor.  Design and utilization of a top hat analyzer for Hall thruster plume diagnostics , 2006 .

[102]  H. Matsuda.  Electrostatic Analyzer with Variable Focal Length , 1961 .

[103]  S. Nishida,et al.  Resolution improvements for hemispherical energy analyzers , 2000 .

[104]  A. M. Cravath.  Magnetic Shielding with Multiple Cylindrical Shells , 1957 .

[105]  M. E. Rudd.  Analog Plotting System for Recording Energy Spectra of Low Energy Charged Particles , 1966 .

[106]  H. Hopman,et al.  Ion energy measurement at the powered electrode in an rf discharge , 1988 .

[107]  R. Tromp,et al.  Angle resolved detection of charged particles with a novel type toroidal electrostatic analyser , 1982 .

[108]  S. Barabash,et al.  Electron optical study of the Venus Express ASPERA-4 Electron Spectrometer (ELS) top-hat electrostatic analyser , 2009 .

[109]  J. Wolfe,et al.  A new electron spectrometer design , 1972 .

[110]  G. A. Harrower.  Measurement of Electron Energies by Deflection in a Uniform Electric Field , 1955 .

[111]  Lyon B. King.  Transport-property and mass spectral measurements in the plasma exhaust plume of a Hall-effect space propulsion system , 1998 .

[112]  T. Mukai,et al.  Cusp type electrostatic analyzer for measurements of medium energy charged particles , 2006 .

[113]  Louis A. Frank,et al.  On the extraterrestrial ring current during geomagnetic storms , 1967 .

[114]  F. H. Read.  The parallel cylindrical mirror electron energy analyzer , 2002 .

[115]  H. Polaschegg.  Optimization of the parameters of the ideal 180° spherical analyzer , 1976 .

[116]  L. Frank,et al.  The plasma instrumentation for the Galileo Mission , 1992 .

[117]  Peter Hawkes,et al.  Advances in Imaging and Electron Physics , 2002 .

[118]  A. Trubitsyn.  A cylindrical mirror analyser with high energy resolution , 1995 .

[119]  R. Compton,et al.  Ionizing collisions of cesium and potassium atoms with water , 1978 .

[120]  D. Gershman,et al.  Modeling extreme ultraviolet suppression of electrostatic analyzers. , 2010, The Review of scientific instruments.

[121]  H. J. Fischbeck,et al.  Effects on focusing properties due to field fringing near the ends of the electrostatic cylindrical mirror analyzer , 1975 .

[122]  M. Yavor,et al.  Two-stage systems with intermediate beam retarding for energy and spatial analysis of photoelectrons , 1999 .

[123]  P. M. Kintner,et al.  Contamination-free sounding rocket Langmuir probe , 2001 .

[124]  F. Mariani.  An Electrostatic Analyzer with No Fringe Field for Measurements of Low Energy Particles on Space Vehicles , 1970 .

[125]  K. Leung,et al.  SIMION study of the fringing field effects in deflector‐type electrostatic electron energy analyzers: A new flexible Jost‐based correction scheme , 1995 .

[126]  J. Rouzaud,et al.  The IMPACT Solar Wind Electron Analyzer (SWEA) , 2008 .

[127]  D. Friedman,et al.  Electron trajectory analysis of the spherical-sector electrostatic spectrometer: focussing properties and multichannel detection capability , 1989 .

[128]  M. Wuest,et al.  Calibration of Particle Instruments in Space Physics , 2007 .

[129]  D. Dahl.  simion for the personal computer in reflection , 2000 .

[130]  Edgar Y. Choueiri,et al.  ELECTRIC PROPULSION. , 1888, Science.

[131]  M. Smith,et al.  Low energy plasma analyzer , 1993 .

[132]  S. Aksela.  Instrument Function of a Cylindrical Electron Energy Analyzer , 1972 .

[133]  J. Stroscio,et al.  Design and performance of a double‐pass high‐resolution electron energy loss spectrometer , 1986 .

[134]  Manuel Grande,et al.  PEACE: A PLASMA ELECTRON AND CURRENT EXPERIMENT , 1997 .

[135]  D. W. Curtis,et al.  The Electron and ion Plasma Experiment for Fast , 2001 .

[136]  T. Zouros,et al.  Optimal energy resolution of a hemispherical analyzer with virtual entry , 2005 .

[137]  M. Avalos-Borja,et al.  Crosslinking of recycled polyethylene by gamma and electron beam irradiation , 1998 .

[138]  S. Kanai,et al.  Optimization of the Herzog correction in the hemispherical deflector analyzer , 1986 .

[139]  A. Donné,et al.  An electrostatic time‐of‐flight analyzer for simultaneous energy and mass determination of neutral particles , 1991 .

[140]  Y. Hamada,et al.  MESH EFFECT IN A PARALLEL-PLATE ANALYZER , 1992 .

[141]  J. Rubio‐Zuazo,et al.  High Voltage-Cylinder Sector Analyzer 300/15: a cylindrical sector analyzer for electron kinetic energies up to 15 keV. , 2010, The Review of scientific instruments.

[142]  A. Hughes,et al.  Re-Focussing of Electron Paths in a Radial Electrostatic Field , 1929 .

[143]  F. Leblanc,et al.  Thermal ion measurements on board Interball Auroral Probe by the Hyperboloid experiment , 1998 .

[144]  T. Matsuo,et al.  The electrostatic potential in a toroidal condenser , 1972 .

[145]  E. P. Szuszczewicz,et al.  Surface contamination of active electrodes in plasmas: Distortion of conventional Langmuir probe measurements , 1975 .

[146]  Edward M. Purcell,et al.  The Focusing of Charged Particles by a Spherical Condenser , 1938 .

[147]  G. Gloeckler,et al.  The Charge-Energy-Mass Spectrometer for 0.3-300 keV/e Ions on the AMPTE CCE , 1985, IEEE Transactions on Geoscience and Remote Sensing.

[148]  B. L. Barraclough,et al.  Simulations of the response function of a plasma ion beam spectrometer for the Cassini mission to Saturn , 1996 .

[149]  H. Daimon.  New display‐type analyzer for the energy and the angular distribution of charged particles , 1988 .

[150]  C. L. Enloe,et al.  Novel bandpass electrostatic analyzer , 1997 .

[151]  I. Papamastorakis,et al.  First multispacecraft ion measurements in and near the Earth's magnetosphere with the identical Cluster ion spectrometry (CIS) experiment , 2001 .

[152]  Alec D. Gallimore,et al.  Development of a 45-Degree Parallel-Plate Electrostatic Energy Analyzer for Hall Thruster Plume Studies: Preliminary Data , 1999 .

[153]  J. Keller,et al.  Evaluation of an elliptical grid mirror electrostatic analyzer for space applications , 1997 .

[154]  W. Feldman,et al.  Observations at Venus Encounter by the Plasma Science Experiment on Mariner 10 , 1974, Science.

[155]  D. Hardy,et al.  Compact ion/electron analyzer for spaceflight or laboratory use , 1992 .

[156]  E. Möbius,et al.  High mass resolution isochronous time-of-flight spectrograph for three-dimensional space plasma measurements , 1990 .

[157]  O. Sise,et al.  Design of electron energy analyzers for electron impact studies , 2007 .

[158]  W. Newell,et al.  A coaxial cone electrostatic velocity analyser. I. Analysis of electron optical properties , 1980 .

[159]  H. Wollnik.  CHAPTER 4.1 – ELECTROSTATIC PRISMS , 1967 .

[160]  Barry H. Mauk,et al.  The Energetic Particle and Plasma Spectrometer Instrument on the MESSENGER Spacecraft , 2007 .

[161]  H. Bolton,et al.  The Electrostatic Analysis of Ionic Beams , 1949 .

[162]  J. Sojka,et al.  A high resolution, low energy electrostatic analyser for rocket payloads , 1976 .

[163]  M. Pessa,et al.  Study of the Electron Optical Properties of an Electron Spectrograph with Coaxial Cylindrical Electrodes , 1970 .

[164]  M. Neugebauer.  SCIENTIFIC EXPERIMENTS FOR RANGER A-1 AND A-2 , 1960 .

[165]  Optimisation of the 180 degrees hemispherical electrostatic deflector , 1978 .

[166]  D. M. Klumpar,et al.  The Time-of-Flight Energy, Angle, Mass Spectrograph (Teams) Experiment for Fast , 2001 .

[167]  S. Pope,et al.  The Solar Wind Around Pluto (SWAP) Instrument Aboard New Horizons , 2008 .

[168]  K. Jost.  Fringing field correction for 127 degrees and 180 degrees electron spectrometers , 1979 .

[169]  V. Rojansky,et al.  On the Analysis of Electronic Velocities by Electrostatic Means , 1929 .

[170]  W. Steckelmacher.  Energy analysers for charged particle beams , 1973 .

[171]  H. Sar‐el.  CRITERION FOR COMPARING ANALYZERS. , 1970 .

[172]  J. S. Cheka,et al.  The spherical condenser as a high transmission particle spectrometer: I. Point source , 1960 .

[173]  R. Leckey.  Recent developments in electron energy analysers , 1987 .

[174]  J. Berthelier,et al.  Optimization of toroidal electrostatic analyzers for measurements of low energy particles in space , 1975 .

[175]  J. Rouzaud,et al.  THE CLUSTER ION SPECTROMETRY (CIS) EXPERIMENT , 1997 .

[176]  D. S. Craig,et al.  Spherical Electrostatic Analyzer for Measurement of Nuclear Reaction Energies , 1951 .

[177]  L. K. Mitryukhin,et al.  High-resolution low-energy electron spectrometer , 1997, Other Conferences.

[178]  I. Rajta,et al.  Design of an electrostatic electron spectrometer for simultaneous energy and angular distribution measurements , 1995 .

[179]  R. Deserio.  Spherical sector electrostatic analyzers for measurements of energy and angular distributions , 1989 .

[180]  J. Kelly,et al.  The 127° Electrostatic Analyzer: Performance as a Spectrometer , 1973 .

[181]  G. Siscoe,et al.  Observations at Mercury Encounter by the Plasma Science Experiment on Mariner 10 , 1974, Science.

[182]  T. Mukai,et al.  Satellite borne energetic ion mass spectrometer for three‐dimensional measurement of velocity distribution , 1993 .

[183]  M. Gough.  An annular curved plate analyser with large geometrical factor and high resolution , 1970 .

[184]  L. M. Chase.  The Geometrical Factor of Large Aperture Hemispherical Electrostatic Analyzers , 1973 .

[185]  H. Sar‐el.  Cylindrical Mirror Analyzer with Surface Entrance and Exit Slots. I. Nonrelativistic Part , 1971 .

[186]  J. Rubio‐Zuazo,et al.  First principle study of the properties of a Cylindrical Sector Analyzer: Complete calculation of the electron trajectory , 2011 .

[187]  H. Liebl.  Stigmatic sector-field energy analyzer without second-order angular image aberrations , 1990 .