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Electrostatic deflector
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Electrostatic deflector
Project details
Geometry and potential
Field accuracy
Axial field function
Optical properties
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Electrostatic deflector

Electrostatic deflector

Project details

  • different harmonic components computed from distribution of electrode potentials, from which the excitation of deflector is evaluated.
  • There are eight electrodes, axis x goes through the electrode, 0.2 deg gaps, voltages 1 and 0.70111 and 0 in the first quadrant
Deflector electrodes

Geometry and potential

Geometry and scalar potential


Field accuracy

To estimate the accuracy of computation, the same coarse mesh was used, but q=1.025, and 10 and 20 points of fine mesh under the deflector. The comparison follows from the plot file below.

Deflection field accuracy

Axial field function

Test of the shape of deflection field for higher multipole components. For this the excitation was given numerically as 10m, where m is the multipole component (10 is the radius of the deflector). The result is shown on the next plot.

Axial field for different multipole components m


Optical properties

Finally, we estimate the optical properties of the deflector. Because there is no lens in the project, we can either do ray tracing, or we can calculate the optical properties as deflection slope and aberration coefficients.

Deflected trajectory

Deflected trajectory


Trace file: D:\TU-EOD1\testuj\edefl\aberrations.EODtrc
Integration method Runge-Kutta Fehlberg 4-5 order
Max. step size  =   0.10000000     mm
Axial fields interpolation: cubic spline
Relativistic correction: off
Particle electron, charge -1e
 Aberrations calculation results
 Fields used for tracing
 1 .\dem1emd-20-1357.EODinp
   Electrostatic deflector - field
      main deflector
      Field is symmetrical
     Interpolation Cubic spline
     Field zmin (original) -60.000000000 mm
     Field zmax (original) 60.0000000000 mm
     Field magnitude       1.00000000000
     Field z shift         0.00000000000 mm
     Field rotation        0.00000000000 deg
        # of points         126
        Field maximum        0.99962 V/mm^0
        Maximum z [mm]       0.00000
        Field width [mm]    50.51249

Particle properties:
Object position zo=        -6.0000000E+01 mm
Energy=                     1.0000000E+04 eV
U=                          1.0000000E+04 eV
Delta Energy=               1.0000000E+00 eV
Aber. for aperture=         5.0000000E-03 rad
Aber. for obj. height=      1.0000000E-03 mm
Deflection X=               1.0000000E+00 mm
           Y=               1.0000000E+00 mm

Image #                           0 (asymptotic), image #  1 not found!
Image position zi=         -6.0000000E+01 mm

Beam rotation=              0.0000000E+00 rad
                            0.0000000E+00 deg
Image magnification=        1.0000000E+00 times

Aberration coefficients related to image

-------------- Main deflection -----------------
Deflection x=               1.6023159E-01 mm
           y=               0.0000000E+00 mm
       total=               1.6023159E-01 mm
Angle=                      0.0000000E+00 rad
Angle=                      0.0000000E+00 deg
Slope x'=                  -2.6705265E-03
      y'=                   0.0000000E+00 mm

Main deflection aberration coefficients
Aberration coefficient                                   | Error in micrometers
 coma length:             5.0000E-01,  0.0000E+00        |   1.8750E-02,  6.2500E-03 um
 field curvature:         6.4269E-03              1/mm   |   6.4269E-02              um
 astigmatism:             3.8057E-03,  0.0000E+00 1/mm   |   0.0000E+00,  3.8057E-02 um
 distortion:              4.6756E-05,  0.0000E+00 1/mm^2 |   9.3511E-02,  9.3511E-02 um
 chromatic:              -1.0000E+00,  0.0000E+00        |  -1.0000E-01, -1.0000E-01 um
 landing error:          -1.6667E-02,  0.0000E+00 rad/mm |  -9.5493E-01, -9.5493E-01 deg
 ----- Total aberration (geom. and. chrom)                   2.0847E-01 um

Mixed aberration coefficients for finite object
 kappa   F=   0.0000E+00,  0.0000E+00   A=  -8.3333E-03,  0.0000E+00 1/mm
 dist.   D1=  0.0000E+00,  0.0000E+00   D2=  0.0000E+00,  0.0000E+00 1/mm^2
         D3=  3.2531E-04,  0.0000E+00   D4=  1.9190E-04,  0.0000E+00 1/mm^2