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DEMO_XY / gallery 8: Slit diaphragm. Problem tries to follow issue: Bohdan Paszkowski, "Optyka elektronowa", page 62 (page 51 in English edition)). Mesh size: 401 x 401 nodes.


Running program

Windows:
DEMO_XY.exe 8

Linux:
./DEMO_XY.run 8

Problem definition.

Numeric meshes

Each pixel of picture represents one mesh node.

white colour - vacuum
red   colour - left electrode  (U = -1.0 [V])
green colour - right electrode (U = +1.0 [V])
blue  colour - diaphragm       (U = +0.0 [V])

Visualization of mesh on picture.

Model parameters

rozmiar siatki numerycznej:

number of rows    ==  401
number of columns ==  401

x_min ==  -200.0 [mm]
x_max ==  +200.0 [mm]
y_min ==  -200.0 [mm]
y_max ==  +200.0 [mm]

mesh step:
h ==  1.0 [mm]

number of iterations

>>> SUCCESS - solution V(x,y) has been found
after 67781 iterations

electrode 1 (red) consists of 3 rectangles: A1, A2, A3
line thickness: ==  9 mesh steps
boundary        ==  +1
voltage         ==  -1.0 [V]

A1
i_row ==  1  .. 401
i_col ==  1  ..  10

A2
i_row ==  1  ..  10
i_col ==  11 .. 190

A3
i_row ==  392 .. 401
i_col ==  11  .. 190


electrode 2 (right) consists of 3 rectangles: B1, B2, B3
line thickness ==  9 mesh steps
boundary       ==  +2
voltage        ==  +1.0 [V]

B1
i_row ==  1   .. 401
i_col ==  392 .. 401

B2
i_row ==  212 .. 391
i_col ==  1   ..  10

B3
i_row ==  212 .. 391
i_col ==  391 .. 401

electrode 3 (blue) consists of 2 rectangles: C1, C2
line thickness ==  20 mesh steps
boundary       ==  +3
voltage        ==  +0.0 [V]


C1
i_row ==  191 .. 211
i_col ==  1   .. 151

C2
i_row ==  191 .. 211
i_col ==  251 .. 401

computation accuracy:
eps ==  1.0E-9 [V]


Computation results


Equipotential lines


Mapping of electrostatic potential [V] to colours

Colormap: grayscale

Colormap: grayscale inverted

Colormap: hot-to-cold

Colormap: hot-to-cold inverted

Colormap: jet

Colormap: jet inverted


Mapping of component x of electric force (E_x) [V/mm] to colours

Important: determinig of exact values of E near electrode surface is generally problematic. These maps have generally illustrative character.

Colormap: grayscale

Colormap: grayscale inverted

Colormap: hot-to-cold

Colormap: hot-to-cold inverted

Colormap: jet

Colormap: jet inverted


Mapping of component y of electric force (E_y) [V/mm] to colours

Important: determinig of exact values of E near electrode surface is generally problematic. These maps have generally illustrative character.

Colormap: grayscale

Colormap: grayscale inverted

Colormap: hot-to-cold

Colormap: hot-to-cold inverted

Colormap: jet

Colormap: jet inverted


Mapping of electric force (E) [V/mm] to colours

algorihm of computation:
E = sqrt(E_x*E_x + E_y*E_y)

Important: determinig of exact values of E near electrode surface is generally problematic. These maps have generally illustrative character.

Colormap: grayscale

Colormap: grayscale inverted

Colormap: hot-to-cold

Colormap: hot-to-cold inverted

Colormap: jet

Colormap: jet inverted


Mapping of square of electric force (E*E == E2) [V2/mm2] to colours

algorithm of computation:
E*E = E_x*E_x + E_y*E_y

Important: determinig of exact values of E near electrode surface is generally problematic. These maps have generally illustrative character.

Colormap: grayscale

Colormap: grayscale inverted

Colormap: hot-to-cold

Colormap: hot-to-cold inverted

Colormap: jet

Colormap: jet inverted


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