DEMO_XY / gallery 3: Plane vacuum diode with two lateral plates at the cathode potential. Mesh size: 201 x 201 nodes.

Running program

Windows:
DEMO_XY.exe 3

Linux:
./DEMO_XY.run 3

Problem definition

Problem described in book: Bohdan Paszkowski pt. "Optyka Elektronowa", wydanie II poprawione i uzupełnione, Wydawnictwa Naukowo - Techniczne, Warszawa 1965 (page 66). English edition of this book also exists (Bohdan Paszkowki, "Electron Optics", Iliffe Books Ltd. 1968) (page 56).

Numeric meshes

Each pixel represents one mesh point.

white colour - vacuum 
red   colour - electrode 1 (cathode, U = -1.0 [V])
green colour - electrode 2 (anode,   U = +1.0 [V])

Visualization of mesh on picture.

Model parameters

mesh size:

number of rows     ==  201
number of columns  ==  201

number of iterations

>>> SUCCESS - solution V(x,y) has been found
after 41553 iterations

electrode 1 (composed of parts A, B and C)
boundary ==  +1
voltage  ==  -1.0 [V]

A
i_col ==  1 .. 10
i_row ==  1 .. 201

B
i_col ==  11  .. 191
i_row ==  192 .. 201

C
i_col ==  11 .. 191
i_row ==  1  .. 10

electrode 2
boundary ==  +2
voltage  ==  +1.0 [V]
i_col    ==  192 .. 201
i_row    ==  1   .. 201

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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