DEMO_XY / gallery 6: Dual-anode magnetron "with smile". Mesh size: 401 x 401 nodes.

Running program

Windows:
DEMO_XY.exe 6

Linux:
./DEMO_XY.run 6

Problem definition

Problem drafted in book: Bohdan Paszkowski pt. "Optyka Elektronowa", wydanie II poprawione i uzupełnione, Wydawnictwa Naukowo - Techniczne, Warszawa 1965 (page 62). English edition of this book also exists (Bohdan Paszkowki, "Electron Optics", Iliffe Books Ltd. 1968) (page 51). Values of electrode potentials are different, that's why this "smile" appears.

Numeric meshes

Each pixel represents one mesh point.

colour white - vacuum
colour red   - electrode 1 (U = -1.0 [V])
colour green - electrode 2 (U = +1.0 [V])
colour blue  - electrode 3 (U = +0.5 [V])

Visualization of mesh on picture.

Model parameters

mesh size:

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

x ==  -200.0 ... +200.0 [mm]
y ==  -200.0 ... +200.0 [mm]

number of iterations

>>> SUCCESS - solution V(x,y) has been found
after 74932 iterations

electrode 1
boundary ==  +1
voltage  ==  -1.0   [V]
x_center ==  +0.0   [mm]
y_center ==  +0.0   [mm]
radius   <=  +200.0 [mm]
y        <   +0.0   [mm]

electrode 2
boundary ==  +2
voltage  ==  +1.0   [V]
x_center ==  +0.0   [mm]
y_center ==  +0.0   [mm]
radius   <=  +200.0 [mm]
y        >   +0.0   [mm]

electrode 3
boundary ==  +3
voltage  ==  +0.5   [V]
x_center ==  +0.0   [mm]
y_center ==  +0.0   [mm]
radius   <   +20.0  [mm]

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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