DEMO_XY / gallery 20: Electrostatic quadrupole with "plate - shaped electrodes". Mesh size: 401 x 401 nodes.

Running program

Windows:
DEMO_XY.exe 20

Linux:
./DEMO_XY.run 20

Problem definition

Problem drafted in books about electron optics (multiple symmetry lenses). For example: Szymański, Mulak, Duda, Romanowski, "Optyka elektronowa" wydanie 2, Wydawnictwa Naukowo Techniczne, Warszawa 1984. Szymański's book mentioned about "non-standard" shape of electrodes.

Numeric meshes

Each pixel represents one mesh point.

colour white - vacuum
colour red   - casing     1 (U = +0.0 [V])
colour green - electrodes 2 (U = +1.0 [V])
colour blue  - electrodes 3 (U = -1.0 [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 21192 iterations


electrode type 1 (casing, red)
boundary ==  +1
voltage  ==  +0.0   [V]
x_center ==  +0.0   [mm]
y_center ==  +0.0   [mm]
radius   >=  +190.0 [mm]

electrodes type 2 (2 elements, green)
boundary ==  +2
voltage  ==  +1.0  [V]
1/2
	x == +100.0 ... +110.0 [mm]
	y ==  -30.0 ...  +30.0 [mm]
2/2
	x == -110.0 ... -100.0 [mm]
	y ==  -30.0 ...  +30.0 [mm]

electrodes type 3 (2 elements, blue)
boundary ==  +3
voltage  ==  -1.0  [V]
1/2
	x == -30.0  ... +30.0 [mm]
	y == +100.0 ... +110.0 [mm]
2/2
	x == -30.0  ... +30.0 [mm]
	y == -110.0 ... -100.0 [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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