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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.

problem xy No. 6 - Dual-anode magnetron 'with smile' (mesh 401 x 401) - electrode points on numerical mesh

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

problem xy No. 6 - Dual-anode magnetron 'with smile' (mesh 401 x 401) - equipotential lines

Mapping of electrostatic potential [V] to colours

Colormap: grayscale

problem xy No. 6 - Dual-anode magnetron 'with smile' (mesh 401 x 401) - distribution of electrostatic potential V(x,y), grayscale colormap

Colormap: grayscale inverted

problem xy No. 6 - Dual-anode magnetron 'with smile' (mesh 401 x 401) - distribution of electrostatic potential V(x,y), inverted grayscale colormap

Colormap: hot-to-cold

problem xy No. 6 - Dual-anode magnetron 'with smile' (mesh 401 x 401) - distribution of electrostatic potential V(x,y), hot-to-cold colormap

Colormap: hot-to-cold inverted

problem xy No. 6 - Dual-anode magnetron 'with smile' (mesh 401 x 401) - distribution of electrostatic potential V(x,y), inverted hot-to-cold colormap

Colormap: jet

problem xy No. 6 - Dual-anode magnetron 'with smile' (mesh 401 x 401) - distribution of electrostatic potential V(x,y), jet colormap

Colormap: jet inverted

problem xy No. 6 - Dual-anode magnetron 'with smile' (mesh 401 x 401) - distribution of electrostatic potential V(x,y), inverted jet colormap

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

problem xy No. 6 - Dual-anode magnetron 'with smile' (mesh 401 x 401) - distribution of x component of electric force E_x(x,y), grayscale colormap

Colormap: grayscale inverted

problem xy No. 6 - Dual-anode magnetron 'with smile' (mesh 401 x 401) - distribution of x component of electric force E_x(x,y), inverted grayscale colormap

Colormap: hot-to-cold

problem xy No. 6 - Dual-anode magnetron 'with smile' (mesh 401 x 401) - distribution of x component of electric force E_x(x,y), hot-to-cold colormap

Colormap: hot-to-cold inverted

problem xy No. 6 - Dual-anode magnetron 'with smile' (mesh 401 x 401) - distribution of x component of electric force E_x(x,y), inverted hot-to-cold colormap

Colormap: jet

problem xy No. 6 - Dual-anode magnetron 'with smile' (mesh 401 x 401) - distribution of x component of electric force E_x(x,y), jet colormap

Colormap: jet inverted

problem xy No. 6 - Dual-anode magnetron 'with smile' (mesh 401 x 401) - distribution of x component of electric force E_x(x,y), inverted jet colormap

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

problem xy No. 6 - Dual-anode magnetron 'with smile' (mesh 401 x 401) - distribution of y component of electric force E_y(x,y), grayscale colormap

Colormap: grayscale inverted

problem xy No. 6 - Dual-anode magnetron 'with smile' (mesh 401 x 401) - distribution of y component of electric force E_y(x,y), inverted grayscale colormap

Colormap: hot-to-cold

problem xy No. 6 - Dual-anode magnetron 'with smile' (mesh 401 x 401) - distribution of y component of electric force E_y(x,y), hot-to-cold colormap

Colormap: hot-to-cold inverted

problem xy No. 6 - Dual-anode magnetron 'with smile' (mesh 401 x 401) - distribution of y component of electric force E_y(x,y), inverted hot-to-cold colormap

Colormap: jet

problem xy No. 6 - Dual-anode magnetron 'with smile' (mesh 401 x 401) - distribution of y component of electric force E_y(x,y), jet colormap

Colormap: jet inverted

problem xy No. 6 - Dual-anode magnetron 'with smile' (mesh 401 x 401) - distribution of y component of electric force E_y(x,y), inverted jet colormap

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

problem xy No. 6 - Dual-anode magnetron 'with smile' (mesh 401 x 401) - distribution of electric force E_1(x,y), grayscale colormap

Colormap: grayscale inverted

problem xy No. 6 - Dual-anode magnetron 'with smile' (mesh 401 x 401) - distribution of electric force E_1(x,y), inverted grayscale colormap

Colormap: hot-to-cold

problem xy No. 6 - Dual-anode magnetron 'with smile' (mesh 401 x 401) - distribution of electric force E_1(x,y), hot-to-cold colormap

Colormap: hot-to-cold inverted

problem xy No. 6 - Dual-anode magnetron 'with smile' (mesh 401 x 401) - distribution of electric force E_1(x,y), inverted hot-to-cold colormap

Colormap: jet

problem xy No. 6 - Dual-anode magnetron 'with smile' (mesh 401 x 401) - distribution of electric force E_1(x,y), jet colormap

Colormap: jet inverted

problem xy No. 6 - Dual-anode magnetron 'with smile' (mesh 401 x 401) - distribution of electric force E_1(x,y), inverted jet colormap

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

problem xy No. 6 - Dual-anode magnetron 'with smile' (mesh 401 x 401) - distribution of square of electric force E_2(x,y), grayscale colormap

Colormap: grayscale inverted

problem xy No. 6 - Dual-anode magnetron 'with smile' (mesh 401 x 401) - distribution of square of electric force E_2(x,y), inverted grayscale colormap

Colormap: hot-to-cold

problem xy No. 6 - Dual-anode magnetron 'with smile' (mesh 401 x 401) - distribution of square of electric force E_2(x,y), hot-to-cold colormap

Colormap: hot-to-cold inverted

problem xy No. 6 - Dual-anode magnetron 'with smile' (mesh 401 x 401) - distribution of square of electric force E_2(x,y), inverted hot-to-cold colormap

Colormap: jet

problem xy No. 6 - Dual-anode magnetron 'with smile' (mesh 401 x 401) - distribution of square of electric force E_2(x,y), jet colormap

Colormap: jet inverted

problem xy No. 6 - Dual-anode magnetron 'with smile' (mesh 401 x 401) - distribution of square of electric force E_2(x,y), inverted jet colormap

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