11.10 Confinement of positive ions and electrons with a static electric and magnetic field

Sitemap    Experiments with the simulation program: exp. 11.10a, b, c, d, 11.11, 1.12

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Experiment 11.10a

In the top side: (see screenshot)

12 positive point charges (red colour) of each 2,78E-7 coulomb
qiUD:=VoltageFourChargesUpDown*1000/(9E9)*0.025;
100 kV -> 100*1000/(9E9)*0.025 = 2,78E-7 coulomb

5 negative point charges (blue colour) of each -0,4 . 2,78E-7 = - 1,1 E-7 coulomb situated in the centre and around the centre of the top side (see screenshot).
for i:=5 to 12 do
begin
fixedcharge[i].q:= - qiUD*0.4;
end;

In the bottom side the same (see screenshot).

A point charge (blue colour) In the centre of each vertical side:
qiS:=VoltageChargesInTheSides*1000/(9E9)*0.025;
100 kV -> 100*1000/(9E9)*0.025 = 2,78E-7 coulomb

In the program dt=1.59E-9  (to see the D+ ions move) and  dt=1.59E-10  (to see the e- ions move, otherwise very fast)

Bfield: 1 tesla (constant)

30 electrons were generated
ve:=3E5 ; {m/s}
electron[i].vx:=0 + (-0.5 + random)*ve;
electron[i].vy:=0 + (-0.5 + random)*ve;
electron[i].vz:=0 + (-0.5 + random)*ve;
electron[i].q:=-qe;
electron[i].x:=0.5+ ( - 0.5 + random) /5; {so they start not in exactly the same point}
electron[i].y:=0.5+ ( - 0.5 + random) /5;
electron[i].z:=0.5+ ( - 0.5 + random) /5;

ve=3E5 m/s {=max. initial speed}
30 H+ ions were generated:
hydrogen[i].vx:=0 + (-0.5 + random)*ve;
hydrogen[i].vy:=0+( - 0.5 + random)*ve;
hydrogen[i].vz:=0 +( - 0.5 + random)*ve;
hydrogen[i].x:=0.5+ ( - 0.5 + random) /5; {so they start not in exactly the same point}
hydrogen[i].y:=0.5+ ( - 0.5 + random) /5;
hydrogen[i].z:=0.5 + ( - 0.5 + random) /10;
 

Exp 11.10 screenshot.jpg

Video exp. 11.10

Both the positive D+ ions and the electrons  stay (more or less) confined in the simulation space!


The total energy of the ions (kinetic + potential) stayed contant = 1.8  0,1E-13 J. Some variation, probably due to the change in dt (1E-9 , 1E1-10 and 1E-11). With dt=1E-9 the movement of the D+ ions can good be visualised, but the simulation is less accurate.

 

Experiment 11.10b

12 positive point charges (red colour) of each 2,78E-7 coulomb
qiUD:=VoltageFourChargesUpDown*1000/(9E9)*0.025;
100 kV -> 100*1000/(9E9)*0.025 = 2,78E-7 coulomb

5 negative point charges (blue colour) of each -0,4 . 2,78E-7 = - 1,1 E-7 coulomb situated in the centre and around the centre of the top side (see screenshot).
for i:=5 to 12 do
begin
fixedcharge[i].q:= - qiUD*0.4;
end;

In the bottom side the same (see screenshot).

A point charge (blue colour) In the centre of each vertical side:
qiS:=VoltageChargesInTheSides*1000/(9E9)*0.025;
-100 kV -> 100*1000/(9E9)*0.025 = 2,78E-7 coulomb

In the program dt=1E-9  (to see the D+ ions move) and  dt=1E-10  (to see the e- ions move, otherwise very fast)

Bfield: 1 tesla (constant)

30 electrons were generated
ve:=3E5 ; {m/s}
electron[i].vx:=0 + (-0.5 + random)*ve;
electron[i].vy:=0 + (-0.5 + random)*ve;
electron[i].vz:=0 + (-0.5 + random)*ve;
electron[i].q:=-qe;
electron[i].x:=0.5+ ( - 0.5 + random) /5; {so they start not in exactly the same point}
electron[i].y:=0.5+ ( - 0.5 + random) /5;
electron[i].z:=0.5+ ( - 0.5 + random) /5;

ve=3E6 m/s {=max. initial speed}
30 H+ ions were generated:
hydrogen[i].vx:=0 + (-0.5 + random)*ve;
hydrogen[i].vy:=0+( - 0.5 + random)*ve;
hydrogen[i].vz:=0 +( - 0.5 + random)*ve;
hydrogen[i].x:=0.5+ ( - 0.5 + random) /5; {so they start not in exactly the same point}
hydrogen[i].y:=0.5+ ( - 0.5 + random) /5;
hydrogen[i].z:=0.5 + ( - 0.5 + random) /10;

Exp 11.10b  distribution of the negative charge in the surrounding sphere

Exp 11.10b  distribution of the negative charge in the surrounding sphere cross section

Exp 11.10b  screenshot

Etotal(particles) =  3,2 0,2 E-13 (with dt=1E-9, is relative large, not accurate, but to see the D+ move)

No electrons escaped (stayed confined), about 3 D+ ions escaped. The electrons oscillated between the upper negative charge and the centre of the cube, and between the down negative charge and the centre of the cube.
They do not cross the centre of the cube.

 

Experiment 11.10c

12 positive point charges (red colour) of each 2,78E-7 coulomb
qiUD:=VoltageFourChargesUpDown*1000/(9E9)*0.025;
100 kV -> 100*1000/(9E9)*0.025 = 2,78E-7 coulomb

5 negative point charges (blue colour) of each -0,4 . 2,78E-7 = - 1,1 E-7 coulomb situated in the centre and around the centre of the top side , but 20 cm above the positive point charges in the top side (see screenshot).
for i:=5 to 12 do
begin
fixedcharge[i].q:= - qiUD*0.4;
end;

In the bottom side the same ( here the negative point charges are situated 20 cm below the positive point charges, see screenshot)

A point charge (blue colour) In the centre of each vertical side:
qiS:=VoltageChargesInTheSides*1000/(9E9)*0.025;
-100 kV -> 100*1000/(9E9)*0.025 = 2,78E-7 coulomb

In the program dt=1E-9  (to see the D+ ions move) and  dt=1E-10  (to see the e- ions move, otherwise very fast)

Bfield: 1 tesla (constant)

30 electrons were generated
ve:=3E5 ; {m/s}
electron[i].vx:=0 + (-0.5 + random)*ve;
electron[i].vy:=0 + (-0.5 + random)*ve;
electron[i].vz:=0 + (-0.5 + random)*ve;
electron[i].q:=-qe;
electron[i].x:=0.5+ ( - 0.5 + random) /5; {so they start not in exactly the same point}
electron[i].y:=0.5+ ( - 0.5 + random) /5;
electron[i].z:=0.5+ ( - 0.5 + random) /5;

ve=3E6 m/s {=max. initial speed} (speed necessary to fuse is about 2E6 m/s)
30 H+ ions were generated:
hydrogen[i].vx:=0 + (-0.5 + random)*ve;
hydrogen[i].vy:=0+( - 0.5 + random)*ve;
hydrogen[i].vz:=0 +( - 0.5 + random)*ve;
hydrogen[i].x:=0.5+ ( - 0.5 + random) /5; {so they start not in exactly the same point}
hydrogen[i].y:=0.5+ ( - 0.5 + random) /5;
hydrogen[i].z:=0.5 + ( - 0.5 + random) /10;

Exp 11.10c  screenshot

Video

Etotal(particles) =  1,1602  0,00005 E-13 (with dt=1E-10)

One D+ ion escaped. No electron escaped.

 

Experiment 11.10d

The same as 11.10c, but both the D+ ions  and electrons got an initial random speed < 3E6 m/s.

All ions and electrons stayed confined!
 

We increased the amount of e- to 100, and the amount of D+ also to 100. With dt=1E-10 s, also no ions or electrons escaped.

 

Experiment 11.11

B= 1 tesla (vertical)

dt variable (1E-9, 1E-10, 1E-11)

No surrounding conducting sphere
Voltage + 160 kV & - 160 kV
100 D+ ions & 100 e-

ve:=3E6;
hydrogen[i].vx:=0 + (-0.5 + random)*ve; {is deuterium D ion}
hydrogen[i].vy:=0+( - 0.5 + random)*ve;
hydrogen[i].vz:=0 +( - 0.5 + random)*ve;
hydrogen[i].x:=0.5+ ( - 0.5 + random) /4; {so they start not in exactly the same point}
hydrogen[i].y:=0.5+ ( - 0.5 + random) /4;
hydrogen[i].z:=0.5 + ( - 0.5 + random) /4;
ve:=3E6;
electron[i].vx:=0 + (-0.5 + random)*ve;
electron[i].vy:=0 + (-0.5 + random)*ve;
electron[i].vz:=0 + (-0.5 + random)*ve;
electron[i].q:=-qe;
electron[i].x:=0.5+ ( - 0.5 + random) /4;
electron[i].y:=0.5+ ( - 0.5 + random) /4;
electron[i].z:=0.5+ ( - 0.5 + random) /4;

Screenshot

All D+ ions and electrons stayed confined.

With +150 kV & - 150 kV & B=1 tesla one D+ ion escaped.
With +140 kV & - 140 kV & B=1 tesla one D+ ion escaped.

With +150 kV & - 140 kV & B=1 tesla one D+ ion escaped.
With +140 kV & - 150 kV & B=1 tesla one D+ ion escaped.

With +150 kV & - 150 kV & B=0,4 tesla all D+ ions and electrons stayed confined.
 

 

Experiment 11.12a

B= 1 tesla (vertical)

dt = 1E-11 s

No surrounding conducting sphere
Voltage + 150 kV & - 150 kV
100 D+ ions & 100 e-

ve:=3E6;
hydrogen[i].vx:=0 + (-0.5 + random)*ve; {is deuterium D ion}
hydrogen[i].vy:=0+( - 0.5 + random)*ve;
hydrogen[i].vz:=0 +( - 0.5 + random)*ve;
hydrogen[i].x:=0.5+ ( - 0.5 + random) /4; {so they start not in exactly the same point}
hydrogen[i].y:=0.5+ ( - 0.5 + random) /4;
hydrogen[i].z:=0.5 + ( - 0.5 + random) /4;
ve:=3E6;
electron[i].vx:=0 + (-0.5 + random)*ve;
electron[i].vy:=0 + (-0.5 + random)*ve;
electron[i].vz:=0 + (-0.5 + random)*ve;
electron[i].q:=-qe;
electron[i].x:=0.5+ ( - 0.5 + random) /4;
electron[i].y:=0.5+ ( - 0.5 + random) /4;
electron[i].z:=0.5+ ( - 0.5 + random) /4;

After 5,5 E-5 s:  Screenshot (simulation running about 48 hours)

All D+ ions and electrons stayed confined.

 

Experiment 11.12b

B= 1 tesla (vertical)

dt = 1E-11 s

No surrounding conducting sphere
Voltage + 180 kV & - 180 kV
100 D+ ions & 100 e-

ve:=3E6;
hydrogen[i].vx:=0 + (-0.5 + random)*ve; {is deuterium D ion}
hydrogen[i].vy:=0+( - 0.5 + random)*ve;
hydrogen[i].vz:=0 +( - 0.5 + random)*ve;
hydrogen[i].x:=0.5+ ( - 0.5 + random) /4; {so they start not in exactly the same point}
hydrogen[i].y:=0.5+ ( - 0.5 + random) /4;
hydrogen[i].z:=0.5 + ( - 0.5 + random) /4;
ve:=3E6;
electron[i].vx:=0 + (-0.5 + random)*ve;
electron[i].vy:=0 + (-0.5 + random)*ve;
electron[i].vz:=0 + (-0.5 + random)*ve;
electron[i].q:=-qe;
hydrogen[i].x:=0.5+ ( - 0.5 + random) /15;   {< 3,33 cm  from the central vertical axis}
hydrogen[i].y:=0.5+ ( - 0.5 + random) /15;
electron[i].x:=0.5+ ( - 0.5 + random) /4;
electron[i].y:=0.5+ ( - 0.5 + random) /4;
electron[i].z:=0.5+ ( - 0.5 + random) /4;

With 180 kV the  D+ ions stayed confined. random speed particles < 1,5E6 m/s
With  less kV one or a few D+ ions escaped upwards/downwards

If random speed particles < 3E6 m/s , then we must increase the voltage to 1000 kV to confine the D+ ions

If random speed particles < 2E6 m/s , then we must increase the voltage to 300 kV to confine the D+ ions

random speed<3E6 m/s
I moved all positive point charges 10 cm to the centre line (x -10, y-10). With  200 kV the D+ ions stayed confined.
Moved all positive point charges 20 cm to the centre line (x-20, y-20).
 

 

Experiment 11.13

B= 1 tesla (vertical)

dt = 1E-11 s

No surrounding conducting sphere
Voltage + 180 kV & - 180 kV
100 D+ ions & 100 e-

ve:=3E6;
hydrogen[i].vx:=0 + (-0.5 + random)*ve; {is deuterium D ion}
hydrogen[i].vy:=0+( - 0.5 + random)*ve;
hydrogen[i].vz:=0 +( - 0.5 + random)*ve;
hydrogen[i].x:=0.5+ ( - 0.5 + random) /4; {so they start not in exactly the same point}
hydrogen[i].y:=0.5+ ( - 0.5 + random) /4;
hydrogen[i].z:=0.5 + ( - 0.5 + random) /4;
ve:=3E6;
electron[i].vx:=0 + (-0.5 + random)*ve;
electron[i].vy:=0 + (-0.5 + random)*ve;
electron[i].vz:=0 + (-0.5 + random)*ve;
electron[i].q:=-qe;
hydrogen[i].x:=0.5+ ( - 0.5 + random) /15;   {< 3,33 cm  from the central vertical axis}
hydrogen[i].y:=0.5+ ( - 0.5 + random) /15;
electron[i].x:=0.5+ ( - 0.5 + random) /4;
electron[i].y:=0.5+ ( - 0.5 + random) /4;
electron[i].z:=0.5+ ( - 0.5 + random) /4;

Moved all positive and negative charges in the up side 20 cm down and the charges in the under side 20 cm up.
Moved the side charges 20 cm to the centre line.
The vacuum chamber is now about 0,6x 0,6x 1 m.

for i:=1 to 4 do {ri}
begin
fixedcharge[i].q:=qiS;
end;
for i:=5 to 12 do
begin
fixedcharge[i].q:=-qiUD*0.4;  {the negative point charges up and down}
end;
for i:=13 to 36 do
begin
fixedcharge[i].q:=+qiUD;
end;
fixedcharge[37].q:=-qiUD*0.4; {the negative point charges up and down in the centre}
fixedcharge[38].q:=-qiUD*0.4;

With  160 kV the D+ ions and the electrons stayed confined.

Exp 11.13 screenshot

The same experiment, but with B=1,5 tesla.
fixedcharge[37].q:=-qiUD*0.8; (was before *0.4)
fixedcharge[38].q:=-qiUD*0.8;
Only one negative point charge up and down (the others had been removed).
After 4,01E-5 s (about 48 hrs simulation time), dt=1E-11s, a few electrons had escaped.

 

 

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