Sem Fusor with two rings

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

Experiments with the simulation program: simplified SEM fusor design with only 2 rings

Fig.1. Exp. 15.1

Only two negatively charged rings and a magnetic field of 0,3 T.

Cross section with the electric field displayed: arrow is direction, color is strenght (the redder, the stronger).

Fig.2. Exp. 15.1

The magnetic field is relatively weak. The particles stay more or less confined. The maximum vertical speed of the D+ ions is about 2,2 E6 m/s (I checked this in the simulation). This is about the speed necessary for fusion.
Because in the simulation there are so few particles, no colisions take place. In reality there would be collisions and some particles also will obtain high speeds in the lateral direction. To stop them from escaping the magnetic field should be stronger, perhaps.

This configuration with only two rings is quite simpler, but the one with three rings and two spheres does confine the particles better.

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Fig.3. Exp. 15.2

Less voltage, a little more magnetic field.

The D+ ions are injected a little below the lower ring, the electrons are injected a little above the lower ring,
more or less vertically.

chcc:=1;
electron[i].m:=chcc*me; {3E20 is the amount of D+ in the vacuum chamber if p=3E-2 torr};
electron[i].vx:=0 + (-0.5 + random)*ve/1000;
electron[i].vy:=0 + (-0.5 + random)*ve/1000;
electron[i].vz:=0 + (-0.5 + random)*ve/1000+vie;
electron[i].q:=chcc*-qe{*3E8}; {3E20 is the amount of D+ in the vacuum chamber if p=3E-2 torr}
electron[i].x:=0.50+ ( - 0.5 + random) /100; {so they start not in exactly the same point};
electron[i].y:=0.50+ ( - 0.5 + random) /100; {so they start not in exactly the same point};
electron[i].z:= 0.5-dr+r2r+0.06; //0.35+ ( - 0.5 + random) /100; {so they start not in exactly the same point};

When the D+ ions are more or less cross the centre region, their vertical speeds are a little bit larger than their initial speeds (about 5,5E+5).

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Fig.4. Exp. 15.3

The speed of the electrons is slowly reduced in the simulation (to simulate Bremsstrahlung).

if DecreaseSpeedElectrons=true then
begin
if t=1 then {if electron}
begin
vx:=vx*0.90; vy:=vy*0.90; vz:=vz*0.90;
end;
end;

It is curious that the speed of the electrons in the vertical direction (z) is a lot more reduced that the speed in the
horizontal direction (x, y). They were generated with small random speeds in the x-y direction.

Fig.5. Exp. 15.3

The same experiment, but a little later in time. The electrons have spread out a little more in the x-y plane.

Fig.6. Exp. 15.3

The same experiment, again a little later in time. The electrons are even more spread out in the
x-y plane. But why? They still have a speed vx and vy, so the magnetic field should impede them to
move outwards..

B = m.v / ( r . q)

With a horizontal speed of 3.10^{3 m/s}-> r = m.v / (B .q) = 9.10 ×10⁻³¹ . 3.10³ / (0,5 . 1.6021×10⁻¹⁹ ) = 3,38 .10⁻⁸ m

Fig.6. Exp. 15.3

The same experiment, again a little later in time. The electrons have even more spread out in the
x-y plane and some have escaped. They seem to escape when they are at a certain distance from the
centre vertical axis.

Exp. 15.3 fig. 7 screenshot.png (part of the screen is made grey, to see the field lines better)

When the electrons escape: as seen in the screenshot, at some distance from the vertical centre axis, the
electric field lines become horizontal. At a sufficient large distance from the vertical centre axis, the two
charged rings can also be considered as a point charge in the centre, and in this way you can understand why they
are repelled upwards or downwards. Sidewards they do not go, because of the vertical magnetic field.

Fig. 8. Exp. 15.4

The speeds of the electrons is reduced, but only as long no one of the vx, vy and vz components are not smaller
than 1E3 m/s:

if (vx>1E3) and (vy>1E3) and (vz>1E3)
then
Begin
vx:=vx*0.90; vy:=vy*0.90; vz:=vz*0.90;
end;

It seems to be that at least one of the speeds vx, vy or vz < 1E3, so the speeds are not further decreased by the program.

But why in 15.4 the electrons do now not spread out, and in experiment 15.3 yes they do?

And why the vz component of the speed of the electrons in experiment 15.3 becomes very small (almost zero), and in experiment 15.2 (without Bremsstrahlung) not ?

When we keep reducing the speeds in the program, the vz component becomes almost zero, but the vx and vy components keep some small value (about 1E2, 1E3 m/s):
Why is this so?

Fig. 9. Exp. 15.5

if DecreaseSpeedElectrons=true then
begin
if t=1 then
begin
if (vx>1E2) and (vy>1E2) and (vz>1E2)
then
Begin
vx:=vx*0.90; vy:=vy*0.90; vz:=vz*0.90;
end;
end;
end;

The electrons keep well confined in the centre area. But there are only few (not 10²⁰).

Again the speed component vz is a lot more reduced than the components vx and vy.

I tried out:

if (vx>1E2) and (vy>1E2) and (vz>1E2)
then
Begin
vx:=vx*0.90; vy:=vy*0.90; {without vz decreasing}
end;

and the component vz did not change. So the vz is reduced by the program, and not because vx and vy are reduced.

Fig. 10. Exp. 15.6

The mass and the charge of the electrons is multiplied with 10⁸in the above experiment.
The particles do interact amongst each other.

The speed of the electrons is decreased:

Begin
vx:=vx*0.90; vy:=vy*0.90; vz:=vz*0.90;
end;

Fig. 10. Exp. 15.6 screenshot1.png
Fig. 10. Exp. 15.6 screenshot2.png
Fig. 10. Exp. 15.6 screenshot3.png

The electrons escape.

Fig. 11

Charging the middle ring with a negative charge, will not stop the electrons from escaping, see the image above
(part of the cross section has been enlarged). The charge and mass of the electrons are the same as in 15.5 (augmented with 10⁸).
The electrons escape.

Fig.12 Exp. 15.7.

Fig. 12. Exp. 15.7 screenshot1.png
Fig. 12. Exp. 15.7 screenshot2.png
Fig. 12. Exp. 15.7 screenshot3.png
Fig. 12. Exp. 15.7 screenshot4.png

Exp.15.7 .mp4

The mass and the charge of the electrons is multiplied with 10⁸in the above experiment.

The speed of the electrons is decreased:
Begin
vx:=vx*0.90; vy:=vy*0.90; vz:=vz*0.90;
end;

The electrons spread out, due to the augmented charge (x 10⁸). Interactions between the particles is on.
(Coulomb and Bios-Savart).

Example that demonstrates that we can not simply represent a group of particles by a few particles.

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Let´s create a negative charge in the centre region.

I was thinking to generate the D+ ions random, but then many of them will colide with the negative charged rings up and down, and this will cause (huge?) losses. It seems to be that the best is to inject both the D+ and the electrons.

In the link below an electron gun is sold with an energy range: 1 eV to 100 keV and a beam current range: 1 nA to 20 mA (or even 50 mA)
https://www.kimballphysics.com/

(1 A = 6.242×10¹⁸ electrons/s)

Let´s take 1 mA -> 1.10^-3A = 1.10^-3C/s -> 1.10^-3C/s / (1,6.10^-19C) = 6,3. 10¹⁵electrons/s

It seems therefore plausible to have an electron gun that produces about 6.3. 10¹⁵electrons/ s ( 1 electron/1,59 10^-16 s)

If the energy of an electron is 1 eV, then:

½ m_eV_e² = 1 eV = 1,602.10^-19J => V_e = √ (2 . 1,602.10^-19/ (9,1095 . 10^-31) ) = 5,931.10⁵m/s

It seems to be possible to give them speeds of 1 . 10⁶m/s (as in the simulation program).

How much charge we have after one minute:

60 x 6,3. 10¹⁵ electrons = 3,8. 10¹⁷ electrons
-> 3,8 . 10¹⁷ ^.1,6.10^-19C = 6,0 10^-2C

In the simulation program we will use the middle ring to simulate, quite approximated, a negative charge in the centre region. How much negative voltage we must give it to be equivalent with 6,0 10^-2C ?