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11.1 Confinement of positive ions and electrons with a static electric and magnetic field
Experiments with the simulation program: exp. 11.1 till 11.6
Experiment 11.1 A positive charge of 5,57E7 C is placed in the points (x,y,z): (Fig._2)
(0,4,0,4,0,1), (0,6,0,4,0,1), (0,6,0,6,0,1),
(0,4,0,6,0,1), In the program dt=1.59E12
A (solitary) sphere with diameter 10 cm and a voltage of +1kV
(to infinity) has a charge of: qi= 1000/(9E9)* 0.05 = 5.56E09 Coulomb.
Bfield: (variable)
B(0.5,0.5,0.5) = 100 gauss
50 B+ ions were generated: Screenshots\Exp 11.1 screenshot.jpg After 2,02E5 sec a few ions have escaped, see screenshot. (Bfield in the centre is only 100 gauss)

Experiment 11.2
A positive charge of 5,57E7 C is placed in the points (x,y,z):
(Fig._2) In the program dt=1.59E10 (a lot faster, but the simulation is less precise)
Bfield: (variable, in the centre less; above, under and near
the sides stronger)
B(0.5,0.5,0.5) = 1000 Gauss
50 H+ ions were generated:
50 B+ ions were generated: Screenshots\Exp 11.2 screenshot.jpg After 6,21E5 sec all ions are still confined.
1,25 T = strength of a modern neodymium–iron–boron
(Nd_{2}Fe_{14}B)
rare earth magnet Screenshots\Exp 11.2 screenshot 8.09E5 s.jpg All ions are still confined. But 48 T is a very strong Bfield and difficult to achieve.

Experiment 11.3 A positive charge of 5,57E7 C is placed in the points (x,y,z): (Fig._2) (5,57E7 C = 200 kV on a sphere with diameter 5 cm)
(0,4, 0,4 , 0,1), (0,6, 0,4, 0,1), (0,6, 0,6 ,0,1),
(0,4, 0,6 ,0,1), In the program dt=1.59E11 Bfield: vertical constant 1 T
50 H+ ions were generated:
50 B+ ions were generated:
Exp 11.3 screenshot 1.92 E5 s.jpg
(one ion did escape) Remarks: The light H+ ions seem to be quite well confined by the magnetic
field (during the short time lapse of the simulation) The ions seem not to interact with each other, but their
dimensions, their amount and their charge is relavively very small. 
Experiment 11.4
The same as exp. 11.3, with Bfield = 1 T (constant, vertical), but the ions did not have an initial speed. dt=1.59E11 hydrogen[i].vx:=0; {initial speed} boron[i].vx:=0; {intitial speed} Exp 11.4 screenshot 1.9E4 s 1 T.jpg The H+ and B+ ions did not escape.

Experiment 11.5
dt=1.59E11
Bfield: (variable)
B(0.5,0.5,0.5) = 100 Gauss ve:=1000000 = 1E6 m/s boron[i].vx:=0;//(  0.5 + random)*ve; {they have
an initial horizontal random speed} Exp 11.5 screenshot 3.67E6 s var B.jpg In this time period no ions did escape. The same experiment, but with a constant Bfield of 2 T. Exp 11.5 screenshot 1.56E6 s constant B 2 Tesla.jpg There seems to be not a lot of difference in
applying a variable Bfield or a constant Bfield. The same experiment, with a constant Bfield of 2 T, but with 300 H+ and 300 B+ ions. Exp 11.5 screenshot 1.59E11 s B 2 T 300 H+ and 300 B+ ions.jpg Exp 11.5 screenshot 1.59E11 s B 2 T 300 H+ and 300 B+ ions with explanation.jpg

Conclusions so far: (see also main page) With a constant magnetic field of about 1 or 2 T (should be possible to realize..), eight positive charges placed up and down (corresponding to four round conductors with a diameter of 10 cm and a voltage of 100 kV, also possible to realize?) and a same positive charge placed in each of the sides, the positive ions are confined in the simulation program (applying Coulomb force and Biot Savart, nonrelativistic); at least during the (short) time period of the simulation. The magnetic field is important: if it is decreased the ions escape away to the sides. No interactions (colisions) between the ions are observed. The reason of this is maybe because the ions are relatively very small and there are only a very few (in reality there would be millions..). When the charge of the ions is increased a 10000000 times, then yes interactions between them are observed. I let one H+ and one B+ ion collide with each other. If the charge is only increased 100000 times, then they did not collide (dt= 1.59E14). With dt=1.59E15 and 100000 times more charge they do collide.

Experiment 11.6 The total energy ( = kinetic energy of all particles + potential energy of all particles ) is calculated. dt=1E10 s Bfield: 1 tesla (constant) ve:=1000000= 1E6 m/s; hydrogen[i].vx:=0 + (  0.5 + random)*ve; {they
have an initial horizontal random speed} boron[i].vx:= ( 0.5 + random)*ve; {they have
an initial horizontal random speed} The voltage of the top and bottom charge is 200
kV, so the positive charge of each point charge is: 5.56E7 Q
(if each point charge should be a sphere wit diameter 10 cm). Because there are now also fixed point charges, the potential energy of the moving particles relative to this point charges is also calculated. We started a experiment with 200 H+ and 200 B+ ions. Exp 11.6 screenshot 3.8 E5 s B 1 T constant.jpg The total energy (= potential+kinetic energy)
stayed constant: 6,0239668.. E12 J. Changed dt=1E9 s. The simulation is less precise,
but faster. Changed dt=1E8 s. Changed dt=1E7 s. Changed dt=1E6 s. Note: with a speed of 1E6 m/s and a height of 1 mtr of the simulation space (cube) , a particle will travel in 1/(1E6) = 1E6 s from one side to another side. So it is obvious that we cannot take dt=1E6 s, and even dt=1E7 is quite big. 
Experiment 11.6b dt:=1E9 s idem for hydrogen B=1,4 tesla (constant) change dt=1E8 > total energy = 1,798 +/ 0.0002, all ions still confined after 0.0044 s change dt=1E7 > total energy = 1,63008 +/ 0.00002, all ions still confined after 0.0076 s change dt=1E6 > total energy = 1,6389 , all ions fly away rapidly

20 February
2014 ..
by
Rinze
Joustra www.valgetal.com