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),
(0,4,0,4,0,9), (0,6,0,4,0,9), (0,6,0,6,0,9), (0,4,0,6,0,9)
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.
100 kV > 5.56E7 Coulomb. .
Bfield: (variable)
xc:=0.5*s/400; {if s=400 then xc=0.5 mtr}
yc:=0.5*s/400;
zc:=0.5*s/400;
r1:=sqrt( sqr(xcx) + sqr(ycy));
r2:=sqrt( sqr(zcz) ); {abs value}
{if r1=0,5s and r2=0, then Bfield=1.75*B at the side and 1B in the centre,
if r1=0 and r2=0,5s then Bfield=1.75*B in Gauss}
Bh:=B+(rcxy*r1+rcz*r2)*B;Bfield:=Bh;
B(0.5,0.5,0.5) = 100 gauss
B(0.5, 0,5, 0.0) = 2 T (20000 gauss)
B(0.5, 0,5, 1.0) = 2 T
B(0.5,0.0, 0.5) = 2 T
B(0.0,0.0, 0.0) = 4.8 T
Bfield is in the centre weak and near the sides/top/bottom stronger.
50 H+ ions were generated:
hydrogen[i].x:=0.5 + (  0.5 + random) /50; {so they start not in exactly
the same point}
hydrogen[i].y:=0.5 + (  0.5 + random) /50;
hydrogen[i].z:=0.25 + (  0.5 + random) /5;
50 B+ ions were generated:
boron[i].x:=0.5 + (  0.5 + random) /50;
boron[i].y:=0.5 + (  0.5 + random) /50;
boron[i].z:=0.75+ (  0.5 + random) /5;
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)
(0,4,0,4,0,1), (0,6,0,4,0,1), (0,6,0,6,0,1),
(0,4,0,6,0,1),
(0,4,0,4,0,9), (0,6,0,4,0,9), (0,6,0,6,0,9), (0,4,0,6,0,9)
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)
xc:=0.5*s/400; {if s=400 then xc=0.5 mtr}
yc:=0.5*s/400;
zc:=0.5*s/400;
r1:=sqrt( sqr(xcx) + sqr(ycy));
r2:=sqrt( sqr(zcz) ); {abs value}
Bh:=B+(rcxy*r1+rcz*r2)*B;
B(0.5,0.5,0.5) = 1000 Gauss
B(0.5, 0,5, 0.0) = 20 T
B(0.5, 0,5, 1.0) = 20 T
B(0.5,0.0, 0.5) = 20 T
B(0.0,0.0, 0.0) = 48 T
50 H+ ions were generated:
hydrogen[i].x:=0.5 + (  0.5 + random) /50; {so they start not in exactly
the same point}
hydrogen[i].y:=0.5 + (  0.5 + random) /50;
hydrogen[i].z:=0.25 + (  0.5 + random) /5;
50 B+ ions were generated:
boron[i].x:=0.5 + (  0.5 + random) /50;
boron[i].y:=0.5 + (  0.5 + random) /50;
boron[i].z:=0.75+ (  0.5 + random) /5;
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
36 T = Strongest continuous magnetic field produced by nonsuperconductive
resistive magnet.
See:
https://en.wikipedia.org/wiki/Orders_of_magnitude_(magnetic_field)#cite_note14
The applied magnetic field is quite strong.... (could
be difficult to realize in the real world..)
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),
(0,4, 0,4, 0,9), (0,6, 0,4, 0,9), (0,6, 0,6, 0,9), (0,4, 0,6, 0,9)
(0,5, 0 , 0,5 ), (0,5, 1 , 0,5), ( 1, 0,5, 0,5), (0,
0,5 , 0,5)
(4 above, 4 under, and 1 in the middle of each vertical side)
In the program dt=1.59E11
Bfield: vertical constant 1 T
50 H+ ions were generated:
hydrogen[i].x:=0.5 + (  0.5 + random) /50; {so they start not in exactly
the same point}
hydrogen[i].y:=0.5 + (  0.5 + random) /50;
hydrogen[i].z:=0.25 + (  0.5 + random) /5;
ve:=1000000 =1E6 m/s;
hydrogen[i].vx:=(  0.5 + random)*ve;{they have some initial horizontal
speed }
hydrogen[i].vy:= (  0.5 + random)*ve;
hydrogen[i].vz:=0;
50 B+ ions were generated:
boron[i].x:=0.5 + (  0.5 + random) /50;
boron[i].y:=0.5 + (  0.5 + random) /50;
boron[i].z:=0.75+ (  0.5 + random) /5;
ve:=1000000; (1E6)
boron[i].vx:=(  0.5 + random)*ve; {they have some initial horizontal speed
}
boron[i].vy:= (  0.5 + random)*ve;
boron[i].vz:=0;
Exp 11.3 screenshot 1.92 E5 s.jpg
(one ion did escape)
Exp 11.3 screenshot 6.13 E5 s.jpg
(two ions did escape, although the escape trail is not seen)
Exp 11.3 screenshot 2.1 E4 s.jpg
Exp. 11 50 H+ 50 B+ 1 T constant
12 point charges 2E4 s.mp4
Remarks:
The light H+ ions seem to be quite well confined by the magnetic
field (during the short time lapse of the simulation)
The heavier B+ ions (11 x heavier than the H+ ions) are
spreading out a bit, and some of them escaped (suppose it were B+
ions that escaped; cannot determine this).
The ions seem not to interact with each other, but their
dimensions, their amount and their charge is relavively very small.
When their charge is increased (10000..0x) , then they do interact
(collide etc.), so the formulas in the program seem to be correct.

Experiment 11.4
(Fig._2)
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}
hydrogen[i].vy:=0;
hydrogen[i].vz:=0;
hydrogen[i].x:=0.5 + (  0.5 + random) /50; {so they start not in
exactly the same point}
hydrogen[i].y:=0.5 + (  0.5 + random) /50;
hydrogen[i].z:=0.25 + (  0.5 + random) /5;
boron[i].vx:=0; {intitial speed}
boron[i].vy:=0;
boron[i].vz:=0;
boron[i].x:=0.5 + (  0.5 + random) /50; {so they start not in
exactly the same point}
boron[i].y:=0.5 + (  0.5 + random) /50;
boron[i].z:=0.75 + (  0.5 + random) /5;
Exp 11.4 screenshot 1.9E4 s 1 T.jpg
Exp.11.4 2E4 s.mp4
The H+ and B+ ions did not escape.

Experiment 11.5 (Fig._2)
dt=1.59E11
Bfield: (variable)
xc:=0.5*s/400; {if s=400 then xc=0.5 mtr}
yc:=0.5*s/400;
zc:=0.5*s/400;
r1:=sqrt( sqr(xcx) + sqr(ycy));
r2:=sqrt( sqr(zcz) ); {abs value}
{if r1=0,5s and r2=0, then Bfield=1.75*B at the side and 1B in the centre,
if r1=0 and r2=0,5s then Bfield=1.75*B in Gauss}
Bh:=B+(rcxy*r1+rcz*r2)*B;Bfield:=Bh;
B(0.5,0.5,0.5) = 100 Gauss
B(0.5, 0,5, 0.0) = 2 T (20000 Gauss)
B(0.5, 0,5, 1.0) = 2 T
B(0.5,0.0, 0.5) = 2 T
B(0.0,0.0, 0.0) = 4.8 T
Bfield is in the centre weak and near the sides/top/bottom stronger.
ve:=1000000 = 1E6 m/s
hydrogen[i].vx:=0 + (  0.5 + random)*ve; {they
have an initial horizontal random speed}
hydrogen[i].vy:=0 + (  0.5 + random)*ve;
hydrogen[i].vz:=0;
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) /1.5; {initial vertical
position quite spreaded}
boron[i].vx:=0;//(  0.5 + random)*ve; {they have
an initial horizontal random speed}
boron[i].vy:=0;// (  0.5 + random)*ve;
boron[i].vz:=0;
boron[i].x:=0.5 + (  0.5 + random) /5;
boron[i].y:=0.5 + (  0.5 + random) /5;
boron[i].z:=0.5 + (  0.5 + random) /1.5; {initial vertical position
quite spreaded}
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.
In the real world I suppose it will be easier to apply a constant
magnetic field..
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
No ions did escape in this time period.

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}
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) /1.5; {initial vertical
position spreaded}
boron[i].vx:= ( 0.5 + random)*ve; {they have
an initial horizontal random speed}
boron[i].vy:=(  0.5 + random)*ve;
boron[i].vz:=(  0.5 + random)*ve;
boron[i].x:=0.5 + (  0.5 + random) /5;
boron[i].y:=0.5 + (  0.5 + random) /5;
boron[i].z:=0.5 + (  0.5 + random) /1.5; {initial vertical position spreaded}
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).
There are four point charges above and four point charges under.
In the sides there are no charges.
See also experiment 9
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.
This should be so; it´s an indication that the formulas in the
simulation program are correct.
Changed dt=1E9 s. The simulation is less precise,
but faster.
At elapsed time = 0,000168 s the the potential energy stayed
constant: 6,023966... E12 J.
At elapsed time = 0,000383 s the the potential energy stayed
constant: 6,023966... E12 J.
Changed dt=1E8 s.
At elapsed time = 0,000537 3 s the potential energy: 6,0240..
E12 J. (a very tiny change).
One ion escaped.
Changed dt=1E7 s.
At elapsed time = 0,00204 3 s the potential energy: 1,738..
E11 J. .
This dt is too big: the simulation is not anylonger precise.
More ions escaped.
Changed dt=1E6 s.
All ions escaped.
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
ve:=1000000 = 1E6 m/s;
boron[i].m:=mb;
boron[i].vx:=0 + (  0.5 + random)*ve;
boron[i].vy:=0 + (  0.5 + random)*ve;
boron[i].vz:=0 + (  0.5 + random)*ve;
boron[i].q:=qe;
boron[i].x:=0.5 + (  0.5 + random) /5;
boron[i].y:=0.5 + (  0.5 + random) /5;
boron[i].z:= 0.5+ (  0.5 + random) /1.50;
idem for hydrogen
B=1,4 tesla (constant)
Top and bottom voltage = 150 V
Sides voltage = 0
time= 0,00408 s
total energy = 1,79871 +/ 0,000002 J
20 H+ and 20 B+
All ions confined
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 