10.9 Physics experiment: simulation of moving electrons, hydrogen and boron ions in a magnetic field
Computer simulation of idea 10 : calculating the kinetic and potential energy of the particles
Experiment 9
The total kinetic energy of all particles can now neither increase
nor decrease (within very small limits). If it changes, then the speed of each
electron is multiplied by 0.999 or by 1.001
in a repeat loop, until the total kinetic energy is again (almost) the
same as the initial kinetic energy of all particles
(there are only 3 H+ and 3 B+ ions, their speed is not altered,
I do not think this is important).
The looses according the Larmor Formula (about 0.1 % in 1 sec) will be neglected for the moment.
The potential energy of all particles will also be calculated.
Fig.1
The electric potential energy U of a system of two point charges q1 & q2 is equal to
(e0 = 8,854E12 F.m^{2},^{ }r = distance between the two point charges)
Just bring q1 to infinity and calculate the work done by the Coulomb force.
The electric potential energy of a system of three point charges (see figure 1) can be calculated in a similar manner
Bring q1 to infinity and calculate the work
done by the combined Coulomb force exerted by q2 & q3 on q1. Then bring q2 to
infinity and calculate the work done by the Coulomb force exerted by q3 on q2.
After this all particles are at an infinite distance from each other which
corresponds with U=0 .
See also Electric potential energy stored in a system of point charges
In the program we calculate U in two repeat loops. If we had only three particles, we would calculate
So and the end we divide by 2.
Part of the program:
Ue:=0; {the total potential energy, first zero} for i:=1 to (AmountE) do
{amountE=amount of electrons} if electron[i].exists and
electron[j].exists then Ue:= Ue+ K*qe*qe/r; Ue:=0.5*Ue; 
Also we calculate the potential energy U between the
electrons and the H+, between the electrons and the B+ ions and between
the H+ and the B+ ions.
Here we do not calculate double pairs (U12 = potential energy
between the first H+ and the second B+ , U21= potential energy between the
second H+ and the first B+),
so here we do not divide by 2. The total potential energy of all particles is
all the time stated in the program.
Experiment 9.001 (30/6/2016) : 20 electrons,
Bfield= 10 gauss, initial kinetic energy of each electron (energy
range) = 100 eV, beam current 0,001 nA, 3 H+ generated with initial
speed=0 (in positions: (0.5, 0.5, 0.25) (0.50125, 0.50125, 0250625),
(0.501246, 0.501246, 0.25125), 3 B+ generated with initial speed=0 (in
positions: (0.5, 0.5, 0.75) (0.50125, 0.50125, 075188), (0.501246,
0.501246, 0.75375) In this experiment the kinetic energy of all particles is NOT kept constant (from experiment 3 it was kept constant).
Screenshot after 1,53E5 sec (53 min
computer time) Just when the 20 e, 3 H+ and 3 B+ were generated
their total potential+kinetic energy = 3,47 E16 J. In the first
screenshot it is 6,23 E16 J. Almost doubled! In the second
screenshot 6,52 E15 J.  Experiment 9.002: The kinetic energy of the particles is 178 times bigger! Because the distance between the electrons has grown, itīs understandable that the potential energy has decreased. The potential energy is, by the way, negligible compared to the kinetic energy.  Experiment 9.1:
Screenshot 49 electrons generated
(total potential energy of the 49 electrons =
6,9E24 J)  Experiment 9.22:  Experiment 9.23:  Experiment 9.24: From the difference between experiment 9.22 and 9.23 we can conclude that increasing the magnetic field and let so the electrons move in small circles, seems to avoid somewhat the spreading out in the vertical direction. Itīs a pity that in experiment 9.24 they yes spreaded out in the vertical directions. We have to find out more about how much a approximation is the program (because we keep the kinetic energy of the electrons constant by multiplying the speed of the electrons with a factor..). I checked the speed v_{z} of the electrons and the force Fz on the electrons in vertical directions, and they never seemed to be oposed.. So the electrons are not stopped spreading out in a vertical directions by the magnetic field produced by themselves... Itīs a pity.. No, in the experiment now running I just saw that sometimes they are opposed... Itīs not clear yet ?? The same experiment again, but with B field 100  1000 G, 100 eV, 0.0000002*sp<vz <0.0000002*sp, 0,5 m 0.001 < z < 0,5m + 0.001 , result: electrons spreading out in vertical direction. Remark: the speed of the electrons with 100 eV = 5,9E6 ms, 0.0000002*sp = 1,2 m/s vertical speed. I suppose this is quite a lot..
Experiment 9.252: Experiment 9.253:
Experiment 9.3:
The total kinetic energy Ek of the electrons
is kept constant by
mulitplying the components of the speed v_{x} and v_{y}
with a factor 0.999 or 1.001; v_{z} is
NOT mulitplied by any factor.
electron[i].vz:=(0.5random)*sp*0.000000002 (2E9)
> 5,9E3 < vz < 5,9E3 m/s (the initial
vertical speed of the electrons)
At the start of the experiment the total potential energy of the
electrons: 8,67 E23 J < Ep < 8,859 E23 J The potential energy of the electrons decreases. It is clearly to see in the last screenshot that the electrons have spread out. The vertical speeds of the electrons have also increased (see screenshot, from a couple of m/s till a couple of 100 m/s to even more than 1000 m/s.  Experiment 9.31: The same as experiment 9.3, but
now the magnetic field changes from B=100 G to B= 1 T. At the start of the experiment Ep= 2,76 E21 J, after 3,78E6 s Ep= 4,8E22 J. The potential energy of the electrons has decreased. The electrons have spread out.  Experiment 9.33:
electron[i].vz:=(0.5random)*sp*0.0000000002; (2E10) At the start of the experiment Ep= about 2,87 E22 J, after 2,76 E6 s Ep= about 2.68 E22 J. The potential energy of the electrons has decreased. The electrons have spread out.  Experiment 9.34:
electron[i].vz:=(0.5random)*sp*0.0000000002; (2E10) At the start of the experiment Ep= about 2,5448 E22 J, after 2,81 E6 s Ep= about 2.543 E22 J. The potential energy of the electrons has decreased. The electrons have spread out.  Conclusion so far: We want that the electrons stay in the centre of the vacuum chamber (the cube in the simulation program). We try this by applying the simple trick "increasing the magnetic field so that the electrons start to move in small circles and are glued together by the magnetic fields they generate themeselves". Intuitive explanation of this in experiment6 . In experiment 9.3, 9.31 & 9.33 the electrons have spread out. The "trick" did not work... It's a pity..
 Experiment 9.35:
The total kinetic energy Ek of the electrons
is kept constant by
mulitplying the components of the speed v_{x} and v_{y}
with a factor 0.999 or 1.001; v_{z} is
NOT mulitplied by any factor.
electron[i].vz:=(0.5random)*sp*0.00000000002; 2E11 m/s
> 5,9E5 < vz < 5,9E5 m/s (the
initial vertical speed of the electrons) Screenshot exp. 9.35 after 1,01 E5 s At the start of the experiment Ep= about 7,2 E23 J, after 1,01 E5 s Ep= about 6,3 E23 J. The potential energy of the electrons has decreased. The electrons have spread out.  Experiment 9.36:
The total kinetic energy Ek of the electrons
is kept constant by
mulitplying the components of the speed v_{x} and v_{y}
with a factor 0.999 or 1.001; v_{z} is
NOT mulitplied by any factor.
electron[i].vz:=(0.5random)*sp*0.00000000002; 2E11 m/s
> 5,9E5 < vz < 5,9E5 m/s (the
initial vertical speed of the electrons) At the start of the experiment Ep= about 6,6 E23 J, after 1,1 E5 s Ep= about 4,07 E23 J. The potential energy of the electrons has decreased. The electrons have spread out. Screenshot exp. 9.36 100 e 10 G  In exp. 9.36 the electrons have spread out a little bit more than in experiment 9.35. Probably because they are closer together.  Experiment 9.37:
The total kinetic energy Ek of the electrons
is kept constant by
mulitplying the components of the speed v_{x} and v_{y}
with a factor 0.999 or 1.001; v_{z} is
NOT mulitplied by any factor.
electron[i].vz:=(0.5random)*sp*0.00000000002; 2E11 m/s
> 5,9E5 < vz < 5,9E5 m/s (the
initial vertical speed of the electrons)
Screenshots experiment 9.37 after 3 E5
At the start of the experiment Ep= about 8,4 E23 J, after 3
E5 s Ep= about 4,2 E23 J. The potential energy of the electrons
has decreased. The electrons have spread out.  Experiment 9.38:
The total kinetic energy Ek of the electrons
is kept constant by
mulitplying the components of the speed v_{x} and v_{y}
with a factor 0.999 or 1.001; v_{z} is
NOT mulitplied by any factor.
electron[i].vz:=(0.5random)*sp*0.00000000002; 2E11 m/s
> 5,9E5 < vz < 5,9E5 m/s (the
initial vertical speed of the electrons) Screenshot experiment 9.38 after 3 E5 At the start of the experiment Ep= about 6,2 E23 J, after 3 E5 s Ep= about 2,7 E23 J. The potential energy of the electrons has decreased. The electrons have spread out.
Experiment 9.393:
The total kinetic energy Ek of the electrons
is kept constant by
mulitplying the components of the speed v_{x} and v_{y}
with a factor 0.999 or 1.001; v_{z} is
NOT mulitplied by any factor. (0,1 nA) if (amountE=100) and not (Already) then begin {Bh:=B + 2r1 + 10r2 (r1= radius in xyplane, r2=vertical distance from center cube, at side r1=0,5 & r2=0,5 m)
electron[i].vz:=(0.5random)*sp*0.00000000002;
2E11 m/s
> 5,9E5 < vz < 5,9E5 m/s (the
initial vertical speed of the electrons)
Screenshot experiment 9.393 after
1,7 E6 (Bfield 880 G,
not yet 1000 G)  Experiment 9.394:
The total kinetic energy Ek of the electrons
is kept constant by
mulitplying the components of the speed v_{x} and v_{y}
with a factor 0.999 or 1.001; v_{z} is
NOT mulitplied by any factor. (0,1 nA) if (amountE=200) and not (Already) then begin
{Bh:=B + 2r1 + 10r2 (r1= radius in xyplane, r2=vertical distance
from center cube, at side r1=0,5 & r2=0,5 m)
electron[i].vz:=(0.5random)*sp*0.00000000002;
2E11 m/s
> 5,9E5 < vz < 5,9E5 m/s (the
initial vertical speed of the electrons)
Screenshot experiment 9.394 after
3,03 E6
 Experiment 9.395:
The total kinetic energy Ek of the electrons
is kept constant by
mulitplying the components of the speed v_{x} and v_{y}
with a factor 0.999 or 1.001; v_{z} is
NOT mulitplied by any factor. (0,01 nA) if (amountE=50) and not (Already) then begin
{Bh:=B(1 + 2r1 + 10r2) (r1= radius in xyplane, r2=vertical
distance from center cube, at side r1=0,5 & r2=0,5 m)
electron[i].vz:=(0.5random)*sp*0.00000000002;
2E11 m/s
> 5,9E5 < vz < 5,9E5 m/s (the
initial vertical speed of the electrons) Screenshot experiment 9.395 1.7 E5 s The electrons did spread out quite a lot.  Experiment 9.396:
The total kinetic energy Ek of the electrons
is kept constant by
mulitplying the components of the speed v_{x} and v_{y}
with a factor 0.999 or 1.001; v_{z} is
NOT mulitplied by any factor. (0,1 nA) if (amountE=100) and not (Already) then begin
{Bh:=B(1 + 2r1 + 10r2) (r1= radius in xyplane, r2=vertical
distance from center cube, at side r1=0,5 & r2=0,5 m)
electron[i].vz:=(0.5random)*sp*0.00000000002;
2E11 m/s
> 5,9E5 < vz < 5,9E5 m/s (the
initial vertical speed of the electrons)
Screenshots experiment 9.396 7.99
E6 s The same experiment again, starting from t=0: Screenshot experiment 9.396 2.02E5 s
The electrons do spread
out...  Experiment 10: To make the simulation more accurate we implemented the Leapfrog method,

2016 by Rinze Joustra www.valgetal.com


