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Using the Leapfrog method
Experiment 10.1:
Discovered an error in the Leapfrog equations/variables in the
program and corrected this!
electron[i].vz:=0.5-random)*sp*0.00000000002; (the
initial vertical speed of the electrons varies)
electron[i].z:=(0.5*s/400
-0.00001/2+random*0.00001);
(the initial vertical position varies
)
dt=1.59E-13
Generated 70 electrons with 100 eV. Then slowly changed
B-field from 10 G to 1000 G in small steps.
Beam current 0.01 nA.
Screenshot exp. 10.1 4,24 E-6 s
The electrons spread out (but had an initial random speed in the
z-direction). ----------------------- Experiment 10.11:
electron[i].vz:=0;
electron[i].z:=0.5*s/400;
dt=1.59E-12
Generated 50 electrons with 100 eV. Then slowly changed
B-field from 10 G to 1000 G in small steps.
Beam current 0.01 nA.
Before introducing H+ and B+ ions, the electrons did not spread out
After introducing H+ and B+ ions, the electrons did spread out, see
screen shot.
Screenshot exp. 10.11 5,22 E-5
s.jpg --------------------------- Experiment 10.12:
electron[i].vz:=0.5-random)*sp*0.00000000002; (the
initial vertical speed of the electrons varies)
electron[i].z:=(0.5*s/400
-0.00001/2+random*0.00001);
(the initial vertical position varies
)
dt=1.59E-12
Generated 100 electrons with 10000 eV. Then slowly changed
B-field from 100 gauss to 1000 gauss in small steps.
Beam current 0.01 nA. Electrons did spread out.
Screenshots exp. 10.12 6 E-6 s.jpg
Then we changed (decreased) the B-field to 10 Gauss:
-------------------- Experiment 10.13:
electron[i].vz:=(0.5-random)*sp*0.00000000002; (the
initial vertical speed of the electrons varies)
electron[i].z:=(0.5*s/400
-0.00001/2+random*0.00001);
(the initial vertical position varies
)
dt=1.59E-12
Generated 200 electrons with 100000 eV.The The
B-field is constant 1000 gauss.
Beam current 0.1 nA. It seems to be that the
electrons did not spread out.
Screenshots exp. 10.13 1.33 E-5 s.jpg
Looking at the vertical forces, itīs evident that the
mayority of the electrons experience a force towards the centre.
It seems to be that the magnetic forces that keep the electrons together
are stronger than the Coulomb forces that drive the electrons apart.
BUT... the speed of the electrons is 1,9 E8 m/s,
which is near the speed of light (3 E8 m/s). The formulas in the program
are (still) not relativistic!
-------------------- Experiment 10.14:
electron[i].vz:=(0.5-random)*sp*0.00000000002; (the
initial vertical speed of the electrons varies)
electron[i].z:=(0.5*s/400
-0.00001/2+random*0.00001);
(the initial vertical position varies
)
dt=1.59E-12
Generated 200 electrons with 10000 eV.The The
B-field is constant 1000 Gauss.
Beam current 0.1 nA. It seems to be that the
electrons did spread out.
Screenshots exp. 10.14 5.9 E-7 s.jpg
Looking at the vertical forces, itīs evident that the
mayority of the electrons experience a force out from the centre.
It seems to be that the magnetic forces that keep the electrons together
are weaker than the Coulomb forces that drive the electrons apart.
The speed of the electrons is 0.,6 E8 m/s. The formulas
in the program are (still) not relativistic.
-------------------- Experiment 10.15:
electron[i].vz:=(0.5-random)*sp*0.00000000002; (the
initial vertical speed of the electrons varies)
electron[i].z:=(0.5*s/400
-0.00001/2+random*0.00001);
(the initial vertical position varies
)
dt=1.59E-14
Generated 300 electrons with 1000 eV. Then slowly
changed B-field from 10 gauss to 1000 gauss in small steps.
The B-field in the centre is smaller than at the sides (see the
screenshot).
Beam current 0.01 nA.
The speed of the electrons is 0.2 E8 m/s. The formulas
in the program are (still) not relativistic.
Screenshots\Exp. 10.15 7.24 E-8 s.jpg
Looking at the vertical forces, itīs evident that the
mayority of the electrons experience a force out from the centre.
It seems to be that the magnetic forces that keep the electrons together
are weaker than the Coulomb forces that drive the electrons apart.
-------------------- Experiment 10.16:
electron[i].vz:=(0.5-random)*sp*0.00000000002; (the
initial vertical speed of the electrons varies)
electron[i].z:=(0.5*s/400
-0.00001/2+random*0.00001);
(the initial vertical position varies
)
dt=1.59E-14
Generated 30 electrons with 1000 eV. Then slowly
changed B-field from 10 Gauss to 1000 gauss in small steps.
The B-field in the centre is smaller than at the sides (see the
screenshot).
Beam current 0.001 nA.
The speed of the electrons is 0.2 E8 m/s. The formulas
in the program are (still) not relativistic.
Screenshots\Exp. 10.16 7.15 E-7
s.jpg
Looking at the vertical forces, itīs evident that the
mayority of the electrons experience a force out from the centre.
It seems to be that the magnetic forces that keep the electrons together
are weaker than the Coulomb forces that drive the electrons apart.
-------------------- Experiment 10.17:
electron[i].vz:=(0.5-random)*sp*0.00000000002; (the
initial vertical speed of the electrons varies)
electron[i].z:=(0.5*s/400
-0.00001/2+random*0.00001);
(the initial vertical position varies
)
dt=1.59E-12
Generated 30 electrons with 1000 eV. Then slowly
changed B-field from 10 gauss to 1000 gauss in small steps.
The B-field in the centre is smaller than at the sides (see the
screenshot).
Beam current 0.01 nA.
The speed of the electrons is 0.2 E8 m/s. The formulas
in the program are (still) not relativistic.
After 9,7E -5 s changed (instantaneously) the B-field back again to 10
gauss.
Screenshots\Exp. 10.17 2.3 E-4
s.jpg
Looking at the vertical forces, itīs evident that the
mayority of the electrons experience a force out from the centre.
It seems to be that the magnetic forces that keep the electrons together
are weaker than the Coulomb forces that drive the electrons apart.
------------------------------------------------
Experiment 10.18:
electron[i].vz:=(0.5-random)*sp*0.00000000002; (the
initial vertical speed of the electrons varies)
electron[i].z:=(0.5*s/400
-0.00001/2+random*0.00001);
(the initial vertical position varies
)
dt=1.59E-12
Generated 20 electrons with 1000 eV. Then slowly
changed B-field from 10 gauss to 1000 gauss in small steps.
The B-field in the centre is smaller than at the sides (see the
screenshot).
Beam current 0.001 nA.
After a while changed the B-field back to 10 gauss ((instantaneously)
The speed of the electrons is 0.2 E8 m/s. The formulas
in the program are (still) not relativistic.
Screenshots\Exp. 10.18 4.5 E-4 s.jpg
Looking at the vertical forces, itīs evident that the
mayority of the electrons experience a force out from the centre.
It seems to be that the magnetic forces that keep the electrons together
are weaker than the Coulomb forces that drive the electrons apart.
Curious that the hydrogen ion above did not bouch back
against the boron ions, and that the boron ions did not move. |
