Sem Fusor, small experiment

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

First I will calculate what magnet is possible to build my self, or to buy.

Let´s assume we have a dc power supply of 100 W.

Electrical cable in Bricodepot.es: 2,5 mm²-> 0,22 € / m (maximum current about 20 A, acc. internet search

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Diameter electromagnet (solenoid) = 60 cm

N = 500 turns, 1 turn = 2 π r = 1,885 m, 500 turn = 942 m (207 €)

For copper the resistivity ρ = R . A/l = 1,7 . 10^-8 ohm meter (R = electrical resistance, l = length, A = cross-sectional area)

R = 1,7 . 10^-8. 942 /( 2,5. 10^-6) = 6.41 ohm

100 W -> P = I² . R -> I =√( P /R) = √ (100 / 6,41) = 3,95 A

B = μ₀. N/l . I (see hyperphysics)

μ₀= 4.π.10^-7 N·A⁻²

N = amount of windings

l = length solenoid, let´s take 1 m

I = current in A

B= 4.π.10^-7 . 500 . 3,95 / 1 = 2,48 . 10^-3 T

rounded- > B = 25 gauss = 25 . 10^-4tesla

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Diameter solenoid = 30 cm (with same lenght of cable)

N = 942 / ( 2 . π . 0,15) = 999

-> B = 50 gauss

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Diameter solenoid = 15 cm (with same lenght of cable)

N = 942 / ( 2 . π . 0,075) = 2000

-> B = 4.π..10^-7 . 2000 . 3,95/ 1 = 99 gauss

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Fig.1. The magnetic field of an electromagnet with an iron core

r₁ = ½.d₁

Volume of the iron core = π (r₁)². (m1 + m2 + m1 + m2 + g + π . (r₂+.r₁ ) . 2 )

Volume of curved part of iron core ≈ 2 . π (r₁)² . π . (r₂+.r₁ )

d1 = 15 cm (r1 = 0,075 m
m1 = 1 m
m2 = 0,30 m
r2 = 0,20 m
g = 0,60 m

Volume = π (0,075)². (1 + 0,30 + 1 + 0,30 + 0,60 + π . (0,20 +0,075 ) . 2 )

= π (0,075)^{2
.}(3,2 + π . 0,55 ) = 0,087 m3 = 87 . 10^-3 m3

ρ_iron= 7.874 g/cm^³ = 7,874 . 10³kg/m³-> mass = 685 kg

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Only an iron core inside the solonoide:

Volume = π (r₁)². m1 = π (0,075)². 1 = 17,7 . 10^-3 m3 -> mass = 139 kg

We could divide it in 14 discs of 10 kg

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Relative permeabiltiy μ/μ₀ iron (99,8 % pure) = 5000 (Wikipedia)

B_{with
iron core} = k B _{without core}, k = μ/μ₀= 5000 ( http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/elemag.html#c4 )

B _{without core}= 50 gauss -> x 5000 => B_{with
iron core}= 250000 gauss = 25 T (inside the core)

The relative permeability of mumetal is 20000 , but mumetal saturates at about 8000 gauss.
Steel saturates around 22000 gauss ( https://www.scienceforums.net/topic/77661-mu-metal-core/ )

The relative permeability of soft iron with 99.95 percent purity is a massive 200,000.

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Suppose we can create a magnetic field of 1000 gauss

Two negatively charged rings at -80kV.
A vacuum chamber with diameter 15 cm and length 30 cm

Fig. 2.

The electrons are injectet upwards vertically, just above the under ring.

During the short simulation time the electrons stay confined.

If the vacuum chamber would be filled with D2 gas, would this gas be ionized and would the electron cloud attract the D+ ions, more or less towards the centre?

Fig. 3.

The D+ are generated randomly all over the "vacuum chamber".

No magnetic field, and a negative charge in the middle (small ring).