Computer program to calculate the net force on a conducting tube inside a solenoid carrying alternating current.

The angle Chi is between the smaller circle centre and the arrow head and the angle Psi is between the larger circle centre and the arrow tail. Z is the extension out of the drawing plane. |

The larger circle is the outside diameter and it represents the coil and the inner circle is the plasma referred to as the inside diameter. It is shown displaced from the equilibrium position.

The alternating current is carried in a coil making it a current sheet and the inside conductor is assumed to be an ionised gas with most of the current flowing in the surface.

Result of one calculation. (Version 1.3)

Private Sub Command1_Click()

Const pi = 3.1415926

Dim OutsideDiameter, InsideDiameter, Displacement, ThetaDeg, PsiDeg, ChiDeg As
Double

Dim Ri, Ro, D, Z, ThetaRad, PsiRad, ChiRad, DeltaTheta, DeltaPsi, DeltaChi As
Double

Dim Pressure, Current, Length, Force, deltaZ, TotalForce, Sign As Double

Dim ret

Current = Val(txtCurrent)

quit = False

ProgressBar1.Value = 0

OutsideDiameter = Val(txtOutsideDiameter)

InsideDiameter = Val(txtInsideDiameter)

Displacement = Val(txtDisplacement)

Length = Val(txtLength)

deltaZ = Length / 1000

If InsideDiameter >= OutsideDiameter Then

ret = MsgBox("Inside bigger that outside", vbCritical, "Error")

Exit Sub

End If

If Displacement >= (OutsideDiameter - InsideDiameter) / 2 Then

ret = MsgBox("Displacement too large", vbCritical, "Error")

Exit Sub

End If

If Displacement > 0 Then Sign = 1 Else Sign = -1

DeltaPsi = pi / 180 * 10

DeltaChi = pi / 180 * 10

For Z = -Length / 2 To Length / 2 Step Length / 1000

For ChiDeg = 0 To 350 Step 10

For PsiDeg = 0 To 350 Step 10

ret = DoEvents()

ChiRad = ChiDeg * pi / 180

PsiRad = PsiDeg * pi / 180

Force = Current ^ 2 * (OutsideDiameter / 2) * DeltaPsi * (InsideDiameter / 2) *
DeltaChi * deltaZ

Force = Force * Sin((ChiDeg + PsiDeg - 180) * pi / 180)

Force = Force / ((InsideDiameter / 2 * Sin(ChiRad) + Displacement -
OutsideDiameter / 2 * Sin(PsiRad)) ^ 2 + (InsideDiameter / 2 * Cos(PsiRad) -
OutsideDiameter / 2 * Cos(PsiRad)) ^ 2 + Z ^ 2)

Force = Force * 4 * pi * 0.0000001 * Sign * -1

Pressure = Pressure + Abs(Force)

TotalForce = TotalForce + Force

If quit Then Exit Sub

Next PsiDeg

Next ChiDeg

If 100 * (Z + Length / 2) / Length Mod 5 = 0 Then

ProgressBar1.Value = 100 * (Z + Length / 2) / Length

End If

Next Z

Pressure = Pressure / (pi * InsideDiameter * Length)

txtTotalForce = Str$(TotalForce)

txtPressure = Str$(Pressure)

End Sub

(Version 1.3)

The result of the calculation indicate that the force is towards the centre and increases as the displacement increases. This would indicate that an ionised gas would be contained near the middle line of a solenoid carrying an alternating current. Extending this idea to a torus, indicates that the plasma would be stably contained within.

Do download the above application to install on your machine. The application has been virus checked with the current version of Norton anti-virus. This is version 1.3 and is for test only I do not promise that it calculates the correct answer.

Chris

24/12/2011