HEDP notes
high energy density plasma is a plasma with pressure above 1 MBar
[math]\displaystyle{ 1 MBar = 1 \times 10^6 \times 10^5 Pa = 10^{11} Pa = 10^{11} (N m)/(m^2) = 10^{11} J/m = 10^{11} (10^7 erg)/(10^6 cm^3) = 10^{12} erg/cm^3 }[/math]
magnetic field produced by single wire (Biot-Savart Law)
[math]\displaystyle{ B[G] = 0.2 \times I(A) / r(cm) }[/math] [math]\displaystyle{ B[T] = 0.2 \times I(kA) / r(mm) }[/math]
- 10 MA at 4 mm radius is 500 T
- 100 kA at 40 um radius is 500 T
- 160 kA at 5 um radius is 6,400 T
magnetic pressure
[math]\displaystyle{ P_m(bar) = 4 \times B(T)^2 }[/math] [math]\displaystyle{ P_m(bar) = 0.16 \times I(kA)^2 \times R(mm)^{-2} }[/math]
- 10 MA at 4 mm radius is 1 MBar
- 100 kA at 40 um radius is 1 MBar
- 160 kA at 5 um radius is 164 MBar
Bennett condition
- magnetic pressure = plasmakinetic pressure
- 14 MBar at 140 kA at 15-um radius (shot 634 with 2x30-um W wires)
- 25 MBar at 150 kA at 12-um radius (shot 657 with 2x30-um Mo wires)
- 100 MBar at 154 kA at 6-um radius (shot 657 with 2x30-um Mo wires)