HEDP notes
high energy density plasma defined as 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]
- 100 kA at 1 mm radius is 20 T
- 10 MA at 4 mm radius is 500 T
- 100 kA at 1 um radius is 20 kT
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]
- 100 kA at 1 mm radius is 1.6 kBar
- 10 MA at 4 mm radius is 1 MBar
- 100 kA at 1 um radius is 1.6 GBar
Bennett condition
- magnetic pressure = plasmakinetic pressure
- 100 kA at 1 um radius is about 1.6 GBar of plasma pressure (wau!! really??!!)