HEDP notes

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high energy density plasma defined as a plasma with pressure above 1 MBar

$1 MBar = 1 \times 10^6 \times 10^5 Pa = 10^{11} Pa = 10^{11} (N m)/(m^2) = 10^{11} J/m = 10^{11} (10^7 erg)/(10^6 cm^3) = 10^{12} erg/cm^3$

magnetic field produced by single wire (Ampere law / Biot-Savart Law)

[math]B[G] = 0.2 \times I(A) / r(cm) [/math]
[math]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] P_m(bar) = (2 \times B(T))^2 [/math]
[math] 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

[math] 5 \times 10^6 G \Rightarrow 1 MBar [/math]
[math] 200 \times 10^6 G \Rightarrow 1,600 MBar [/math] 

Bennett condition

• magnetic pressure = plasmakinetic pressure
• so our plasma pressure (at 100 kA at 1 um radius) is about 1,600 MBar (wau!! really??!!)