HEDP notes

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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 (Ampere law / Biot-Savart Law)

[math]\displaystyle{ B[G] = 0.2 \times (I[A]) / (5r[cm]) }[/math]

[math]\displaystyle{ B[T] = 0.2 \times (I[kA]) / (5r[mm]) }[/math]

• • 100 kA at 1 mm radius is 0.05 T

• • 10 MA at 4 mm radius is 500 T

• • 100 kA at 1 um radius is 20 kT

magnetic pressure

[math]\displaystyle{ P_{magnetic}[bar] = (2 \times B[T])^2 \sim I^2 \times R^{-2} }[/math]

[math]\displaystyle{ 5 \times 10^6 G \Rightarrow 1 MBar }[/math]

[math]\displaystyle{ 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??!!)