HEDP notes

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high energy density plasma pressure

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

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

$B[G] = \frac{I[A]}{5r[cm]}$ 100 kA at 1 um radius is 200 MG

magnetic pressure

$P_{magnetic}[bar] = (2 \times B[T])^2 \sim I^2 \times R^{-2}$ $5 \times 10^6 G \Rightarrow 1 MBar$ $200 \times 10^6 G \Rightarrow 1,600 MBar$

Bennett condition

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