HEDP notes: Difference between revisions

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[https://wiki.iac.isu.edu/index.php/RS#Pulsed-power_applications_.282-LTD-driver_and_more.29 go back]
[https://wiki.iac.isu.edu/index.php/RS#Pulsed-power_applications_.282-LTD-driver_and_more.29 go back]


*high energy density plasma pressure
=high energy density plasma pressure=


<math>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>
<math>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)
=magnetic field produced by single wire (Ampere law / Biot-Savart Law)=


<math>B[G] = \frac{I[A]}{5r[cm]}</math>
<math>B[G] = \frac{I[A]}{5r[cm]}</math>
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*magnetic pressure
=magnetic pressure=


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


*Bennett condition


**  magnetic pressure = plasmakinetic pressure
=Bennett condition=


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

Revision as of 19:50, 25 September 2015

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high energy density plasma pressure

[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] = \frac{I[A]}{5r[cm]} }[/math]

100 kA at 1 um radius is 200 MG


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??!!)
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