Difference between revisions of "HEDP notes"

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

100 kA at 1 um radius is 200 MG


magnetic pressure

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

[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??!!)