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 defined as a plasma with pressure above 1 MBar=
=high energy density plasma is a plasma with pressure above 1 MBar=
<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 (Biot-Savart Law)=


<math>B[G] = 0.2 \times I(A) / 5r(cm) </math>
<math>B[T] = \mu I / ( 2\pi r ) </math>


<math>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
*10 MA at 4 mm radius is 500 T
*100 kA at 1 um radius is 20 kT
*100 kA at 40 um radius is 500 T
*160 kA at 5 um radius is 6,400 T


=magnetic pressure=


<math> P_m(bar) = 4 \times B(T)^2 </math>
<math> P_m(bar) = 0.16 \times I(kA)^2 \times R(mm)^{-2} </math>


=magnetic pressure=
*10 MA at 4 mm radius is 1 MBar
<math> P_{magnetic}[bar] = (2 \times B[T])^2 \sim I^2 \times R^{-2} </math>
*100 kA at 40 um radius is 1 MBar
*160 kA at 5 um radius is 164 MBar


<math> 5 \times 10^6 G \Rightarrow 1 MBar </math>
=Bennett condition=
*magnetic pressure = plasmakinetic pressure


<math> 200 \times 10^6 G \Rightarrow 1,600 MBar </math>


*14 MBar at 140 kA at 15-um radius (shot 634 with 2x30-um W wires)
*25 MBar at 150 kA at 12-um radius (shot 657 with 2x30-um Mo wires)
*100 MBar at 154 kA at 6-um radius (shot 657 with 2x30-um Mo wires)


=Bennett condition=
=Links=
* magnetic pressure = plasmakinetic pressure
*[http://www.nap.edu/read/10544/chapter/1 Frontiers in High Energy Density Physics THE X-GAMES OF CONTEMPORARY SCIENCE]
* so our plasma pressure (at 100 kA at 1 um radius) is about 1,600 MBar (wau!! really??!!)

Latest revision as of 18:13, 31 May 2017

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high energy density plasma is 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 (Biot-Savart Law)

[math]\displaystyle{ B[T] = \mu I / ( 2\pi r )  }[/math]
  • 10 MA at 4 mm radius is 500 T
  • 100 kA at 40 um radius is 500 T
  • 160 kA at 5 um radius is 6,400 T

magnetic pressure

[math]\displaystyle{  P_m(bar) = 4 \times B(T)^2  }[/math]
[math]\displaystyle{  P_m(bar) = 0.16 \times I(kA)^2 \times R(mm)^{-2}  }[/math]
  • 10 MA at 4 mm radius is 1 MBar
  • 100 kA at 40 um radius is 1 MBar
  • 160 kA at 5 um radius is 164 MBar

Bennett condition

  • magnetic pressure = plasmakinetic pressure


  • 14 MBar at 140 kA at 15-um radius (shot 634 with 2x30-um W wires)
  • 25 MBar at 150 kA at 12-um radius (shot 657 with 2x30-um Mo wires)
  • 100 MBar at 154 kA at 6-um radius (shot 657 with 2x30-um Mo wires)

Links

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