Updates on Radiative Shocks and Pulsed Jets

1D Radiative Shocks

I have been trying to come up with a better way to figure out the cooling length and thus the appropriate length scale for these runs. While I was reading through the literature, I found a better way to calculate the immediate post-shock conditions, and I made some neat plots.

The points represent some of the actual runs that I am doing based on the grid of parameters that Pat sent me. Each line represents a different shock velocity. You can see that stronger shocks get closer to that maximum compression ratio of 4. I should note that this is the initial compression ratio across the shock jump; with cooling, the density compresses much more behind the shock. Also, a decrease in beta (stronger field) results in a smaller compression ratio. Furthermore, the field has no real noticeable affect until around beta = 10, and then a much greater affect as it gets close to and less than 1.

Similarly, the immediate post-shock temperature decreases with increasing field strength.

Figuring out the cooling length is much less straightforward. This is because it depends on the cooling function lambda. Even if I had a simple function for lambda (which I don't), the cooling length that you might calculate at the shock front is not what the actual cooling length will be. This is because lambda, as well as all other variables, are changing as you move farther behind the shock. The only solution I see is to figure out the cooling length numerically on a case by case basis with trial and error. However, that's essentially what my simulation does and it defeats the purpose of trying to predetermine the cooling length.


2.5D Pulsed Jets

I found a very useful paper that covers a lot of what I am trying to do (​de Colle & Raga 2006). There are several main differences that my research will explore:

  • I will be using Pat's cooling tables which, as a reminder, include forbidden line emission.
  • The differences between helical and toroidal field geometries.
  • I have implemented the capability for pseudo-random jet velocities instead of sinusoidal pulses.
  • Results will show other emission lines besides H-alpha.
  • Eventually, moving to full 3D simulations might change the evolution.

I have a few runs of these jets with different beta. These runs are not pulsed yet, they have a constant jet velocity of 60 km/s, and they are characterized by their minimum beta.

minimum beta density beta emission
INF (hydro run)
346.6
38.2
3.11
0.026


A note on pressure profiles and beta

A lot of times, you'll see these jets defined by a plasma beta as: However, if you look at the pressure profiles, you realize that this is not the minimum beta inside the jet. The minimum beta is actually: This is the beta that I use when I characterize my jets in the above table. Alpha is a parameter that is defined by the radius at which B reaches its maximum (Rm = 0.6 for my runs). Alpha, Rm, and Bmax are not independent. You have to be careful with how you define these. For a given Rm, there is a maximum B you can use that will keep alpha and thus the thermal pressure positive. The equation for MHD equilibrium, the resulting pressure profiles, and other useful equations are given in several papers, including the one I already linked to above. Here is what the profiles look like when plotted:

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