FFS Research

[jamesr]

The link to the pdf doesn’t seem to work for me.

[asymmetric_implosion]

I’m having trouble with the link as well.

From the description it seems interesting, but 2D, two-fluid MHD simulations of the plasma focus have been around since the 1970’s (D. E. Potter). The problem moving forward seems to be how to go from a fluid approximation to a kinetic calculation. The pinch conditions don’t lend themselves to fluid approximations. Some recent work by Dale Welch in Physics of Plasmas describes full kinetic simulations of a Z-pinch implosion. In addition to the usual complications of the particle transport, is the radiation from the boron going to create problems due to opacity? Kinetic simulation is hard and radiation transport added to kinetic simulation is beyond state of the art in published lit.

[BSFusion]

Multiphysics

[jamesr]

In lieu of the google docs link working, can you email me the pdf directly. Cheers.

I wasn’t going to comment on the write-up until I’d read the full paper, but since asymmetric already mentioned it, I too am surprised a two/multi-fluid approach would capture the behaviour properly. The kinetic vs fluid debate rages on in most areas of plasma physics. My own research, for example, uses 3D two-fluid simulations for modelling turbulence driven oscillations in the steep edge density & temperature gradient region of tokamaks, where it wins out over gyrokinetics. It really depends on what assumptions you make to simplify it (I make a lot!!), and what higher moments you include in the energy, heat flux etc to close the set of equations.

The horrible radiation terms are definitely what makes the problem hard, and I guess are the main reason for going fluid rather than PIC.

I can sympathise with Warwick on the numerical difficulties of capturing the shocks properly, thankfully I don’t get those.

I too busy right not trying to write up my thesis, but I’d be interested to know the initial conditions for the simulation (if its not detailed fully in the paper) so it could be replicated in other codes, There is a new rad-hydro code being developed in my department using a new variant of an ALE (Arbitrary Lagrangian Eulerian) type method, which although aimed at laser-plasma interactions may one day be able to cope with DPF type conditions.

[asymmetric_implosion]

BSFusion wrote: Multiphysics

In what context? How do you go from using a fluid assumption to a kinetic description when you have to track extra variables you didn’t track before? You have to make assumptions on the transition. Depending on the problem the assumptions are reasonable. The plasma focus does not lend itself to a nice transition. I know a group at Livermore is working on a pure kinetic simulation and it takes days of computational time on something like 100 processors and they model only the last 100 ns of the implosion. Fluid-kinetic hybrids have yet to demonstrate agreement with experimental data. MHD models have generally been better when everyone knows they don’t work. Another group in the UK is working the problem on the plasma focus. I’m not familiar with Dr. Dumas, but the Imperial College group has a solid computational base and a 3D MHD code as a starting point.

[benf]

The link to the PDF is fixed now, sorry for the hang up.

[jamesr]

benf wrote: The link to the PDF is fixed now, sorry for the hang up.

Thanks Ben.

Warwick/Eric/John,

I realise the paper is still work-in-progress, and the model as a whole seems a pretty solid 1D scheme. But one thing struck me, you seem to be assuming the ions are singly charged, so the quasi-neutrality condition is simply n = n_e = n_i, and subsequently the current is J_z=qn(v_e – v_i). Would it not be easier to set the ion species charge as q=Ze, so
n=n_e = Zn_i and J_z=en(v_e – Zv_i). The step up from a deuterium plasma to one with a higher Z_effective is then carried through in all the equations.

You can say these simulations are for deuterium so Z=1, but having it explicitly in the equations always seems clearer to me.

[em]NB: read underscores as Latex style subscripts[/em]

I look forward to seeing the full results when finalised

[jamesr]

Just watching the video http://www.youtube.com/watch?v=Mg3KU8pkoEc. I see the shock issues are still there to some degree. Do you not have any shock viscosity term? I thought this would be essential, unless you go to a more involved (but much better physically) Godunov type scheme with an iterative Riemann solver.

It would also be interesting to see in addition to the density & temperature(s) evolution, the pressure, magnetic pressure and total pressure evolution (and plasma beta), as there are stages where across the shock it switches from high temperature/low density to low temp/higher density suggesting the shock in pressure is much weaker. This is also, I seem to remember, why a lot of codes use density and ion/electron pressure as their fundamental variables or even density and total energy, rather than density & temperatures.

[benf]

There are actually two videos to view:

Video 1

“This simulation of a current filament in a plasma focus fusion device shows the outward motion of a shock wave (black density line) and its reflection back from a neighboring filament, disrupting it before magnetic fields could pinch it to high density.”

Video 2

“This simulation of a current filament in a plasma focus fusion device shows the outward motion of a shock wave (black density line) and its reflection back from a neighboring filament. Because of the greater spacing to the neighbor, there is enough time for magnetic fields to pinch it to high density. But that process will be visible only in upcoming 2-D simulations that show the motion of the filament. Stay tuned!
”

(Simulations generated by Focus Fusion Society-LPP team of Dr. Warwick Dumas, Dr. John Guillory and Eric Lerner)

[ikanreed]

How do you validate the simulation?

It’s nice to know that we’re working on simulating plasmas better, but how can you validate that the simulation was programmed correctly? As a software developer myself, I know that every piece of code has at least a few bugs. Is there some kind of well known test-case to compare against?

[asymmetric_implosion]

Depending upon the simulation there are test cases that have analytical solutions that can be compared to. Sadly, the most common test is to take experimental data and compare. I say sadly because the limited shot rate and the ability of diagnostics to resolve all the key parameters is limited. My observation of high density plasma simulation codes on devices like plasma foci is to keep patching the code until it gives you the same answer as the experiments within reason. Even after these comparisons, the codes don’t always conserve all the necessary parameters like momentum, energy and mass.

[Francisl]

Here is some related research. I don’t see any reference to hard data but maybe they could be convinced to collect some.

[Warwick]

jamesr wrote:

The link to the PDF is fixed now, sorry for the hang up.

I realise the paper is still work-in-progress, and the model as a whole seems a pretty solid 1D scheme. But one thing struck me, you seem to be assuming the ions are singly charged, so the quasi-neutrality condition is simply n = n_e = n_i, and subsequently the current is J_z=qn(v_e – v_i). Would it not be easier to set the ion species charge as q=Ze, so
n=n_e = Zn_i and J_z=en(v_e – Zv_i). The step up from a deuterium plasma to one with a higher Z_effective is then carried through in all the equations.

You can say these simulations are for deuterium so Z=1, but having it explicitly in the equations always seems clearer to me.

You make a valid point, but the model changes to do p-B11 will actually have to be a lot more complicated. We are now contemplating a model with many different species (still in context of deuterium) which clearly would be different with decaborane.

[Warwick]

jamesr wrote: Just watching the video http://www.youtube.com/watch?v=Mg3KU8pkoEc. I see the shock issues are still there to some degree. Do you not have any shock viscosity term? I thought this would be essential, unless you go to a more involved (but much better physically) Godunov type scheme with an iterative Riemann solver.

It would also be interesting to see in addition to the density & temperature(s) evolution, the pressure, magnetic pressure and total pressure evolution (and plasma beta), as there are stages where across the shock it switches from high temperature/low density to low temp/higher density suggesting the shock in pressure is much weaker. This is also, I seem to remember, why a lot of codes use density and ion/electron pressure as their fundamental variables or even density and total energy, rather than density & temperatures.

I do not know what exactly you mean by a shock viscosity term. The approach here is simply Backward Euler, applied to a spatially discretised scheme that is not exactly finite volume, but has a finite volume sort of feel to it. The approach presently being investigated for 2D is different.

The red curve on the bottom left plot is thermal pressure.

[Warwick]

ikanreed wrote: How do you validate the simulation?

It’s nice to know that we’re working on simulating plasmas better, but how can you validate that the simulation was programmed correctly? As a software developer myself, I know that every piece of code has at least a few bugs. Is there some kind of well known test-case to compare against?

The code for the next iteration will be open source so there will be some scope for interested people to try and spot mistakes for themselves.

[Author]

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