Hi everyone, think this might be the first time i’ve posted on this forum: I’m one of many following you guys and FoFu from over at Talk-Polywell.org.

I posted this question (below) as a comment against the post at http://www.lawrencevilleplasmaphysics.com/index.php?view=entry&year=2011&month=10&day=19&id=48:new-record-fusion-yields-as-fofu-1-shows-rapid-scaling&option=com_lyftenbloggie&Itemid=90 a couple of days ago, then thought it would have been better posted here first (a feeling confirmed by the fact its just now been ‘removed’ from the comments on the other site)

My question was (from memory):

{ “rcain”::}

i wonder is there any (detailled) response to the apparent ‘saturation’ limits to theoretical scaling law, due to ‘axial phase dynamic resistance’ factor, as described in this recent paper:

http://www.mdpi.com/1996-1073/3/4/711/

{” http://www.mdpi.com/1996-1073/3/4/ “::}
...
A global scaling law for neutron yield as a function of storage
energy was uncovered combining experimental and extensive numerical data, showing that scaling deterioration has been wrongly interpreted as neutron ‘saturation’. However in keeping with conventional terminology, the effect of scaling deterioration will continue to be referred to as neutron
‘saturation’. The cause of neutron ‘saturation’ as device storage energy is increased was found to be the axial phase ‘dynamic resistance’. With the fundamental cause discovered, it is suggested that beyond ‘present saturation’ regimes may be reached by going to higher voltages, and using plasma current enhancement techniques such as current-steps.
...

(they are not totally pessimistic about the future of the DPF approach.)

i managed to find out in this forum that Eric Lerner is certainly aware of this work and the ‘dynamic resistance’, but it didn’t give away many details,

He made a short response on the FoFu forum last year ( http://focusfusion.org/index.php/forums/viewthread/746/P15 -  22 November 2010) :

{“Lerner”::}
Right now, we think that we will get to a demonstration of feasibility at around 2.8 MA, which is below Lee’s limit. Going much beyond our planned 45 kV will involve significant changes to the facility—power supply, capacitors, insulation, etc. Of course, as a practical matter, if we got very close and were on a rising curve, we should be able to stop and make major changes to increase voltage. Hopefully, that won’t be needed.

consensus on that forum seems to be that a voltage of around 90kV should ‘break the barrier’ - which, since it is expensive to rig for, Lerner is only prepared to do once all other feasibility questions have been resolved (as per his response above).

can anyone offer any further elucidation?

thanks (and apologies if i’ve inadvertently breached etiquette on my other post - but the comment button suggested i was invited to ask).

In theory - light is a wave and a particle, Schrodinger’s cat is both alive and dead, and good pitching beats good hitting.
But, sometimes theory and reality do not coincide.  That is why we play the game. 

And, it seems to me that LPPX has provided more open sourced real world data at a realistic price than any other
group out there. 

We can assume things scale up or scale back.  But, until the experiments are done - those are only
assumptions.

The experiments are presently showing scaling at I^4.7

As with any scaling, whether empirical or theoretical, it will have physical bounds.  The I^4.7 scaling is very good but other than the effects mentioned above governing factors like the inductance of the circuit and so the rise time. If the peak current is increased much more the pinch forces on the conductors will create stresses beyond that any material can withstand.  Also the Ohmic heating of the thin skin in which the current flows becomes an issue, causing differential thermal expansion and further material stresses.

Run it hard find what breaks build that steonger repeat.

This paper taolks about how difficult it is to acheive very high currents with DPF. But the FF-1 device is intended to get high fusion yeilds at curretns less than 3 MA—currents that have alreayd been acheived in other devices, like Gemini in Las Vegas.

Another interpretation of Lee’s paper on dynamic impedance is that the electrodes needs to be shaped differently in >2MA machines.  In a conventional plasma focus, the electrodes are in a coaxial geometry with right circular cylinders.  Higher neutron yields have been realized when the anode, the inner electrode, is made into a cone.  The same can be done with the cathode rods. 

The dynamic impedance is a velocity effect of the moving plasma sheet in the axial phase of the plasma focus.  You cannot slow down the plasma without reducing the yield, however, you can alter the electrodes.  The inductance of a coaxial geometry is given as the mu_0/(2*Pi)*ln(r_c/r_a)*z, where r_c is the cathode radius, r_a is the anode radius and z is the axial position and mu_0 is the permeability of free space.  If the ratio of r_c to r_a is decreasing with axial position, the effective dynamic impedance can be reduced.