To do a proper RF drive design, assuming I can extrapolate more or less correctly from the numbers in the Miley book, we needed to know
the dynamic impedance of the main grid, and in this case, were curious how it might have changed with the ion source on or off.
So, we took numbers both ways - and we got the expected different results. With no ion source, more main grid current results in more ions, and thus more conductivity, making the curve "steeper". When the ion source is on, most all the gas is ionized already, and the curve is flatter and more linear.
Thanks to Bill for sitting behind the toolbox and writing down rapidly shouted numbers for an afternoon!
Here's the raw stuff:
And here with the ion source on (and a little less gas so we didn't fry things)
Now, these were the numbers reported on the power supply. Those don't tell you there's loss in the ballast R, which in our case is 50k.
So, I wrote a perl program to correct for that loss, then curve fit a least squares line, and calculate the resistance. The sharp-eyed will note we are NOT dealing with pure R here, it's more like a zener or a neon bulb, hence the intercept being negative - the current rises more quickly with voltage than a pure resistor would in either case, just that it's even more without the ion source, due to more current making more ions and even more conductivity, whereas with the ion source on, it's pretty much all already "there".
To generate this output, I manually averaged where there were more than one current value per voltage setting - things were moving around a little during these runs as the temperature changed. You might also notice that for each run, we did it "both ways", in other words, starting at high voltage and working down, letting things cool, the starting at low voltage and working up. This should have smeared out some of the "cleanup" or gas loss we were seeing during the runs. No adjustment was made deliberately during any run, it's just that when starting from very clean (haven't run for awhile), we manage to get some gas to implant into the fusor walls, and it's lost for awhile, especially if it's "far from the action".
For what it's worth, we hit 3.1 million neutrons/second on the second run at max power input in the "stable DC" mode most use for a fusor.
Here's the report and results of the perl script run:
It's the last line of each run that shows the least-squares fitted resistance
for the values we got today. The R on each lines assumes a linear resistor
that would have an intercept at 0,0, but we don't have that here, we have something more
like a zener diode or neon bulb. So that's why we took all those numbers.
The program corrected the KV readings you took (in the BL1.raw and BL2.raw files)
to the actual kv seen at the grid through the 50k ballast resistor.
I manually averaged the cases with 2 currents at the same volts.
This isn't precise to N decimals, it's just a rough number, but we
had NO number before. Now we have one and I can do a real design.
You will notice (I hope) that the effective resistance/impedance is much
greater (I used the word flatter curve) with the ion source on.
That's because everything was already ionized, and futher main grid current
didn't cause more ionization and thus more conductivity.
The result is that the AC load on the RF will be less with the ion source on.
Notice that the computed resistance just using one number is way the heck off, that's because this isn't really a resistor, it has a funny I/V shape. That's why we took the extra data and fitted it.
And now I can design a proper tank circuit for an RF amplifier to drive tihs guy in POPC mode.
Console output from runs:
doug@dev ~/Public/FusorAq/Sept3_2014 $ ./balcor BL1.raw // this is without the ion source
new kv:50.05, ma:25.0, R, Mohm 2.002
new kv:48.4, ma:12, R, Mohm 4.03333333333333
new kv:47.4525, ma:10.95, R, Mohm 4.33356164383562
new kv:45.61, ma:7.8, R, Mohm 5.8474358974359
new kv:44.67, ma:6.6, R, Mohm 6.76818181818182
new kv:39.845, ma:3.1, R, Mohm 12.8532258064516
new kv:41.735, ma:5.3, R, Mohm 7.87452830188679
new kv:42.715, ma:5.7, R, Mohm 7.49385964912281
new kv:43.645, ma:7.1, R, Mohm 6.14718309859155
new kv:44.61, ma:7.8, R, Mohm 5.71923076923077
new kv:45.575, ma:8.5, R, Mohm 5.36176470588235
new kv:46.5, ma:10, R, Mohm 4.65
new kv:47.65, ma:11, R, Mohm 4.33181818181818
new kv:48.385, ma:12.3, R, Mohm 3.93373983739837
new kv:49.25, ma:15, R, Mohm 3.28333333333333
Slope:1.53359108737799, intercept:-60.2690228744591
Fitted R = 0.652064300732026 Megohm
doug@dev ~/Public/FusorAq/Sept3_2014 $ ./balcor BL2.raw // this is WITH the ion source, effective R is larger
new kv:39.56, ma:12.8, R, Mohm 3.090625
new kv:39.785, ma:12.3, R, Mohm 3.23455284552845
new kv:41.675, ma:12.5, R, Mohm 3.334
new kv:44.35, ma:13, R, Mohm 3.41153846153846
new kv:46.3, ma:14, R, Mohm 3.30714285714286
new kv:47.59, ma:14.2, R, Mohm 3.35140845070423
new kv:49.635, ma:15.3, R, Mohm 3.24411764705882
new kv:49.395, ma:18.1, R, Mohm 2.72900552486188
new kv:47.29, ma:14.2, R, Mohm 3.33028169014085
new kv:44.385, ma:12.3, R, Mohm 3.60853658536585
new kv:41.69, ma:10.2, R, Mohm 4.08725490196078
new kv:39.525, ma:9.5, R, Mohm 4.16052631578947
Slope:0.490406518102305, intercept:-8.50784452379852
Fitted R = 2.03912461006766 Megohm
doug@dev ~/Public/FusorAq/Sept3_2014 $
It's really not a lot of code, and due to CPAN, I didn't even have to write the tweaky parts anyway.
Zipped because the board won't eat anything the looks like code - it might be dangerous.
Note we still don't have any actual clue about what the real AC (or would that be complex/imaginary) impedance is yet. But now I know how to design an inductor that I can use as a transformer secondary and measure that and have it not be so far off I can't get a measurement. There's obviously some stray capacity to ground even in a vacuum. Now, with massive charged (both flavors) particles in there...well, we'll just measure it vs frequency in the range of interest.
Sometimes the universe is its own best model and it runs in real time. If any math geeks beat me to the punch here, that's fine, you have my admiration - in particular if what you come up with has any relation to what I measure, which thing at least I'm good at.