## Sunday, February 3, 2008

### LC POPS

A resonant circuit at the natural POPS frequency might be a way to generate POPS energy without an RF supply.

It should go in series with the DC supply and be just before the grid input connection to the reactor.

This would make any RF generated naturally synchronized with the internal oscillations of the reactor. Phasing could be adjusted some by detuning the tuned ckt.

A good low impedance capacitor from the HV input to the LC circuit to the ground side of the supply would be a very good idea.

This is beginning to look a lot like Tesla Coil country. In fact this Tesla Coil CAD program might be of some use for coil winding and calculating resonant frequencies. Or formulas if you want to check the prepackaged calculators or roll your own. A list of Tesla CAD programs. A self resonance coil calculator.

You can check them against this equation as long as the coil desired is at least as long as its diameter.

Fmhz = (29.85 x (H/D)1/5)/(N*D)

F= self resonant frequency in Mhz of an 'isolated' coil
H= coil height in meters
D= coil diameter in meters
N= total number of turns

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Update: 03 Feb 008 0714z

If the coils are made close to self resonance then a very small capacitor can be used to resonate the coil. That means the unit could be tuned over a small range by putting a sheet of dielectric between the capacitor plates.

The first thing to do is to get your fusor operating properly and then use a spectrum analyzer or 100KHz to 30 MHz radio receiver to find out what the natural frequency is.

A high frequency capacitive voltage divider with a diode detector hooked to the HV between the LC and the grid would be a good idea for tuning the coil. Tune for maximum RF.

The HV side could be from .5 to 2 pF (depending on frequency). With the low side capacitance on the order of 50 to 200pF (dependent on the high side capacitance). What you want is 100:1 divide ratio. Roughly. To start. If you use a 1N4148 diode as a detector. You should be able to go from about 100 VAC to 3000 VAC (diode limit is 3750 VAC - actually 1/2 of 75 PIV guaranteed*100). If the voltages you get are outside that range adjust your divider accordingly. The exact range is not too important as you are using it for tuning and not measurement. A voltage in the range of 5 to 10 V at peak output should give plenty of margin and yet give good tuning indication.

A lot is going to depend on lead dress. Keep everything as short as possible. The leads and everything that they contact is now part of your tuned circuit. As much as possible on the HV DC go for a single point ground.

What I'm thinking is that we have a Q multiplier here. If we use Q multiplication to raise the RF at the grid that should enhance the production of RF further raising the RF drive.

It will be interesting to see if it has any effect on fusion output. And what it does to losses.

Any way there is something like a 10% or 20 % chance we will do it this way. If it works you could control the feedback by adjusting the tuning.

Another way to tune it to start would be to use a fluorescent tube in the vicinity and tune for maximum brightness. That should be good enough to start.

Let me add one minor word of caution. We may not use this on the initial test devices until we are sure of the stability and frequency of POPS. For testing it would be more useful to have a power amplifier driven system with octave band output filters.

I have put a bit up at fusor.net about this and it seems there is an interested party. If he gets results I might change my attitude.

A while back some folks were fantasizing about how to use a Tesla coil to run a fusion machine. It looks like it might be the other way around.

Update:

Here is another design idea for how to do POPS that will be a little safer. The coil and tuning capacitor both have one end grounded. Again. A star ground for the HV will tend to reduce common mode voltages and currents.

Note that C includes coil self capacitance.

If the output of POPS is low a good rough indicator would be a NE-2 neon lamp [pdf]. Get the ones with leads. You can also raise the sensitivity by applying an AC voltage (mains power) to the lamp.

I built one of these 50 years ago when I was in the process of getting my my first Amateur license, K0NMR. They work pretty good.

Update: 04 Feb 008 0521z

Have a look at the wiki on Klystron Tubes. It uses the natural bunching of electrons to create microwave frequencies. Since we will be using ions which weigh 3600 times as much as an electron (D-D) the frequencies will be 60 times lower.

POPS oscillation is proportional to (Vwell/Mion)0.5/Rwell according to the POPS paper by Park. For a 30 KV supply voltage POPS should be around 6 MHz in a small Reactor. In any case it has a very high probability of being in the .1 to 30 MHz range.

Note that like a klystron the POPS oscillator frequency changes with operating voltage. Suppose we got an impossibly high Q of 1,000 for the tuned circuit. that would mean we needed to hold the frequency within better than .1% (1 part in 1,000) to get the maximum effect of the tuned circuit. That means holding the voltage steady to better than .2%. Difficult. Not impossible. Of course with lower Qs wider excursions are possible. It means low ripple and low voltage servo variations. Servo variations of under .1 % imply open loop gains in the passband of over 1,000. Some fun.

Say we use 80 stacked 1,000 V @ 10 A supplies. The supplies would have to regulate to better than 1 V at full output and have less than 1 V ripple. At 30 KHz operating frequency that implies an output capacitance of 22 uF @ 1500 V rating. Able to carry 5A 30KHz AC without excessive dissipation.

Since this will effectively be an 80 phase supply due to the sequential firing of the stacked modules there will be some reduction of output ripple due to the stacking. That will come in handy at lower voltages where the allowable ripple becomes less.

The allowable bandwidth of the voltage control servo is in the 1 KHz to 3 KHz range due to the 30KHz operating frequency of the switching supplies.

It may also be possible to mechanically slew the tuned circuit frequency by .2% with a speaker capable of 10 KHz response connected to a small segment of the tuning capacitor. If that was the case, as long as the system was relatively stable in the 100 microsecond time frame the tuned circuit could be kept on frequency. A VSWR detector in the HV line could do that. What you would do is compare the phase of the RF current in the line with the phase of the RF voltage on the tuned circuit and use that to servo the speaker.

Here is how POPS might be done with Amplifiers. We might need to add in an automatic phase adjuster or a PLL to keep things properly tuned up. You can click on the dwg to make it larger.

Back of the envelope calculations say that for a 50 KV DC 50 Amp grid supply (2.5 MW) an RF Amplifier capable of 250 w to 1,000 w should do the trick if using an LC circuit is not practical.

I used the wrong envelope. If the p-p voltage required is 4% of the DC voltage that represents 2,000 V p-p. That would be roughly 1,500 VRMS. Assuming a the real component of the load is 1,000 ohms (same as the DC load) that gives about 25 KW. Doubling the p-p voltage would require about 100 KW.

At those kinds of powers it may be useful to run the RF generators from the HV DC supply.

Dave said...

Very interesting.

Can't wait till we get some hard data on what POPS will do to fusion power and losses.

classicpenny said...

Sorry for my ignorance, but re POPS, several obvious (admittedly wild-eyed lunatic) questions come to my mind:
1. Will POPS work with the Polywell?
If so:
2. Could R.A. Nebel be working toward a POPS modification to the Polywell? (Considering some of his previous work at Los Alamos.)
And:
3. Would the output current of a commercially viable POPS modified p-B Polywell pulsate at the POPS frequency?
And if so;
4. Could the POPS frequency of said p-B Polywell be tuned to 60 Hz or some other frequency appropriate for a commercial power transformer?
And if so;
5. Could this possibly solve the HVDC to lower voltage AC conversion problem that has been under discussion elsewhere in this blog?

M. Simon said...

1. We don't know. The odds are good. Experiments need to be done.

2. Very likely. However, it can't be reasonably tested on a pulsed machine.

3. Yes. However, the filtering will be easy.

4. No. Not unless you make the machine impossibly large.

5. No. HVDC to AC is not a serious challenge. The design is straight forward.

Unknown said...

You are missing one important thing. Oscillations in plasma are anharmonic and the resonance frequency is function of not only ion mass and depth of the potential well. The resonance frequency also depends on the amplitude of oscillation. Any small increase or decrease in amplitude of oscillations will “detune” the resonance from your driving frequency. Therefore, all this discussion about frequency and DC voltage stability is irrelevant.

M. Simon said...

alex,

Dr. Nebel and Park who did the original research say it is amplitude invariant.

Which is fairly true of any oscillator within its limits. Think pendulum. Small perturbations in motion limits do not alter the base frequency by much. Why? The pendulum travels faster if the arcs are longer.

Unknown said...

Simon,

Yes, they tried to make oscillations harmonic and achieve amplitude invariant resonance. That could work only at very low ion concentrations, as long as ion-ion interactions can be ignored.
In order to achieve any measurable fusion, much higher ion concentration is needed. In this case, the resonant frequency increases as the ion concentration and/or oscillation amplitude goes up. The resonant frequency will increase because the ion-ion repulsion effectively stiffens restoring force non-linearly.

M. Simon said...

I'm not sure I agree with your points, but in any case it doesn't matter. You use driven POPS with HF ion gauge feedback.

M. Simon said...

As the stiffness of the spring increases the mass also increases. Now if the increase in force did not match the added mass that would be a problem. I think it does not. However all that means is that the frequency goes up as the square root of the density. At worst.

Tests will need to be done.

Lots of experiments need to be done.

M. Simon said...

Alex,

After thinking further I believe that POPS in a BFR will be different.

The frequency will just depend on the grid potential and the well depth. The grid potential/well depth being the spring and the mass of the particle will be the mass.

I'm sure compression will affect that but that should only be at one end of the cycle.

It will be interesting to see what happens in an operating reactor.