Voltage and current - what are the lower/upper/ideal limits?

[waltsphotos]

as a primer I quote from a post of Richard's,

"Voltage changes and current changes in any given device will have easily understood functions. More voltage = More probablitiy of fusion...to a point...easily ploted on a already extant cross sectional curve. More current = More ions that are avaialble for fusion. And, that is that."

so I ask what are the lower/upper/ideal limits of current and voltage for fusion?

I have asked this question in part in a previous post: what is the lowest voltage needed to get fusion?
Richard Hull answered it saying 10Kv is the lowest "recorded"

I the upper limit (before drop off) I read once as being near 500Kv

and the Ideal being near 150Kv

As for current....

What is the lower limit of Current?
what is the Ideal?
What is the upper limit?
(yes, I know, like voltage this is some what limited by feedthoughs)

so the point of my question; I believe that with a high enough current , the lower limit of voltage to get fusion could be lower. ie higher current has higher electrostatic pressure and therefore would have higher fusion rates due to higher ion density.

[Raymond Jimenez]

Hi Walt,

The problem with current is that current and pressure are directly related. So, as you increase current at a given voltage, the pressure also has to increase. When pressure goes up, you get a shorter mean free path, which means that the fusor gets less and less ideal (ie due to collisions you rarely get ions actually traveling at the target energy).

This is why you can run several amps at maybe 8kV and not see anything, though the cross-section graph is still above zero.

What I've experienced is that you need to increase voltage if you need to increase amps. The better question to ask might be what the most efficient combination of volts/amps/pressure is.
(Though it'll probably vary widely from fusor to fusor...)

Raymond J

[Chris Bradley]

This comes down to a question about the change of reaction rate with collision energy (= drive voltage).

The fusion cross-section is an exponential function of the collision energy, but the actual propability rate of interactions is also increased with an increase of velocity (which corresponds to sqrt collision energy) so the overall reaction rate is a more complex function of drive voltage and for DD ramps up very quickly around 10kV drive voltage.

'Beam Current' is simply the total number of particles at that energy, so double the beam current should simply, and only, double the rate. (I presume beam current and drive current are linearly linked, for the purposes of this discussion.) Whereas double the drive voltage from 8kV to 16kV will bring on a ~ x66 increase in reaction rate (by my calculations). But after that the increase is not so great and once you're into the 30-100kV range you may be as well off to increase current than try to increase voltage (if you're limited to a particular power maximum). I did a graph on reaction rates against drive voltage somewhere on this site that is based on certain assumptions that I think are correct.

If the fusor is behaving in a dark discharge 'Townsend regime' (I presume they may function in this regime for certain pressures/voltages) then you should find that voltage becomes self-limiting to some maximum (within a small range), yet you can dial up whatever current you want up to the point that you get a breakdown condition and a glow discharge results. So if you crank up the voltage on a fusor, I presume (though not having a working one limits my ability to check experimentally) that it will tend to top itself out at high voltages nudging breakdown voltage. So the fusor might well answer your question for you!

[Carl Willis]

There is no physical "lower limit" on voltage. The DD reaction is exothermic, kinematically possible at any energy. The lowest voltage for measurable fusion (with large He-3 detectors) is in the ballpark of 5 - 10 kV, as various experimenters have found.

An upper voltage limit, from only the nuclear efficiency perspective, would relate to how much loss occurs to competing, endothermic reactions (Oppenheimer-Phillips, a.k.a stripping, which requires 2.2 MeV to happen). Since little is to be gained in the way of thick-target yield from the DD fusion reactions above a few hundred keV, and since the onset of stripping losses would occur at about 500 kV applied voltage, there's practically nothing to be gained by exceeding 500 kV. The thick-target yield's relation to voltage depends in a complicated way on how exactly the particular fusor works: whether it is a high-vacuum gunned approach with a narrow particle energy spectrum, a medium-vacuum hollow-cathode-discharge approach with a wide particle energy spectrum, a machine with a radially-bunched beam, etc.

There is no physical lower limit or upper limit on current. All other variables being held constant (not possible in most experimental setups), yield would be expected to be proportional to a * I^2 + b * I where a and b are coefficients that depend on the machine. The b applies if the yield comes from charged-neutral collisions, the a applies if the yield comes from beam-on-beam collisions. In reality there will always be contributions from both kinds of collisions. As current rises, the squared term dominates. It pays to have arbitrarily high current.

-Carl

[Chris Bradley]

Carl refers to theory on the coefficients 'a' and 'b'. It is inevitable that 'a' is a real, finite value and no doubt will vary between different set-ups, fuels and pressures. I would, however, suggest it is safer to presume 'b' is considerably larger than 'a' by orders of magnitude in the first instance, if it is a matter of practical experimental planning. That is; if you're planning an experiment to examine the effect of ramping up the current with stable voltage (and please do!), then don't plan on getting an I^2 factor increase in output, just an I factor. If you get more than this, then that'd only be for the better!

[Richard Hull]

It is important to remember we all have real world electrodes in this system.

When speaking of limits, the ultimate limit is a combination of voltage and current relating to the dissipation of energy allowed before the electrodes, (most normally the inner grid), melts.

So, theoretically, there is no real limit on current at any voltage where you aren't stripping, until the real world muscles its way into one's theoretical dream world and the grid melts, ending all fusion.

In short, there is no answer to the original question posed that is satisfying or even workable without several paragraphs of gotcha's, catch 22's, theoretical limitations linked to mechanical and electrical bothers to get you tangled up in your own underwear.

It is rare in the fusion biz where the realty of operation is a striaght forward process that is cut and paste to the point where you have a simple "volume control" to turn up the reaction.

The reason?.....Nature doesn't want a universe made up of almost pure fuel, being easy to burn; or, once going in localized areas, catch everything else ablaze.

Richard Hull