Fall 1997 Issue

Comments, Questions and Answers

All questions with their answers for the fall '97 issue will be posted on this page.

J. Va'vra, J. A. Maly, and P. M. Va'vra
"Soft X-Ray Production in Spark Discharges in Hydrogen, Nitrogen, Air, Argon, and Xenon Gases"

Comment from Dr. V. Fisher, Weizmann Institute, Rehovot, Israel:
"I had a pleasure to read you paper and I am going to mention it as one of demonstrations of non-Maxwellian distribution function in transient plasmas in our paper on plasma composition simulations.
I still think that the X-rays are emitted by keV-energy free electrons, which appeared in the spark due to fast compression of magnetic flux F, i.e., due to dF/dt term in the circuit equation. The emission may be caused by (i) radiative recombination, (ii) collision with the surface, and (iii) less probable, free-free transitions.
Obtaining quantitative results for comparison with your measurements require detailed simulation of entier experiment. It is interesting but huge full-time work. As I see my current plans in the lab, it is impossible to add something to them, unfortunately."
Answer from Dr. J.Va'vra (one author):
"I appretiate your suggestion to mention our paper in your paper. I understand that you are very likely to be right with the explanation based on the known physics.
However, what bugs me is that the Dirac and Schroedinger equations do allow these DDL states. Our math was checked by several independent theorists, so I have a temtation to believe that it might be OK. The experience has showed, that any valid solution of Dirac equation cannot be lightly ignored (for example, a prediction of positron). Therefore, I will still continue with my measurements. I will let you know what is new. Perhaps, at the end, I might also help in some way the plasma physics. Again, I do appretiate your comments, and I hope we can stay in touch in future."

Comment from Dr. V. Fisher, Weizmann Institute, Rehovot, Israel:
"I would accept new physics if you would measure new peaks in the X-ray energy distribution, namely, the peaks which correspond to one-photon radiative transitions between the DDLs."
Answer from Dr. J.Va'vra (one author):
"The classical theory of transitions between atomic states is based on the perturbation theory, i.e., it assumes that the transition is a small perturbation. Indeed, for normal atomic transitions only a single photon is emitted. This may not be true for transitions between the normal atomic states and the DDL states, where energy level separation is large (for example, ~500 keV for hydrogen). A new theory of atomic transitions may have to be introduced, which could yield a multi-photon emission. If that would be the case, a measurement of a single photon would not yield peak in the energy distribution.
However, one should expect single photon emissions when one is dealing with transitions between the DDL states only.
We have looked (Table IV in J. A. Maly, J. Va'vra, "Electron Transitions on Deep Dirac Levels IV. Electron densities in the DDL atoms", Submitted to Fusion Technology, September 11, 1995) at the absorption spectra from our Sun taken from Ch. Moore et al.,"The solar spectrum 2935 A to 8770 A", National Bureau of Standards, 1966. Interesting point is that there are some measured absoption lines which are not identified, and could be close to our DDL model predictions. For example, we predict lines 3671.10, 4322.86, 5400.25 A; the nearest unidentified measured lines are 3671.090, 4322.828 and 5400.263 A. Clearly, the whole problem of matching of the predicted DDL lines and the observed lines from the stars, such as our Sun, has to be studied in more detail, and I have not done that yet to my satisfaction. For example, some other examples of close matches in our Table IV are corresponding to identified measured lines, but I am not sure how well or if there is some ambiguity, etc. Finally, one has to match also lines in the X-ray and UV regions."

Comment from Dr. G. Godfrey, SLAC:
"Could the plasma hot spots be related to local "Thermal Bremsstrahlung" spots with the extremely high temperatures (>10**8 degK), which are then responsible for the X-ray spectra ? In the paper you mention it as one of the possibilities, but exclude it, based on the argument that the majority of photons liberated in the spark are visible photons, and therefore one deals with much smaller temperatures on average."
Answer from Dr. J.Va'vra (one author):
"This is perhaps a question for the plasma theorist. I would argue that the "Thermal Bremsstrahlung" needs the establishment of some sort of thermal equilibrium, which is difficult to imagine on the scale of few hundred nanoseconds. Dr.Fisher argues that the fast electrons are created by the fast compression of the magnetic flux, i.e. a dF/dt term in the circuit equation".

Comment from Dr. G. Godfrey, SLAC:
"I would say that there may be enough time to reach the thermal equilibrium. I would use the following simple minded arguments:
1) Let's assume that the gas has a pressure of 10**-4 atm. The mean free path in argon gas is about Lambda ~0.1cm. The electron energy gain during this mean free path is Ee ~ 1e x 10**3 V/cm x 0.1cm = 100eV.
2) The column of ionized gas begins to grow, electrons going across the spark gap in ~1usec, positive ions in ~1msec. This results in increase of the magnetic field B aroung the column of electrons, which creates a pressure on the electrons and ions within the column.
3) The magnetic pressure is proportional to B**2 ~ 1/r**2. It squeezes the electron column until a balance is reached between the magnetic pressure and the gas pressure. Since Ee ~ 100eV and the experiment detects ~10keV X-rays, one could argue that the magnetic field creates a compression factor of about 100. Therefore the mean free path Lambda = 0.1 cm/100 = 10 um. An electron of 10keV will have velocity of about 6x10**9cm/sec, which gives the mean free time between collisions tau = 10um/(6x10**9cm/sec) = 0.1 psec between collisions. In 100 ns interval, when the X-rays are produced, one could have N=100ns/0.166psec = 6x10**3 collisions. This is a lot of collisions, which means that the electrons could thermalize."
Answer from Dr. J.Va'vra (one author):
"This looks like a plausible qualitative argument to me. Perhaps, the "Thermal Bremsstrahlung" is one of the possible explanations. However, it is not simple to do the correct calculations in such sparks. Only 1-dimensional spark models exist at present. I am told by the plasma expert that a 3-dimensional Monte Carlo transport calculations are 10-15 years away. Therefore I do not know if one can reach such high temperature (>10**8degK) in these plasma points in our experiment. Of course, the authors were interested to prove the DDL model as a possible explanation. Clearly, this is yet to be done".

Comment from Dr. G. Godfrey, SLAC:
"Have you considered that the "Ball Lightning" may be the higher pressure version of your 10um 10**-4atm plasma points ?"
Answer from Dr. J.Va'vra (one author):
"No, I did not. What a interesting idea."

Last modified: 3 Feb 1998, Jochen.