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 XRay 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 nonMaxwellian distribution function in transient
plasmas in our paper on plasma composition simulations.
I still think that the Xrays are emitted by keVenergy 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, freefree transitions.
Obtaining quantitative results for comparison with your measurements
require detailed simulation of entier experiment. It is interesting but
huge fulltime 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 Xray
energy distribution, namely, the peaks which correspond to
onephoton 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 multiphoton 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 Xray 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 Xray 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
Xrays, 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 Xrays 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
1dimensional spark models exist at present. I am told by the plasma expert
that a 3dimensional Monte Carlo transport calculations are 1015 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.