Laboratory sparks and tokamak disruptions
Knowledge about spark formation has made huge progress in recent years. On the formation of laboratory sparks, see for instance: Experimental study on hard X-rays emitted from metre-scale negative discharges in air, 2015
In this experiment, the voltage applied between the electrodes is less than 1.1 MV. This means that even in the absence of any losses, the maximum energy an electron could reach is < 1.1 MeV. Nevertheless "signals" with energies substantially higher than this upper limit have been detected. Therefore the concept "pile-up" has been introduced. From the above mentioned paper:
This "pile-up" hypothesis is: coincidence of independent photons. My alternative hypothesis is: photons interdependent by stimulated emission.
Before a spark can emerge, streamers (plasma channels) have to form, which essentially are conducting pieces between the two spark electrodes. A merger of such streamers can lead to oscillations, and the spark starts with a final merger (leading to a continuous channel).
The energies measured by gamma-detectors are far too high for being simply caused by ionization radiation. Because induced emission leading to random laser pulses has been dismissed from the beginning, the only explanation seems to be high-speed "runaway" electrons, now seemingly confirmed by Relativistic electrons from sparks in the laboratory, 2016.
According to the Stefan–Boltzmann law, the power emitted per unit area of a black body is directly proportional to the fourth power of absolute temperature. As average frequency is proportional to temperature, we deduce that energy density per volume of a "typical random laser pulse" is proportional to the fourth power of frequency. In case of a pulse of a given number of coherent photons, an increase in energy per photon of 10 entails an increase in pulse energy-density of 10'000.
Another argument against a possible composition of seeming x-rays by lower-energy photons (stemming essentially from ionization energies) is this: Photons from plasma ionization are in the extreme ultraviolet range, which is "the most highly absorbed component of the electromagnetic spectrum, requiring high vacuum for transmission" (Wikipedia). Yet there are exceptions. From Free-electron laser FLASH (DESY):
Could there be other transmission windows with respect to other media for other photon-frequencies? Even in the small frequency range of visible light (from 1.8 eV to 3.1 eV), absorption depending on "attenuators" is far from being regular. Can we be sure that attenuation resp. absorption of a coherent pulse is identical to absorption of the same number of independent photons (of the same frequency)?
We cannot conclude from the average decay time of a water molecule in a given chemical environment to the decay time of a water droplet in the same environment. Because of oxidation, pure aluminum in the form of individual atoms cannot "survive" in our atmosphere. Nevertheless aluminum droplets "survive" as they get protected by an oxide layer. In a similar way, a coherent pulse consisting of numerous coherent extreme-ultraviolet resp. soft-gamma photons could behave in attenuation experiments differently from the same number of separate photons. "Reciprocal stabilization" by neighboring photons could substantially decrease absorption probability.
Also this hypothesis cannot apriori be excluded: Either (almost) all photons of a coherent pulse are absorbed almost simultaneously, or (almost) no photons of the pulse are absorbed, by analogy with the abrupt crystallization of supercooled water droplets in clouds.
The currently prevailing explanation of such gamma-pulses during spark formation (quote from the first-mentioned paper):
"Energies above 100 eV" seems innocuous, yet a kinetic energy of 100 eV corresponds to an electron temperature of around one million degrees Kelvin, and to an electron speed of 0.02 c = 6000 km/s. At this kinetic energy, friction is maximal: more than 300'000 eV/cm (see Implications of x-ray emission from lightning, Dwyer, 2004, Figure 1). In the absence of an electric field, such an electron would lose its 100 eV within a distance of only 3.3 μm (for comparison "mean free path" at ambient pressure: 0.068 μm).
In any case, an electric field stronger than 300'000 V/cm is a prerequisite for the "runaway" explanation, as an electron with v = 0.02 c needs more than 300'000 eV/cm in order to further accelerate despite friction. As average voltage between the two spark electrodes is only 10'000 V/cm, sufficiently stable regions between the electrodes with an electric field of more than 300'000 V/cm seems rather unlikely.
The hypothesis that during approximation of opposite streamers, sufficiently stable and strong enough electric fields can emerge has already been challenged in Dwyer, 2004:
In the meanwhile a similar objection seems to have been confirmed. Quotes from Increase of the electric field in head-on collisions between negative and positive streamers, 2015:
We should also take into account that drift velocities of electrons in metallic conductors are very low, typically less than 1 mm/s. Nevertheless the propagation speed of the resulting current is around 2/3 c = 200'000 km/s. There seems to be no reason to assume that (average) drift velocities of electrons during spark formation and discharge are substantially higher than drift velocities in metallic conductors, as the number of mobile electrons in plasma is not very different from metallic conductors.
This means that a "relativistic" electron would represent around 10 orders of magnitude more current than a normal electron participating in streamer and spark formation. One single electron would transport as much charge, as normally in the order of 1010 electrons do! A mechanism leading to such an uneven distribution of charge transport seems rather unlikely, especially in case of positive streamer growing: The electrons move in opposite direction of streamer propagation.
Also the damage attributed to runaway electrons in tokamak plasma-disruptions could originate from random laser pulses caused by induced emission, with photon energies substantially lower than currently assumed.
Quote from Runaway generation during disruptions in JET and TEXTOR, 2006:
From Wikipedia, Challenges in neutron detection in an experimental environment:
If the "random laser pulse" hypothesis is true, then one should prevent the formation of plasma regions which can act as gain medium for random laser pulses.
The decisive question which should be answered: Can random laser pulses consisting of extreme-ultraviolet or of soft-gamma photons be confused with hard x-rays (and with neutrons or even electrons)?
Cheers, Wolfgang
Knowledge about spark formation has made huge progress in recent years. On the formation of laboratory sparks, see for instance: Experimental study on hard X-rays emitted from metre-scale negative discharges in air, 2015
In this experiment, the voltage applied between the electrodes is less than 1.1 MV. This means that even in the absence of any losses, the maximum energy an electron could reach is < 1.1 MeV. Nevertheless "signals" with energies substantially higher than this upper limit have been detected. Therefore the concept "pile-up" has been introduced. From the above mentioned paper:
"This 2 MeV signal can only be explained by pile-up since the maximum of the applied voltage is 1.1 MV, and since ionization with two elementary charges (2e) is negligible."
This "pile-up" hypothesis is: coincidence of independent photons. My alternative hypothesis is: photons interdependent by stimulated emission.
Before a spark can emerge, streamers (plasma channels) have to form, which essentially are conducting pieces between the two spark electrodes. A merger of such streamers can lead to oscillations, and the spark starts with a final merger (leading to a continuous channel).
The energies measured by gamma-detectors are far too high for being simply caused by ionization radiation. Because induced emission leading to random laser pulses has been dismissed from the beginning, the only explanation seems to be high-speed "runaway" electrons, now seemingly confirmed by Relativistic electrons from sparks in the laboratory, 2016.
According to the Stefan–Boltzmann law, the power emitted per unit area of a black body is directly proportional to the fourth power of absolute temperature. As average frequency is proportional to temperature, we deduce that energy density per volume of a "typical random laser pulse" is proportional to the fourth power of frequency. In case of a pulse of a given number of coherent photons, an increase in energy per photon of 10 entails an increase in pulse energy-density of 10'000.
Another argument against a possible composition of seeming x-rays by lower-energy photons (stemming essentially from ionization energies) is this: Photons from plasma ionization are in the extreme ultraviolet range, which is "the most highly absorbed component of the electromagnetic spectrum, requiring high vacuum for transmission" (Wikipedia). Yet there are exceptions. From Free-electron laser FLASH (DESY):
"The water window is a wavelength region between 2.3 and 4.4 nanometers [from 280 to 540 eV]. In the water window, water is transparent to light, i.e. it does not absorb FEL light."
Could there be other transmission windows with respect to other media for other photon-frequencies? Even in the small frequency range of visible light (from 1.8 eV to 3.1 eV), absorption depending on "attenuators" is far from being regular. Can we be sure that attenuation resp. absorption of a coherent pulse is identical to absorption of the same number of independent photons (of the same frequency)?
We cannot conclude from the average decay time of a water molecule in a given chemical environment to the decay time of a water droplet in the same environment. Because of oxidation, pure aluminum in the form of individual atoms cannot "survive" in our atmosphere. Nevertheless aluminum droplets "survive" as they get protected by an oxide layer. In a similar way, a coherent pulse consisting of numerous coherent extreme-ultraviolet resp. soft-gamma photons could behave in attenuation experiments differently from the same number of separate photons. "Reciprocal stabilization" by neighboring photons could substantially decrease absorption probability.
Also this hypothesis cannot apriori be excluded: Either (almost) all photons of a coherent pulse are absorbed almost simultaneously, or (almost) no photons of the pulse are absorbed, by analogy with the abrupt crystallization of supercooled water droplets in clouds.
The currently prevailing explanation of such gamma-pulses during spark formation (quote from the first-mentioned paper):
"We now briefly describe the process of electron run-away responsible for the X-ray production... If free electrons are exposed to an electric field in ambient air, they will be accelerated in the field and lose their kinetic energy in inelastic collisions with air molecules, and in this manner they will approach some average drift velocity in the field. However, they can also get into the run-away regime, where they gain more energy in the field than they lose in collisions. For this to happen the electron need to reach energies above 100 eV; for this energy the momentum transfer collision frequency and hence the effective friction is maximal."
"Energies above 100 eV" seems innocuous, yet a kinetic energy of 100 eV corresponds to an electron temperature of around one million degrees Kelvin, and to an electron speed of 0.02 c = 6000 km/s. At this kinetic energy, friction is maximal: more than 300'000 eV/cm (see Implications of x-ray emission from lightning, Dwyer, 2004, Figure 1). In the absence of an electric field, such an electron would lose its 100 eV within a distance of only 3.3 μm (for comparison "mean free path" at ambient pressure: 0.068 μm).
In any case, an electric field stronger than 300'000 V/cm is a prerequisite for the "runaway" explanation, as an electron with v = 0.02 c needs more than 300'000 eV/cm in order to further accelerate despite friction. As average voltage between the two spark electrodes is only 10'000 V/cm, sufficiently stable regions between the electrodes with an electric field of more than 300'000 V/cm seems rather unlikely.
The hypothesis that during approximation of opposite streamers, sufficiently stable and strong enough electric fields can emerge has already been challenged in Dwyer, 2004:
"However, unless this electric field enhancement occurs very quickly, ionization and charge transport should neutralize the field, preventing this 'cold' runaway from occurring."
In the meanwhile a similar objection seems to have been confirmed. Quotes from Increase of the electric field in head-on collisions between negative and positive streamers, 2015:
"Encounters between streamers of opposite polarities are believed to be very common in nature and laboratory experiments. In particular, during the formation of a new leader step, the negative streamer zone around the tip of a negative leader and the positive streamers initiated from the positive part of a bidirectional space leader strongly interact and numerous head-on encounters are expected."
"We observe the occurrence of a very strong electric field at the location of the streamer collision. However, the enhancement of the field produces a strong increase in the electron density, which leads to a collapse of the field over only a few picoseconds. … We conclude that no significant X-ray emission could be produced by the head-on encounter of nonthermal streamer discharges."
"We observe the occurrence of a very strong electric field at the location of the streamer collision. However, the enhancement of the field produces a strong increase in the electron density, which leads to a collapse of the field over only a few picoseconds. … We conclude that no significant X-ray emission could be produced by the head-on encounter of nonthermal streamer discharges."
We should also take into account that drift velocities of electrons in metallic conductors are very low, typically less than 1 mm/s. Nevertheless the propagation speed of the resulting current is around 2/3 c = 200'000 km/s. There seems to be no reason to assume that (average) drift velocities of electrons during spark formation and discharge are substantially higher than drift velocities in metallic conductors, as the number of mobile electrons in plasma is not very different from metallic conductors.
This means that a "relativistic" electron would represent around 10 orders of magnitude more current than a normal electron participating in streamer and spark formation. One single electron would transport as much charge, as normally in the order of 1010 electrons do! A mechanism leading to such an uneven distribution of charge transport seems rather unlikely, especially in case of positive streamer growing: The electrons move in opposite direction of streamer propagation.
Also the damage attributed to runaway electrons in tokamak plasma-disruptions could originate from random laser pulses caused by induced emission, with photon energies substantially lower than currently assumed.
Quote from Runaway generation during disruptions in JET and TEXTOR, 2006:
"For the detection of the runaways the neutron rate is used. An increase of the neutron rate during the current quench was taken as indicator. In this way, runaway electrons with energies exceeding about 10 MeV are detected."
From Wikipedia, Challenges in neutron detection in an experimental environment:
"Thus, photons cause major interference in neutron detection, since it is uncertain if neutrons or photons are being detected by the neutron detector. Both register similar energies after scattering into the detector from the target or ambient light, and are thus hard to distinguish."
If the "random laser pulse" hypothesis is true, then one should prevent the formation of plasma regions which can act as gain medium for random laser pulses.
The decisive question which should be answered: Can random laser pulses consisting of extreme-ultraviolet or of soft-gamma photons be confused with hard x-rays (and with neutrons or even electrons)?
Cheers, Wolfgang
!