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Relativistic Runaway Breakdown Model for Lightning



Original poster: Greg Leyh <lod@xxxxxxxxxxx>

Hi All,

An interesting paper by A.V. Gurevich and K.P. Zybin appears in the May issue of Phys Today, titled "Runaway Breakdown and the Mysteries of Lightning." If you have access to a copy of Physics Today I strongly recommend reading this article.

One of the mysteries they address is how natural lightning can originate and propagate with an average electric field of only [200kV/m] -- an order of magnitude below what is needed to breakdown air at STP [2MV/m]. They provide a compelling argument that a relativistic electron chain reaction, initially triggered by a cosmic ray-induced shower, is the principal mechanism for generating the ionization necessary to trigger the main lightning strike.

The theory for Relativistic Runaway Breakdown states that as an electrons' energy increases, the braking force due to collisions decreases as 1/energy, until the electron starts to become relativistic and reaches a 'critical runaway energy' of 0.1 to 1MeV. At this point, if the electron is in an electric field greater than about 200kV/m it will actually accelerate; it's frictive forces now being less than the accelerating forces. The relativistic electron can now ionize other atoms, spawning new relativistic electrons in a chain reaction. The electric field cannot by itself originate the first relativistic electrons, as there's too much friction on the slow, classical electrons. However, a cosmic-ray-induced shower can provide the seed electrons. The authors provide a substantial amount of fascinating data, collected from both terrestrial observation stations and from spacecraft, to support their theory.

One of the collaborating researchers, G.Milikh, recently gave an interesting powerpoint presentation outlining the Relativistic Runaway Breakdown process, and how runaway electron beams can produce some of the diffuse, high altitude discharges observed between thunderclouds and the ionosphere. Milikh's presentation can for the present time be downloaded from here:
http://www.lc.leidenuniv.nl/lc/web/2005/20050509/presentations/Milikh.ppt


This theory has some very interesting implications for large coils.
Assuming classical electron behavior, there is a critical maximum size for a disruptive coil, beyond which it's ability to produce longer sparks falls to zero. This is due to the Fo larger coils becoming so low that the minimum possible time between firings starts to exceed the ion recombination times in air, allowing the arc channel to fully extinguish between firings.


However if one allows for relativistic runaway breakdown effects, there is a critical *minimum* coil size that reaches the state where only 200kV/m is needed to generate the arc channel. Both Gurevich and Milikh calculate that the characteristic length needed in air for the exponential growth of a relativistic runaway breakdown is about 50m.
Milikh suggests that the electric field needs to be supported over a length several times this, about 150m. To achieve this scenario, a twin coil system is required with a physical scale of about 240ft high, 50ft diameter each tower, and a tower to tower spacing of about 450ft. Each tower would need to generate a peak voltage of about 15MV. These are back-of-the-envelope calculations of course, but such a coil structure is arguably practical. Perhaps the most important point, however, is that there might not be a maximum limit on coil size, but rather a 'dead zone' between the maximum classical limit and the minimum relativistic limit described above.


-GL