Relativistic Runaway Breakdown Model for Lightning

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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