Acceleration of charged particles to extremely large energies by a sub-Dreicer electric field
Acceleration of a fraction of initially low-energy electrons in a cold, collisional plasma to energies orders of magnitude larger than thermal is shown to be possible with a sub-Dreicer electric field. Because such an electric field does not satisfy the runaway condition, any acceleration will be statistical. Random scattering collisions are probabilistic such that there is 63% chance that a particle collides after traveling one mean free path and a 37% chance of not colliding. If one considers only the electrons that do not collide on traversing a mean free path and also considers that the collisional mean free path scales quadratically with particle kinetic energy, one realizes that there will be a small fraction of electrons that never collide and are accelerated to increasingly high energy. Because the mean free path scales quadratically with kinetic energy, after each successfully traveled mean free path, continued acceleration becomes more likely. This model is applied to an MHD-driven plasma jet experiment at Caltech and it is shown that electrons are accelerated by an electric field associated with a fast magnetic reconnection event occurring as the jet breaks apart. This statistical acceleration model indicates that a fraction ∼1.3 × 10^(−7) of electrons with initial energy distributed according to a Maxwellian with T = 2 eV will be accelerated to 6 keV in the Caltech experiment and then collide to produce the observed X-ray signal. It is shown that the statistical acceleration model provides a credible explanation for the production of solar energetic electrons.
© 2019 Published under license by AIP Publishing. Submitted: 15 November 2018; Accepted: 11 March 2019; Published Online: 2 April 2019. This material is based upon the work supported by the NSF/DOE Partnership in Plasma Science and Engineering via the U.S. Department of Energy Office of Science, Office of Fusion Energy Sciences Award No. DE-FG02-04ER54755 and by the Air Force Office of Scientific Research via Award No. FA9550-11-1-0184.
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