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\begin{document}

\title{Dependence of streamer propagation on background field conditions}



\author[1]{Nikolai Lehtinen}%
\affil[1]{University of Bergen}%


\vspace{-1em}



  
  \date{May 22, 2024}


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\begin{abstract}
Positive and negative electric streamers are column-shaped discharges
which are an important stage in lightning development. The mechanism, by
which the streamer acquires a certain velocity and radius of its head,
had been a long-standing puzzle. In {[}1{]}, we proposed a parametric
streamer model (PSM), which may explain this mechanism, as well as the
mechanism of the streamer threshold electric field. The PSM results for
a positive isolated streamer in constant uniform external electric field
are verified by comparing with hydrodynamic calculations of a
`steady-state' streamer, namely a streamer whose length is kept constant
by synchronizing the position of the electrode to which it is attached
with the moving streamer head. For this particular streamer
configuration, we found that both velocity and radius of a streamer
increase with its length, a results which was also observed in
previously performed hydrodynamic calculations and experiments. Beside
the velocity and radius of the streamer, PSM allows to quickly estimate
all other streamer parameters, such as the maximum field at the streamer
tip and the field inside the streamer channel. The relatively low,
compared to, e.g., hydrodynamic or particle-in-cell (PIC) models,
computational costs of PSM suggest that generalizion of PSM principles
to more complicated streamer structures may be very valuable. In the
present work, we generalize PSM to evaluate how different background
conditions affect streamer propagation. In particular, we find that,
unlike the uniform-field case described above, (1) for the non-uniform
electric field such as that of a spherical electrode, the streamer
velocity decreases with length; (2) for a streamer propagating parallel
to other similar streamers (as in a streamer ``bunch'`), both velocity
and radius stabilize to an approximately constant value. {[}1{]} N. G.
Lehtinen, ``Physics and mathematics of electric streamers,''
Radiophysics and Quantum Electronics, 2021, in print {[}Russian version:
DOI: 10.52452/00213462\_2021\_64\_01\_12{]}.%
\end{abstract}%



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