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Bibliography: improved citations (#4513)
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* Fix up months and whitespace alignment

* Replace arxiv citations with published versions

* Author initials, Physics of Plasmas, delete empty lines, replace et al

* Comment urlretrieve in conf.py

* VayJCP13 redundant

* refs.bib author touch ups

* Uncomment conf.py

* alphabetize refs.bib entries

* Remove more "et al" from bib files

* Whitespaces and page numbers
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eebasso authored Dec 14, 2023
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8 changes: 4 additions & 4 deletions Docs/source/latex_theory/Boosted_frame/Boosted_frame.tex
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Expand Up @@ -175,7 +175,7 @@ \subsection{Numerical Stability and alternate formulation in a Galilean frame}
the simulation, and the artificial ``bump'' is again an arbitrary correction
that departs from the underlying physics.

A new scheme was recently proposed, in \cite{KirchenARXIV2016,LeheARXIV2016}, which
A new scheme was recently proposed, in \cite{KirchenPOP2016,LehePRE2016}, which
completely eliminates the NCI for a plasma drifting at a uniform relativistic velocity
-- with no arbitrary correction -- by simply integrating
the PIC equations in \emph{Galilean coordinates} (also known as
Expand Down Expand Up @@ -217,7 +217,7 @@ \subsection{Numerical Stability and alternate formulation in a Galilean frame}
\emph{themselves} are not only translated but in this case, the physical equations
are modified accordingly. Most importantly, the assumed time evolution of
the current $\vec{J}$ within one timestep is different in a standard PSATD scheme with moving
window and in a Galilean PSATD scheme \cite{LeheARXIV2016}.
window and in a Galilean PSATD scheme \cite{LehePRE2016}.

In the Galilean coordinates $\vec{x}'$, the equations of particle
motion and the Maxwell equations take the form
Expand All @@ -235,7 +235,7 @@ \subsection{Numerical Stability and alternate formulation in a Galilean frame}

Integrating these equations from $t=n\Delta
t$ to $t=(n+1)\Delta t$ results in the following update equations (see
\cite{LeheARXIV2016} for the details of the derivation):
\cite{LehePRE2016} for the details of the derivation):
%
\begin{subequations}
\begin{align}
Expand Down Expand Up @@ -271,5 +271,5 @@ \subsection{Numerical Stability and alternate formulation in a Galilean frame}
Note that, in the limit $\vgal=\vec{0}$,
(\ref{eq:disc-maxwell1}) and (\ref{eq:disc-maxwell2}) reduce to the standard PSATD
equations \cite{Habericnsp73}, as expected.
As shown in \cite{KirchenARXIV2016,LeheARXIV2016},
As shown in \cite{KirchenPOP2016,LehePRE2016},
the elimination of the NCI with the new Galilean integration is verified empirically via PIC simulations of uniform drifting plasmas and laser-driven plasma acceleration stages, and confirmed by a theoretical analysis of the instability.
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