%
%  address and date declarations
%
%\newcommand{\address}{
%\centerline{Institute for Fusion Studies}
%\centerline{The University of Texas at Austin}
%\centerline{Austin, Texas~~78712} }
%
%\newcommand{\addresstwo}{
%\centerline{Department of Physics and Institute for Fusion Studies}
%\centerline{The University of Texas at Austin}
%\centerline{Austin, Texas~~78712} }
%
%\newcommand{\today}{\ifcase\month\or January\or February\or March\or April\or
%May\or June\or July\or August\or September\or October\or
%November\or December\fi\space\number\day, \number\year}
%
%  latin
%
\newcommand{\etal}{\mbox{\em et al.\/}}
\newcommand{\adhoc}{\mbox{\em ad hoc\/}}
\newcommand{\perse}{\mbox{\em per se\/}}
%
%  Bold-face
%
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\newcommand{\bfC}{{\bf C}}
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\newcommand{\bfY}{{\bf Y}}
\newcommand{\bfy}{{\bf y}}
\newcommand{\bfZ}{{\bf Z}}
\newcommand{\bfz}{{\bf z}}
%
%  Bold-face Greek
%  PMB stands for "poor man's bold"
%
\newcommand{\pmb}[1]{ \setbox0=\hbox{$#1$}\kern-.025em\copy0\kern-\wd0
              \kern.05em\copy0\kern-\wd0\kern-.025em\raise.0385em\box0 }
%
\newcommand{\bfepsilon}{\pmb{\epsilon}}
\newcommand{\vdel}{\pmb{\nabla}}
\newcommand{\del}{\pmb{\nabla}}
%
%  Calligraphic
%
\newcommand{\clA}{{\cal A}}
\newcommand{\clC}{{\cal C}}
\newcommand{\clE}{{\cal E}}
\newcommand{\clF}{{\cal F}}
\newcommand{\clL}{{\cal L}}
\newcommand{\clO}{{\cal O}}
\newcommand{\clP}{{\cal P}}
\newcommand{\clR}{{\cal R}}
\newcommand{\clS}{{\cal S}}
\newcommand{\clW}{{\cal W}}
%
%  Math equation environments--abbreviations
%
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\newcommand{\beqs}{\begin{eqnarray}}
\newcommand{\eeqs}{\end{eqnarray}}
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\newcommand{\eeqsn}{\end{eqnarray*}}
\newcommand{\bdarr}{\begin{array}}
\newcommand{\edarr}{\end{array}}
\newcommand{\bdarrn}{\begin{array*}}
\newcommand{\edarrn}{\end{array*}}
%
%  derivative macros 
%
\newcommand{\pa}{\partial}
\newcommand{\ppi}[1]{ \frac{\partial}{\partial #1} }
\newcommand{\ppii}[1]{ \frac{\partial^2}{\partial {#1}^2} }
\newcommand{\ppai}[2]{ \frac{\partial #1}{\partial #2} }
\newcommand{\ppaii}[2]{ \frac{\partial^2 #1}{\partial {#2}^2} }
%
\newcommand{\ddi}[1]{ \frac{d}{d #1} }
\newcommand{\ddii}[1]{ \frac{d^2}{d {#1}^2} }
\newcommand{\ddai}[2]{ \frac{d #1}{d {#2}} }
\newcommand{\ddaii}[2]{ \frac{d^2 #1}{d {#2}^2} }
%
%  miscellaneous constructions
%
\newcommand{\newsection}[1]{\vspace*{0pt} { \parindent 0pt \centering
	\large \bf #1\par \nobreak \vskip 30pt   } }
%
\newcommand{\bothfct}[2]{\left\{\begin{array}{c}#1\\ #2\end{array}\right\}}
%
%  miscellaneous math symbols
%
\newcommand{\kpar}{k_\parallel}
\newcommand{\kper}{k_\perp}
\newcommand{\vpar}{v_\parallel}
\newcommand{\vper}{v_\perp}
\newcommand{\deltatee}{\delta t}
\newcommand{\Deltatee}{\Delta t}
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\newcommand{\akapc}{\kappa_\chi}
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\newcommand{\epsc}{\epsilon_\chi}
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\newcommand{\rmax}{r_{\rm max}}
\newcommand{\barDelti}{\bar\Delta_i}
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\newcommand{\lar}{\leftarrow}
\newcommand{\ora}{\overrightarrow}
\newcommand{\ola}{\overleftarrow}
\newcommand{\oda}{\overdoublearrow}
\newcommand{\ti}{\tilde}
\newcommand{\delsq}{\nabla^2}
\newcommand{\delsqc}{\delsq_c}
\newcommand{\onehalf}{\frac{1}{2}}
%
\def\nms{\mathsurround=0pt}
\def\gtapprox{\mathrel{\mathpalette\overapprox>}} % greater than or approx.
\def\ltapprox{\mathrel{\mathpalette\overapprox<}} % less than or approx.
\def\overapprox#1#2{\lower 2pt\vbox{\baselineskip 0pt \lineskip - 1pt
    \ialign{$\nms#1\hfil##\hfil$\crcr#2\crcr\approx\crcr}}}
\def\gtsim{\mathrel{\mathpalette\oversim>}} % greater than or sim.
\def\ltsim{\mathrel{\mathpalette\oversim<}} % less than or sim.
\def\oversim#1#2{\lower 2pt\vbox{\baselineskip 0pt \lineskip 1pt
    \ialign{$\nms#1\hfil##\hfil$\crcr#2\crcr\sim\crcr}}}
\def\gtequal{\mathrel{\mathpalette\overequal>}} % greater than or equal.
\def\ltequal{\mathrel{\mathpalette\overequal<}} % less than or equal.
\def\overequal#1#2{\lower 2pt\vbox{\baselineskip 0pt \lineskip 1pt
    \ialign{$\nms#1\hfil##\hfil$\crcr#2\crcr=\crcr}}}
\def\leftrightarrowfill{$\nms \mathord\leftarrow \mkern-6mu
       \cleaders\hbox{$\mkern-2mu \mathord- \mkern-2mu$}\hfill
       \mkern-6mu \mathord\rightarrow$}
\def\overdoublearrow#1{\vbox{\ialign{##\crcr
      \leftrightarrowfill \crcr\noalign{\kern-1pt\nointerlineskip}
        $\hfil\displaystyle{#1}\hfil$\crcr}}}

%\def\RR{I\kern-.3emR}
%\def\II{I\kern-.3emI}
%\def\nvarep{\ep\kern-.3em/}
%\def\mapright#1{\smash{\mathop{\longrightarrow}\limits^{#1}}}
%\def\ibar{\thinspace\iota\kern-.6em-}
%\def\undertext#1{$\underline{\smash{\hbox{#1}}}$}
%\tolerance=10000
%\parindent=3pc
%\def\bs{{\pmb\ast}}    
%\newcount\referencenumber
%\def\clearref{\referencenumber=0}
%\def\ref{\global\advance\referencenumber by 1
%\item{\the\referencenumber.}}
%\hfuzz=3pt
%\def\cntl{\centerline}
%\def\rule#1{\quad\vrule height.5pt width#1truein depth.5pt}
%\def\margins{\textwidth 6.5in
%             \evensidemargin -0.0in
%             \oddsidemargin -0.0in
%             \marginparwidth 0.0in
%             \textheight 8.5 in
%             \topmargin -.5in
%             \topskip 0.0in}
