\dvidoc % comment or delete this line to format for laserwriter \ifdvidoc\else \magnification\magstep1 \fi % \def\date{\number\month/\number\day/\number\year \headline={\ifnum\pageno>1 {\fiverm ZED \hfil\fi \footline={\tenrm \ifnum\pageno<2 {\fiverm\date\ \hfil \else \rlap{\fiverm\date \hss\folio\hss \fi % \def\codevar#1{\ifdvidoc\uppercase{#1\else{\tt #1\fi % \def\cmdhead #1\par{\medbreak\longitem{\codevar{#1 % % \longitem is like \item except its argument is left adjusted, and if it’s % wider than \parindent then the text following is pushed over to make room. \def\longitem#1{% B. Langdon, 11/88. \setbox0=\hbox{#1\enspace \dimen0=-\wd0 \hangindent=\parindent \advance\dimen0 by \hangindent \ifdim\dimen0<0pt \relax \dimen0=0pt \fi \leavevmode\kern -\hangindent \unhbox0 \kern\dimen0 \ignorespaces % \let\hfilbreak=\allowbreak % this gives overfull hboxes with default tolerance. %\def\hfilbreak{\hfil\penalty9999\hfilneg % this almost always breaks %\let\hfilbreak=\relax % \def\newline{\hfil\break %———————————– \def\H/{\codevar{history % TeXbook, p. 204; spaces after \H/ are not lost. \def\S/{\codevar{state % \centerline{\bf ZED (Zohar EDitor) \medskip \centerline{A. Bruce Langdon \centerline{Physics Department \centerline{Lawrence Livermore National Laboratory

\bigskip {\narrower ZED is an interactive code, able to read, manipulate and display graphically the time-dependent data from simulation codes. ZED was begun in 1974 by B. Langdon and B. Lasinski to postprocess time history files from runs of ZOHAR, a 2D electromagnetic particle-in-cell code. At Berkeley, Princeton and Livermore MFE it was applied and extended in imaginative ways to other codes by W. Nevins, N. Otani,..., and others. In its original (1974-1987) form, the commands were individually interpreted in LRLTRAN, adding new commands was clumsy, and the command syntax was stilted. The versions at LCC (the internal Livermore center) and at NMFECC evolved separately for years. In 1987 Nevins suggested that ZED be reborn as a Basis ‘package’. Basis is a combined interactive interpreter/graphics/code system to which anyone can readily add commands and the Fortran subprograms to implement them. This document describes the Basis implementation of ZED. \par

\bigbreak \centerline{\bf Availability \nobreak\medskip

\tolerance=5000 At MFECC, ZED for the Cray-2 is publicly available from CFS directory \hfilbreak \hbox{\codevar{/zohar/cray2/zed. The files include:

\codevar{xzed is the executable file.

\codevar{zedlib is a LIB file which includes \codevar{zedmac, the part of ZED written in the Basis language, and the sources files needed to make \codevar{xzed. Also, \codevar{zed.tex is the \TeX\ source for this manual; \codevar{zed.doc \ifdvidoc (what you are reading now) \fi is a straight ASCII file to print or view on a terminal. \codevar{ebal is a Basis-language file; read after \codevar{init, it will read and display the various particle and field energies and fluxes and form an energy balance. \codevar{pbal is like \codevar{ebal, but for the $x$-component of momentum.

\bigbreak \centerline{\bf How to use ZED now \nobreak\medskip

First, get a copy of the Basis system manual[1] and read the first chapter.

Commands implemented now let you create Basis variables that contain the time histories of physical variables from their time histories saved in the \H/ and \S/ files. You then have the full power of Basis to do as you will with them. This already empowers you to do much of what old ZED did, and much more that it didn’t.

The time dependence of many quantities in the simulation is written into the file \H/. The file \S/ contains in addition the time step, particle species’ names, etc, and descriptive information about the simulation (plus other data like the electromagnetic fields that pertains only to the time step when the state file was made.) \H/ and \S/ are not human readable text files, they hold numbers and text in Cray hardware representation.\footnote{(a){The format of \H/ and \S/ is indicated in source files \codevar{szedc and \codevar{var.zed in \codevar{zedlib, and of course in the ZOHAR routines \codevar{writstat, \codevar{readstat, \codevar{tset and \codevar{mdset. The Fortran functions \codevar{getstate and \codevar{gethist, together with the Basis-language functions \codevar{init, \codevar{readh, etc., read from \S/ and \H/ and create Basis variables holding the interesting values.

\bgroup \ifdvidoc \parindent=10em \else \parindent=5em \fi \tolerance=1000 % make alignment of narrow paragraphs less strict. \cmdhead init

The first command you give is \codevar{init. Often the files are renamed to indicate the problem name (e.g., \codevar{hprob, \codevar{sprob) or time step (e.g., \codevar{h6000, \codevar{s6000). Then you run ‘\codevar{init prob’ or ‘\codevar{init 6000’.

\cmdhead get

A list of variables to be read from \H/ is accumulated. Variable ‘\codevar{elg’ is added to the list by the command \hfilbreak ‘\codevar{get elg’. This translates to \hfilbreak ‘\codevar{gets("elg")’. You may call ‘\codevar{gets’ directly if the variable name is computed. For example, ‘\codevar{gets("ke"//format(is,0))’ when \codevar{is=2 adds ‘\codevar{ke2’ to the list.

\cmdhead readh

This command takes the list accumulated by the ‘\codevar{get’ commands, reads from \H/, and creates Basis arrays holding the time series. In the example above, after readh there will be two new arrays, \codevar{elg and \codevar{ke2. You then could do ‘\codevar{plot elg, time’ to plot the electrostatic field energy {\it versus time.

\cmdhead steps first, last [, iskip]

Usually \codevar{readh reads from step 0 to the last step of the simulation. This command confines the times steps to \hfilbreak\codevar{(first,last). Optionally it resets \codevar{iskip, whose meaning is that only time steps that are multiples of \codevar{iskip are retained. If \codevar{iskip=2, then e.g., \codevar{elg(i) corresponds to time step 2\codevar{i and \codevar{elg is subscripted roughly \hfilbreak \codevar{(first/2:last/2). \par\hang If indexed variables are to be used, \codevar{iskip must be a multiple of \codevar{ismode (see \codevar{modes).

\cmdhead modes

\H/ is divided into two parts. The first holds time records for quantities that are more or less global, like kinetic energy for all electrons, or are particular, like the $x$ position of a planar shock. The records present are printed by \codevar{init. The second part holds time records of quantities that have a name and one or two indices, like a field at a particular grid point, or a coordinate of a particle. The list in human-readable form is in array \codevar{lblm. \par\hang At present, \codevar{get and \codevar{readh work with only one part at a time. You toggle between them with the \codevar{modes command. \par\hang Values in the modes section are not in general saved every time step, but at steps that are multiple of \codevar{ismode, an input variable to ZOHAR. In ZOHAR by default \codevar{ismode=2.

\cmdhead ploth xyz

plots history variable \codevar{xyz versus time. If \codevar{xyz is a complex variable, the real and imaginary parts are plotted using solid and dashed lines in the lower half of the frame. In the upper half, the modulus squared is plotted, semilog. (Of course you can also use the Basis plot interface.) \par\hang If \codevar{xyz is from the history file, i.e., it is in the \codevar{varsh or \codevar{varsm list, it is labelled instead with the corresponding “nice” name from \codevar{lblh or \codevar{lblm (see ‘Variable naming’).

\cmdhead spect(f)

Value is the Blackman-Tukey power spectra of time variable \codevar{f. To get spectrum for subinterval of the full time step range \codevar{(istepl,istepu), do \codevar{spect(f(il:iu)). Remember, \codevar{il and \codevar{iu are the actual steps divided by \codevar{iskip.

\cmdhead sparam lagwidth [datawidth [wmax]]

Set lag window and data window widths (in steps) and maximum frequency to be displayed by default in spectrum plots.

\cmdhead ints var [wmin wmax]

(Soon) Integrate spectrum in \codevar{var. \ifdvidoc\else $$ (\hbox{\codevar{ints f w1 w2)_\omega = \int_{\hbox{\codevar{w1^\omega\, f(\omega), \quad \codevar{w1 \le \omega < \codevar{w2 $$ \fi Useful in finding out how much power is {\it between two frequencies.

\cmdhead mem

(Later) Form ‘maximum entropy method’ spectra.

\cmdhead reset

Clears memory. Might be used before switching to another ZOHAR run.

\cmdhead fll

Prints ZED’s memory size.

\egroup % restore normal \parindent

\bigbreak \noindent \centerline{\bf Variable naming \nobreak\medskip ZOHAR history records include items whose names have blanks or characters not legal in Basis variables: ‘\codevar{field px’, ‘\codevar{ex-ey’. So you must refer to ‘\codevar{fieldpx’ and ‘\codevar{exey’ instead. Worse, indexed records have a name and two indices, and an index may be negative. For example, \allowbreak ‘\codevar{Bz(x,ky) 20 3’ is field \ifdvidoc Bz, Fourier transformed over y, evaluated at x grid point 20, mode 3. \else $B_z$, Fourier transformed over $y$, evaluated at $x$ grid point 20 ($x=20\Delta x$), mode 3 ($k_y = 3\times 2\pi/L_y$). \fi This is stored in Basis variable ‘\codevar{bzxk20\$3’. The \$ separates the two indices. In a negative index number, a \% replaces the minus. Arrays \codevar{varsh and \codevar{varsm hold the list of these ugly things for globals and modes, respectively, while \codevar{lblh and \codevar{lblm hold the list of nice names. You may wish to use Basis’ \codevar{define so you can refer to these by nicer names.

\bigbreak \noindent \centerline{\bf ZOHAR’s variables in \codevar{history \nobreak\medskip While the modes variables are entirely specified by user input and there may not even be any, the global variables are chosen by statements at the beginning of subroutine \codevar{tset. These vary slightly from version to version and the number of particle species, but the following are standard:

\cmdhead n1, n2, ...

are the number of active particles of species 1, 2, ...

\cmdhead ke1, px1, ke2, ...

are the kinetic energies and momenta of active particles of species 1, 2, ...

\cmdhead kl1, kl2, ...

are cumulative kinetic energies of particles of species 1, 2, ... {\it lost due to particles leaving through the left or right side. Particles entering make a {\it negative contribution.

\cmdhead l pxl1, r pxl1, ...

are cumulative $x$ momenta of particles of species 1 {\it lost due to particles leaving through the left or right side, respectively. Particles entering make a {\it negative contribution.

\medskip\hang ..and similarly for \codevar{py1, etc.

\cmdhead field px

Electromagnetic momenta in x direction, etc.

\cmdhead l pxlf, r pxlf

cumulative fluxes of the $x$ component of the field momentum out of the system, i.e. the time integral of the Maxwell stress tensor averaged averaged over $y$ at the left and right sides.

\cmdhead elg, ex-ey, bz

field energies associated with the ‘electrostatic’ field, $E_x$ plus $E_y$, and $B_z$, respectively.

\cmdhead wleybz, wreybz

cumulative Poynting fluxes. The electromagnetic energies into the left side and out through the right side, averaged over $y$.

\medskip\hang ..and similarly for \codevar{bx-by, \codevar{ez, \codevar{wlezby and \codevar{wrezby.

\cmdhead bz left, bz right

is $B_z$ averaged over $y$ at the left and right sides. The contribution of the incoming electromagnetic waves is subtracted; this only really works in vacuum.

\medskip\hang ..and similarly for \codevar{ez left and \codevar{ez right.

\cmdhead clock

is the real clock time in decimal hours. Use this to review your strategies for getting production time.

\medbreak In the relativistic shock version (\codevar{code $=$ “zirs”), there are in addition:

\cmdhead l bflux, r bflux

Cumulative magnetic field flux through the left and right sides. \ifdvidoc\else The change in magnetic flux inside the system is $$ \int_0^T dt \int_0^{L_x \int_0^{L_y dx\,dy {\partial B_z \over \partial t = c \int_0^T dt \int_0^{L_y dy [E_y(x=0) - E_y(x=L_x)] $$ in which we used Faraday’s law and integrated by parts. \fi

\cmdhead xshock

\medbreak \noindent Notes

The energies and momenta are the totals divided by $L_y$ in versions periodic in $y$, and by $L_x L_y$ in versions periodic in $x$ and $y$.

\bigbreak \noindent \centerline{\bf The future \nobreak\medskip

User experience will guide evolution of ZED and of this report.

It would not be difficult to teach ZED to read field information from \codevar{state and to read the particle files.

\bigbreak \centerline{\bf Customizing ZED \nobreak\medskip

The simplest customization is to add your own functions and macros in a file to be read by Basis in addition to \codevar{zedmac.

Other versions of ZOHAR, and other codes that write \codevar{history files, have \codevar{state laid out differently, or no \codevar{state file at all. You can revise \codevar{init and \codevar{getstate accordingly; all the files are available in CFS.

\bigbreak \centerline{\bf Acknowledgements \nobreak\medskip ZED derives its extensibility and its new power from the Basis system. We are grateful for additions to Basis that ZED depends on.

\bigbreak \centerline{\bf References \nobreak\medskip \def\ref#1. {\item{[#1] \bgroup\parskip=\medskipamount

\ref 1. P. Dubois, Z. Motteler, P. Willmann {\it et al, “The Basis System”, LLNL report M-225, available on-line at the LCC and NMFECC.

\ref 2. ZOHAR is described in “Electromagnetic and Relativistic Plasma Simulation Models”, A. B. Langdon and B. F. Lasinski, in {\it Methods in Computational Physics, ed.\ by B. Alder, S. Fernbach and M. Rotenberg, vol.\ ed.\ J. Killeen, (Academic Press, New York, 1976), Vol.\ 16, p.\ 327-366.

\egroup % restore old parskip

\bigbreak \centerline{\bf Appendix: How it works \nobreak \bye

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