&FIELD: PLOT-FIELD

CONTOUR

Produces a plot of the lines of equal function values.

Contours are drawn in the part of the viewing plane that is located within the current AREA box.

The contours are labelled with the function value if the LABEL option is active (which is by default the case).

If you request AUTOMATIC scaling of the range, contours are drawn at round values of the function over a range that covers the function values in the current AREA. The number of contours is used to compute a first estimate of the distance between two contours. This distance is rounded downwards to the first 10-fold multiple of 1, 2 or 5. The number of contours actually drawn is therefore usually larger than the number you requested.

Contours are plotted starting from their crossings with a regular GRID covering the AREA. Very small contours are not found if the grid is course. It is therefore usually preferable to use a fine grid for contours, even though plotting the contours takes more time.

You may also wish to optimise the CONTOUR-PARAMETERS, especially if your AREA is very small or highly non-isometric.

The contours are drawn with the representation CONTOUR-NORMAL and are labelled with CONTOUR-LABELS.

[The default function is V and the contours range by default from the highest to the lowest potential present in the cell. By default, 20 contours are plotted.]

GRAPH

The function is evaluated on the track or on the curve specified with the ON keyword.

The geometric aspects of the track, if used, should be set by means of the TRACK command before calling PLOT-FIELD. Other aspects of the track, such as the clustering model, are not used in the present context.

A curve should be parametrised in terms of T which will run from 0 to 1. All 3 coordinates of the curve should be specified. Note that ON expects only one argument, the parametrisation should therefore be enclosed in quotes, e.g.

   on 'cos(pi*t),sin(pi*t),0'

would produce a graph over a semi-circle in the z=0 plane.

The SCALE option can be used to force a vertical scale in the plot, this can for instance be useful if you intend to overlay various graphs.

If you select the PRINT option, then the values plotted in the graph will also be printed out. Re-routing of the output (>\ file) can be used to write the values to a file.

The number of sampling points can be set with N, default is 200.

[The default function is V.]

HISTOGRAM

The function is sampled over a GRID of points in the part of the current viewing plane that is located inside the AREA box. The function values are entered in an histogram.

This kind of plot can be useful to estimate the field homogeneity, provided the range has been tuned properly.

The automatic search for proper binning (AUTOMATIC) uses the first few entries to set the range. Since the grid is scanned in a regular sequence, these entries are not necessarily representative for the entire sample, in particular if the number of bins is small compared to the grid size. See AUTOSCALE for details on the automatic binning procedure.

[The default function is E. The number of bins is preset to 100 and the range is by default chosen automatically.]

SURFACE

The function is sampled over a GRID of points in the part of the current viewing plane that is located inside the AREA box. The function values are presented as a three dimensional plot.

The plot is first rotated by \φ degrees around the z-axis and then tilted by \θ degrees from the z-axis.

This plot is decorative but it is generally agreed upon that it is hard to extract any meaningful information from it\ ...

[The default function is V. The default viewing angles are 30\° and 60\°. The viewing angles are remembered from one call to the next.]

VECTOR

This plot shows the flow of a 3-vector sampled over a GRID of points in the part of the current viewing plane that is located inside the AREA box. The vectors are projected onto the viewing plane.

The z-component is set to 0, if not explicitly specified. For other than (x,y) views, this may give incorrect impressions.

The vectors are normalised in 3\ dimensions when they are plotted - the length of the vectors shown does not contain information on the magnitude of the quantity that is plotted. A vector that appears point like has no component in the viewing plane.

If used for (Ex,Ey,Ez), which is the default, one can pick out the location of the zeroes of the field and hence figure out roughly what the acceptance of a wire is.

It is advisable to have roughly equal ranges in view of the scaling that is performed on the vectors.

The vectors are plotted using the FUNCTION-1 representation. The appearance of the arrow is influence by the ARROW-TIP-ANGLE and ARROW-TIP-LENGTH settings.

[The default functions are EX, EY, EZ.]

function

All functions (f1, f2 ... f7) should be expressions in terms of the following quantities:

Name	Meaning	Unit
`X or R`	x- or r-Coordinate of a point	cm
`Y or PHI`	y- or \φ-Coordinate of a point	cm or degrees
`Z`	z-Coordinate of a point	cm
`EX or ER`	x- or r-Component of the electric field	V/cm
`EY or EPHI`	x- or \φ-Component of the electric field	V/cm
`EZ`	z-Component of the electric field	V/cm
`E`	Norm of the electric field	V/cm
`V`	Electrostatic potential	V
`BX`	x-Component of the magnetic field	100 G = 0.01 T
`BY`	y-Component of the magnetic field	100 G = 0.01 T
`BZ`	z-Component of the magnetic field	100 G = 0.01 T
`B`	Norm of the magnetic field	100 G = 0.01 T

Note: The variables BX and BY should not be used with cells that have been described in polar coordinates.

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Formatted on 21/01/18 at 16:55.