This HTML version of the manual is made available so that youcan get an idea of the capabilities and user interface of BiotSavart.It is not as complete as the hardcopy manual which accompaniesthe program diskette.
BiotSavart is a general purpose interactive program to calculatemagnetic fields resulting from collections of current-carryingconductors. Features of the program are
To start BiotSavart, open (or double-click) the applicationicon or an existing BiotSavart document. The conductors describedin the document will be displayed on the configuration window.Field probes, if any, will not be recalculated, in order to allowyou to modify the configuration before embarking on a time-consumingcomputation.
In order to exit BiotSavart, choose Quit (cmd-Q) fromthe File menu. If the configuration has been changed since itwas last saved, you will be asked whether or not to save the changes.
If there is no configuration window, create one by choosingNew (cmd-N) from the File menu. Conductors are added tothe configuration using the Config menu.Conductor types are Loop, Solenoid, Revolved,Wire, and Racetrack. Whenever you add a conductoran edit window will appear to allow youto change the specifications. After modifying the specifications,register the changes using the Set button. The Donebutton is the same as Set, but also dismisses the edit dialogwindow.
Conductors may also be read from other BiotSavart documentsor your own conductor files using the Readfile... command on the Config menu.This command will prompt for a file to read, and extract fromit the conductor descriptions and current supply values. Probesare not extracted.
To select a conductor, click on its picture on the configurationwindow. Clicking with the shift key depressed adds the conductorto the selection list (if it is already selected, this removesit from the list). You can tell which conductors are selectedby looking at the Modify menu.
Selected conductors can be deleted by selecting Cut(cmd-X) or Clear from the Edit menu when the configurationwindow is the active one.
In order to make changes to a conductor, you must create anedit window for the conductor. There are several ways to do this.The fastest is to double-click the conductor on the configurationwindow. Choosing the conductor by name from the Modifymenu will accomplish the same thing. Also, if one or moreconductors is selected, the Modify command (cmd-I) on theEdit menu will create an edit window for each conductor selected.
Changes to the source code of a conductor do not take effectuntil they are registered using the Set or Donebuttons on the edit window. Changes may be discarded by usingthe Revert command. Note that pressing Set or Doneregisters the changes with the configuration database, but writesnothing to disk unless the Autosave option is set. To closea dialog window without saving the changes, press the Cancelbutton.
The name of a selected conductor may be changed using the Name...command on the Edit menu when either its edit window or the configurationwindow is active.
To measure and display the magnetic field, you create fieldprobes using the Config menu. Thereare two types of probes: Linear, aone-dimensional probe, and Planar,a two-dimensional probe. When a probe is created an edit windowappears containing the description of the probe and the formatof the display of the calculated field profile.
The probe window displays the calculated field profile. Thename of the window is the name of the field probe preceded bythe symbol Pi (for product).
Selection, deletion, and modification of probes is done inthe same manner as conductors.
In order to save a new or modified configuration to disk, theconfiguration window must be the active one. Then use the Savecommand (cmd-S) on the File menu. If you are working on an existingBiotSavart document, then this will overwrite the old versionof the file. If instead you wish to save the configuration undera new name, then use the Save As... command.
After making changes to the configuration, you will want BiotSavartto recompute the magnetic field and update the field probe displays.To do this, use the Recompute command (cmd-R) on the Fieldmenu. This command is only enabled when the field needs to berecalculated.
If AutoRecompute is enabled, the program will recalculatethe field whenever a change is saved from an edit window intothe configuration. Selecting AutoRecompute from the Fieldmenu toggles it between enabled (ticked) and disabled (not ticked).Note that creating a new conductor or probe disables Autorecompute.
If you want to modify several conductors or probes before recalculation,disable AutoRecompute, make and save the source code modifications,and then trigger the recalculation by re-enabling AutoRecomputeor by using the Recompute command (cmd-R).
During the field calculation, the cursor will be cycling throughan action sequence. This indicates that the program may be interruptedholding down the cmd- button and typing a period (.).
The values of the current supplies are set via the Modify menu.It is also possible to specify a bias magneticfield.
Can be used to Save changes to configuration, or exportfield probe results.
The functioning of the Edit menu depends on which type of BiotSavartwindow is the active one.
When the configuration window is the active one:
If no objects are selected, then Copy places a copyof the picture in the configuration window onto the clipboard.
When an edit window is active, then the Edit menu can be usedto Cut, Copy, and Paste text.
The Config menu is used to add conductors or probes to theconfiguration. It is also used to read conductors from other BiotSavartdocuments, and to set options.
The Make conductor submenu creates conductors, or sourcesof magnetic field:
The Make probe submenu creates objects which measurethe magnetic field:
Other commands on the Config menu are
The names of all conductors and probes appear on the Modifymenu, partitioned into three groups: current supply object, conductors,and probes. Selecting a name from the menu selects the objectand creates an edit window for you to modify it. The current supplyobject is only accessible through this menu.
This menu also shows the selection list: the names of selectedobjects in the configuration are ticked.
The Field menu controls the recalculation of magnetic field.
Permits activation of windows which may or may not be visible.The first window listed is the configuration window. Other windowsare listed in alphabetical order.
There is one configuration window, which displays a pictureof the conductor configuration you are working on. At the topare several small icons which can be used to control the picture:
Sets the configuration windowto select mode. The cursor will be an arrow, and can be used toselect an object by clicking at it. The selected object will becolored red and its name will appear at the bottom of the window.Double-click an object to edit it.
Sets the configuration windowto zoom mode. The cursor will be a magnifying glass when overthe configuration. To zoom in on a rectangle on the picture, moveto the upper left hand corner, depress the mouse button, dragto the lower right corner, and then release the button. The picturewill zoom in on the rectangle. Clicking without dragging willzoom in on the point specified. Zooming with the shift key depressedzooms out instead of in.
This button zooms back outso that all of the objects are visible.
Selects two or three dimensional viewing of the configuration.The two-dimensional view mode draws the cross section of axisymmetricobjects like solenoids.
In three-dimensional mode there are two additional buttons:
Launchesa viewing direction choice window. Changing the view directionalso zooms the view out so that all conductors are visible.
Removes the hidden lines fromthe drawing. This can be time consuming. Note that later changingthe viewing direction will put the lines back in, but that zoomingwill not.
Objects are selected by clicking on them. When a single objectis selected, its name appears at the bottom of the configurationwindow. Clicking on objects with the shift key depressed addsit to the selection list, permitting selection of more than oneobject. The names of all conductors and probes are listed in theModify menu, with selected objects ticked.With the configuration window active, selected objects can becut, pasted to and copied from the Clipboard, deleted or duplicated,using the Edit menu. Selecting Modify (cmd-I) from the Edit menucreates edit windows for the selectedobject(s). To edit a single object, one can just double-clickon it. If an object is not visible, the Modify menu can be usedto bring up an edit window. This also selects the object.
Using the Print... command on the File menu, the picturemay be printed. It is recommended, however, that you copy thepicture to a word processor document and then print it.
The Copy command, with no objects selected, copies the pictureto the clipboard. You can then Paste it into a word processorwhen preparing documentation of the configuration.
The ViewSet window is used to set the direction from whichwe view a three-dimensional picture.
This window, which is summoned using the eyeicon on the graphics window, displays a globe with lines oflatitude and longitude. To set the viewing direction drag thesmall rectangle on the globe or, to align with a coordinate axis,click on the coordinate label.
Modification of a particular conductor or probe is done throughits Edit window, which is summoned by double-clicking the objecton the configuration window or by using the Modify menu. The details of the Edit windoware described in the section Conductors- General considerations.
After modifying the information in the dialog boxes, use theSet or Done button to implement the changes. The magnetic fieldwill update automatically if AutoRecompute (on the Field menu)is enabled. The Edit menu may also be used to change the nameof the conductor. The Edit menu can be used for cutting and pastingtext, between objects for example.
The results of magnetic field probes are plotted in probe windows.The name of the probe window is the name of the probe object precededby the symbol Pi.
When a probe window is the active one, the Copy commandcopies the plot to the clipboard. To print the plot, paste itinto a word processor document. Printing the plot directly, usingthe Print Graph... command, is possible, but is not a supportedfeature.
The mouse can be used to select specific calculated points,and to zoom the graph. On a linear probe plot, the cursor keyswill move the selected point. On a contour plot, clicking themouse will give the (bilinearly interpolated) field value. Clickingwith the shift key depressed gives the value of the nearest contour.
The field profile may be written to disk using the SaveData As... command on the File menu. You will be promptedfor the name of the file to be written. Each line of the fileconsists of seven tab-delimited floating point numbers:
x y z Bx By Bz B
The file is readable by programs such as Cricket Graph or Igor(from Wavemetrics).
Conductors are specified in the configuration file by a sequenceof command lines. In previous versions of BiotSavart, tomodify the conductors this sequence had to be edited by hand.Now the Edit window for a conductor is more user friendly, withcommand language restricted to the description of the path ofa wire through space, for example.
To edit an existing conductor, double-click on its pictureon the configuration window, or selectits name from the Modify menu. Thiscreates an edit window for the conductors, which looks like this(for a solenoid):
The name of the edit window is the name of the object beingmodified. Just below the name is the type of the object (e.g.,Loop, Solenoid, etc.). Below that is the page selector, whichallows you to select information on the object by category.
Once you have modified all of the parameters that you wantto, the changes must be transmitted to the configuration windowby pressing the Set button (or the Done button tosimultaneously close the edit window). If AutoRecompute is enabled,the magnetic field will be recalculated immediately.
As usual, the Cancel button dismisses the Edit windowwithout transmitting the changes.
The above image is of the Edit window for a Solenoid, on theSpecs page. This page describes things like the physicaldimensions of the object or, in the case of a wire,its path through space. Note that the dimensions of the objectmay have units, just type them in after the number.
| m | cm | mm | ft | in |
| meter | 0.01m | 0.001m | 12in | 2.54cm |
The orientation of the conductor is specified by three Eulerangles. For an axially symmetric conductor such as a loop or solenoid,eulerPsi has no effect on the magnetic field. Anglesare specified in degrees, and default values are zero. The conductoris rotated about the origin of its own coordinate system, beforebeing moved to its position.
The details of the current supply is set on the Supplypage:
All conductors have an associated current supply, whose namecan be any string not containing blanks. Several conductors canuse the same current supply. The use of labelled supplies greatlyaccelerates recalculation of the magnetic fields when only thecurrent is changed. To use current supply named ithacofor the conductor enter this name into the currentIDbox on the supply page of the edit window, as shown above. Anoverall scale factor for the current is specified by the currentScalebox. A typical use of currentScale would be to set itto -1 to reverse the power supply connections. The current suppliesthemselves are set by bringing up an edit window for the Currentobject (using the Modify menu).
To indicate the number of windings use the windingbox. For bulky conductor types (Solenoid and Racetrack) both thewireDiameter and winding parameters appear onthe Supply page. Between these parameters are two buttons: anarrow and a packing. The number of windings is calculated fromthe wireDiameter parameter if the arrow button pointsdown; to make the calculation go the other way click the arrowup. The wire packing used in this calculation is selected by thepacking button:
Square packing. To calculatethe winding from the wireDiameter the crosssectional area is divided by the square of wireDiameter,rounding to the nearest integer. The reverse calculation is donewithout rounding, since wireDiameter need not be integral.
Hexagonal packing. The waywires pack naturally, a bit tighter than square packing.
Note that the choice of packing does not change the packingof pseudoconductors used in the field calculation, only the relationbetween wireDiameter and winding.
Note that the number of turns is better specified in the windingbox rather than as CurrentScale because for inductancecalculations these are very different quantities.
The Looks page describes aspects of the conductor whichdo not influence its magnetic field, only the way it looks on-screen.For example, to make the conductor invisible just check the invisiblecheckbox.
The Loop object is a loop or collection of coaxial loops. TheSpecs page of the edit window for a loop is a table ofradius, altitude, and winding numbersfor the loops. The table expands as you type more loops. Rowswith missing radius will vanish from the table when you pressthe Set or Done buttons.
The wireDiameter box on the Supply page maybe used to specify a wire radius to be used for all loops. Givingthe wire a finite radius has two effects. Firstly, the wire isdrawn with the specified thickness. Secondly, the field divergenceassociated with a filamentary conductor is avoided, since thefield is calculated assuming uniform current density within thewire. BiotSavart uses a formula valid in the limit that the wirediameter is much smaller than the loop diameter.
Although the field due to the loop is calculated using CompleteElliptic Integrals, the loop is drawn using straight segments.The number of segments is set by the nphi box. One canalso specify a range of angles to draw, but keep in mind thatthe field is that of a whole loop! Quantities on the Lookspage have no effect upon the calculated field.
The shape of a solenoid is specified by its inner and outerradius, and its length. The center of the solenoid is at the pointspecified by the coordinates positionX, positionY,and positionZ. The number of turns is specified by windingwhich can be specified or calculated from the wireDiameter.Fields on the axis of the solenoid are found using an analyticform. Off axis, however, the field is found by decomposing thesolenoid into loops and summing the loop fields. The finesse ofthis decomposition is set by the resolution box, e.g.,
resolution 2mm
The resolution should be chosen wisely; too large a value willgive unrealistic fields, too small may make the calculation unbearablyslow. If the resolution is zero or omitted, then it is assumedto be equal to the wire diameter. If both are zero then the solenoiddegenerates into a filamentary current loop. It is possible tospecify a near-axis or paraxial calculation by giving a nonzerovalue to paraxialR. Closer to the axis of the solenoidthan paraxial, an expansion is used which can be verymuch faster than summing over loops. Similarly to a loop, thenumber of angular steps used to draw the solenoid is given bythe nphi command, and a partial range of phi can be drawn.
The revolved conductor type is a cylindrically symmetric currentsheet obtained by revolving a polygon about an axis. Since therevolved object is used to represent a body uniformly magnetizedparallel to its axis, the surface current density is proportionalto cos(theta), where theta is the angle betweenthe axis and the surface normal. The current of the powersupply is interpreted as the magnetization in tesla. For thisobject, a command sequence must be entered to specify the polygonto be revolved. First you must specify the density of loops whichwill be used in the calculation of the magnetic field, by thecommand resolution 0.5 mm If resolution is zeroor missing, then wireDiameter is used instead. Specifythe polygon by giving the starting point and sequence of motionsin the (x,z) plane. For example, a truncated cone:
start 2 0 mmgoto 8 -6 mmgoto 1 -6 mmgoto 1 0 mm
The resolution can be changed during the specificationto allow some parts of the polygon to be described by a higherdensity of loops. The polygon should be specified clockwise inthe x-z plane. If specified counter-clockwise, includethe command reverse in the path description. The revolvedpolygon is drawn using nphi angular steps. The valueof nphi has no effect on the magnetic field.
The source code for a wire describes the current path in three-dimensionalspace. For this description object coordinates are used, beforeEuler angle rotation and translation to the position determinedby the position parameter. We begin a wire by givingthe starting point (in object coordinates)
start 2 2 0 ; we begin here
As always, the default length unit is meters. To draw a straightline segment we simply say where to go:
goto 0.5 0 0
To make an arc, we can specify a center and normal. For example,if we are in the x-y plane and want to turn about the z-axis,we set
center 0 0 0normal 0 0 1
and then turn, starting at the present position. Before makingthe arc, we must first specify the finesse of the turn:
dtheta 20 ; stepsize in degrees
Then the turn command is used to create the arc:
turn 90; angle in degrees
Another way to make an arc is use the axis command,which uses two points to specify an axis. For example, to makethe axis of rotation parallel to the z-axis, but passing throughx=y=2, the command is
axis 2 2 0 2 2 1
The distance between the two points is immaterial. After anaxis command, the turn command makes an arcabout the specified axis. A helix is simply a turn with pitch.The pitch is specified by giving the length per turn
pitch 1mm
Since the main use of pitch is to make multi-turnwindings, the turn command will accept turn units:
turn 5t
Finally, to close the wire (this is optional) the command is
close
The wireRadius command can be used to suppress divergenceof magnetic fields near the conductor. This does not affect theappearance of the wire on the configuration window; it is alwaysdrawn as a filament.
Racetracks are used in particle accelerators and neutral atomtraps. BiotSavart implements planar racetracks. The dimensionsof the racetrack are specified by the quantities
| length | straight section length |
| span | distance between straights |
| width | width of conductor (in plane) |
| height | height (out of plane) |
The turns at the ends of the racetrack are semicircular. Thisis approximated, both in drawing and field calculation, by finiteangular steps. The number of steps in the semicircle is set by,e.g., nturn 10. The computation time is proportionalto nturn+2, so it is best to use a small number unlessan accurate depiction of the end fields is desired. The magneticfield is calculated by subdividing the racetrack into filamentarywires. The finesse of the subdivision is set by the resolutionbox. Choose it wisely. Suppression of field divergence insidethe conductor is automatic.
There exists an invisible object whose task it is to keep trackof the settings of the various current supplies connected to theconductors of the configuration. To change the settings of thecurrent supplies, bring up an edit window using the Modify menu.The Specs page is a table of supply names (any text withoutblanks) and the associated current in amps.
The bias box is provided to permitapplication of a uniform bias field (in the z direction).
Once you have modified the currents, the changes must be registeredby pressing the Set or Done button. If AutoRecomputeis enabled, the magnetic field will be recalculated immediatelyto reflect the new current supply and bias field settings.
The field probes are used to investigate the magnetic fieldprofile. Probes are made in the same way as conductors, by choosingthe appropriate type from the Config menu.Field probes have associated with them a window which displaysthe calculated field graphically. The name of the window is thename of the probe object preceded by the symbol Pi, meaning product.This section describes the field probe parameters, which controlboth the placement of calculated points and the plotting of theresults.
The linear probe calculates the magnetic field along a specifiedtrajectory, and plots the result. The field unit is tesla. Toset the points at which the field is calculated the source codeis
resolution 1 mmstart 0 0 0goto 1.3 0 0 cm resolution 0.5 mmgoto 1.3 0 2 cm
Points are placed uniformly on each segment, with points onthe starting and ending position such that the points are no furtherapart than the present resolution. The plot itself iscustomized by additional commands. By default, the field magnitudeB is plotted versus the distance s along the line.The x, y, or z components of the field canbe plotted as well, with the abscissa given by either x,y, z, or the arclength s.
Normally the plot is scaled to show all the data. This canbe changed by specifying a minimum and maximum ordinate.
This probe calculates the magnetic field on a flat surfacespecified by two displacement vectors u and v, specifiedon the Specs page of the edit window. Also give nuand nv, the number of subdivisions in each directions.
Next Recompute, a window will appear to display a contourplot of the field surface. Only one component or the magnitudeof the magnetic field may plotted at a time. The default plotrange is the entire range of calculated fields. The contour spacingis normally one-tenth of the plot range, but can be changed byfilling in the appropriate boxes. The quantity contouris the contour spacing in Tesla. Contours start at the lower limitof the plot range.
BiotSavart saves the conductor configuration in a text file.This makes it easy to generate a configuration using your ownsoftware and import it into BiotSavart for analysis. The requisitefile format is described in the non-HTML manual which comes withthe software. You can either open the file from within BiotSavartor you can drop it onto the BiotSavart icon in the finder.