The reality was two hours of sifting through chaff, downloading worthless PDF documents and sinking into sites willing to sell me the arcane data for only $30. It’s amazing what the search term STEEL 1018 BH CURVE will dredge up.

I finally succeeded, but the disproportionate effort required to get such fundamental data set me to reflecting. When will we admit that the Search Engine model applied to the Internet repository is a failure when you need “knowledge”. It’s true that the Internet is a valuable sources of “information,” like the telephone number of your nearest ZipLube or the shotputter with the unusual name in the 1952 Olympics that you need for the Sunday crossword. But substance? Never!

Perhaps I am always disappointed with Internet searches because my expectations are not diminished enough. I can remember going to the two-room library in the small town where I grew up and finding exactly what I wanted by flipping through the catalog cards. In contrast , the Internet is equivalent to filling that library with 3 feet of dead leaves and adding a catalog entry for each leaf. To make matters worse, a leaf could get pushed toward the top of the list by making a small contribution.

In any case, this article is not intended to be a complaint; rather, it is an experiment. I am actually putting useful information information on the Internet: those BH curves that were so difficult to obtain. How many people will find them? To help, I picked a can’t-miss title for the article. Here are is a link to download the data:

steel_bh.zip

The tables are averages over the instances I found. They are in a format for use in our PerMag program. The raw values of B0 = ?0*H versus B are listed as comment lines (starting with an asterisk). The code uses a table of the form B versus ?r = B/B0. To ensure convergence in numerical codes, I extended the tables analytically to high values of B using the method described in a previous article:

http://fieldp.com/myblog/2008/iron-in-magnetic-field-calculations-2/

UPDATE: Is my face red! I entered the term “steel 1018 bh curve” in Google the day after I posted this blog, and the link turned up on the first page of the search results! Attribute my complaints to a brief Andy-Rooney moment.

We recently released a technical report that shows that the first stage of the design process for sheet-beam injectors is relatively simple. The primary goal is to create a space-charge-limited beam of specified length L and height W where the current density is uniform and the electron trajectories are parallel to the axis. A analytic solution developed in 1940 by J.R. Pierce addresses the case where L ? ?. The theory gives the shapes of the anode and an extension to the cathode that create the boundary conditions of an infinite beam on the edge of a finite beam.

In the technical report, I review the Pierce derivation. I then use Trak calculations to confirm that the Pierce electrode shapes apply to circular guns. The only change necessary to achieve a high-quality beam is to relax the intersection angle of the cathode focusing electrode from 22.5° to 20.3°.

The results suggests a simple paradigm to produce a sheet beam of finite length L. As shown in the figure, the electron emission surface is a rectangle of width W and length L with rounded ends of radius W/2. The focusing electrode follows the standard Pierce prescription (22.5°) along the straight section, transforming to a figure of revolution at angle 20.3° around the ends. The resulting assembly looks like an old-time college football stadium.

Sheet-beam injector: cathode and focusing electrode

The 3D calculations illustrate the quality of both the design and the OmniTrak methods. The code value of the total current is within 0.1% of the Child-law current density multiplied by the cathode area. Electron orbits over the full extraction area are parallel to within 0.002 radians. The input files for the demonstration 3D calculation  (with prefix SHEETBEAM) have been added to the OmniTrak example library. Please use this link to download the full technical report: sheetbeam.pdf.

• A comprehensive set of parametric models for common coil configurations (solenoids, helices,…).
• Interactive dialogs to modify the geometry, position and orientation of components.
• Versatile graphical displays to show the state of the assembly.

Although the previous version of Magwinder featured high-quality 2D and 3D plots of coils, it did not have the provision to display objects in the finite-element mesh (iron pole pieces, permanent magnets,…). Such a display would allow users to confirm the size, orientation and placement of coil assemblies.

In response to user requests, we added a 3D mesh-display capability. The figure shows the working environment of the new program. There are four associated commands (represented by new entries on the tool bar):

• Load a mesh definition file (MDF) created by MetaMesh
• Set the displayed mesh regions and the plot style. The region boundary facets may be shown as solid or as a wirefame. The boundary may be displayed as a continuum or as a set of facets.
• Set clipping planes for region facets
• Close the mesh file to display only the coils.

The interactive environment features the standard set of AMaze controls to move around in 3D space. Note that the plot shown in the figure has three-dimensional shading as well as hidden-line removal for both current elements and mesh object boundaries.

MagWinder working environment

• We couldn’t begin to duplicate all the advanced features of dedicated CAD programs for professional engineers.
• Users often have detailed drawings of assemblies that would be laborious to duplicate in another program.

As the medium of exchange, we picked the DXF text format. Like the STL format used by our 3D MetaMesh program, DXF is an open, relatively neutral format that must be supported by all CAD manufacturers.

Over the years, we went through some difficult times with the DXF interface, largely caused by the elephant in the room, AutoDesk. There was a period when they regularly changed their DXF standards. At one time, AutoCAD recorded layer information in a format different than AutoSketch! On top of that, the program was expensive for a casual user. We suggested free or low-cost alternatives like QCAD and TurboCAD, but such programs tended to be underpowered or quirky.

Dassault Systèmes, the makers of SolidWorks, have released a new 2D CAD editor, DraftSight, available at no charge. The cost is right for casual users and the program appears to have sufficient power for engineers. Most important, DraftSight can read and write all flavors of DWG and DXF files and covert between them. I downloaded the program and tested it for compatibility with Mesh. The program can understand DXF files created by the Mesh Drawing Editor. There are many options for DXF export. To be conservative, I picked one of the earlier available formats, “R2000-2002 ASCII Drawing (*.dxf)”. Mesh had no trouble reading the resulting file. Even if you don’t plan to use DraftSight as your 2D CAD program of choice, it is worth downloading it as a format converter. Here’s the link:

http://www.3ds.com/products/draftsight/

DraftSight working environment

Of course, the standard rules for DXF import in Mesh apply. Here is a review:

• Mesh recognizes basic objects like lines, arcs, circles and simple polylines.
• Mesh ignores non-geometric information (like text) and advanced shapes like splines.
• Valid objects are assigned to numbered regions if they are in layers labeled “1″, “2″, … , “250″
• Valid objects in other layers are assigned to the default “Region 0″. You can move selected objects to a valid numbered region in the Drawing Editor.

Note: Field Precision is a SolidWorks Partner.

High-energy accelerators employ quadrupole lenses and bending magnets. The convention is to designate the local beam axis as z, with transverse motion in x (bending plane) and y (vertical plane). In such a system, particle motions in x and y are decoupled. In this case, we can define separate emittance values ?x and ?y. To make an ideal emittance calculation, we make a plot of x (displacement from the main axis) and x’ = dx/dz (angle with respect to the main axis) for the particle distribution at a given location in z. The quantity ?x is the trace-space area of the minimal ellipse that encloses the distribution divided by ?. An ideal distribution at a beam waist is one that uniformly fills ellipses with dimensions x0-x0′ and y0-y0′. In this case, the emittances are

Equation 1

Generally, the non-uniform trace-space distributions of real beams add ambiguity to the definition of the bounding ellipse. A resolution is to employ the RMS (root-mean-squared) expressions of Lapostolle (P. Lapostolle, IEEE Trans. Nucl. Sci. NS-18, 1101 (1971).):

Equations 2 and 3

The overline symbols on the right-hand side denote averages over the particle distribution. The equations hold for tilted distributions (diverging or converging beams) as well as upright distributions. The factor of 4.0 is included to ensure that the expressions give the same value as Eq. 1 for a uniform distribution inside an upright ellipse.

Equations 2 and 3 are included in most books on beam physics and listed on several Internet sites. Unfortunately, they do not apply to circular beams where motions in x and y are coupled. Beams in solenoid magnet lenses have an ordered azimuthal velocity. In this case, the results of Eqs. 2 and 3 are meaningless. There are many important applications for circular electron beams guided by solenoid lenses, from the low-current beams of electron microscopes to the intense beams of pulsed radiographic accelerators. It is essential to have a consistent figure for radial emittance to use in the cylindrical paraxial ray equation.

For radial RMS emittance calculations in the Trak code, Carl Ekdahl of Los Alamos National Laboratory suggested I use the expression derived in E. Lee and R. Cooper, Particle Accelerators 7, 83 (1976). Although this result has great practical importance, I could not find it on the Internet or in any accelerator texts (including my own). Therefore, I thought it would be valuable to record it here as a potential search target:

Equation 4

I have written the equation in a useful form for particle codes like Trak. Such codes trace a large number of model particles to represent a beam. The codes generates values of position (x,y,z) and momentum (px,py,pz). The Lee-Cooper expression has three useful features:

1. The value of RMS radial emittance remains invariant for beams moving through solenoid lenses.
2. The result does not depend on whether the azimuthal distribution of particles is uniform. This is important in 2D codes like Trak where a circular beam is represent by a collection of model particles at a single azimuth. For calculations of the beam-generated electric and magnetic field, the model particles represent an annulus of charge and current.
3. The relationship <?r> = <?x> = <?y> holds for a beam with zero canonical angular momentum in regions where the magnetic field is zero.

I added the radial emittance calculation to Trak and GenDist. The tutorial Emittance Calculations for Circular Beams describes numerical tests I carried out to confirm validity and consistency.

The STL capabilities of MetaMesh (for importing parts from SolidWorks, ProE,….) are quite reliable as long as the input files are valid. The nodes and sides of triangular facets must be logically connected and cover a contiguous three-dimensional surface. It’s important to realize that CAD programs don’t always generate valid STL output.

As an example, in a recent consulting project I received a faulty STL file as a part of a large assembly. Several hours evaporated while I narrowed down the cause of mesh distortions. Ironically, the part in question was simple: a cylindrical cathode with a cylindrical concavity in the emission surface (first figure below). The problem is apparent in a wireframe view of the cathode near the emission surface (second figure). The object was not originally constructed as a single part in the CAD program. Instead, a dished cap was added to a cylinder in a manner that did not preserve the logical continuity of facets. In fact, the cap doesn’t even fit correctly. Such a combination should not be represented in a single STL file. Usually MetaMesh will soldier through and create something acceptable, even with a corrupt file. In this application, the cathode surface was adjacent to a thin gap separating it from a focus electrode. Perfect fitting was essential. The obvious way to resolve the issue would be to ask the mechanical engineer to regenerate the STL file. Unfortunately, the design had evolved from multiple levels of multiple organizations through multiple CAD programs.  It would have taken a historian to find the original designer.

The time had arrived to stop pushing buttons and attack the problem the old fashioned way. An inspection of standard mechanical drawings of the part showed that it could be constructed from native MetaMesh solid models. I started with a cylinder and then machined the emission surface using an extrusion with a cylindrical side and the physical properties of vacuum. Fabricating the part did involve some work:

1. I had to do some trigonometry to find the vector outline of the extrusion.
2. I had to do some head-scratching and sketching to figure how to rotate the extrusion into position.
3. I had to think about the order for adding parts and the fitting specifications so that the trimming extrusion did not affect the focus electrode. (Note that the focus electrode was successfully represented by an STL model).

Although building the cathode from basic parts was harder, it certainly was quicker. It took less than half an hour to build the part from scratch. I cite this episode in support of some anachronistic views about computer simulations:

1. It’s often better to sit in a quiet place with a paper and pencil that to pound on the computer.
2. A simple approach is usually better than a sophisticated approach.
3. The best way to waste time is to let the computer do all the thinking.

One lesson from the experience is that you should check the STL models when mesh generation problems occur. We have added a new STL viewer to Geometer to help in this process.

For reference, here’s the full MetaMesh specification that I created for the cathode:

PART
* Make the cylinder
Region: CATHODE
Name: Cathode
Type: Cylinder
Fab: 3.1600 0.6000
Shift: 0.0000 0.0000 -23.4500
Surface Region Vacuum
END

PART
* Machine the surface
Region: EmitDef
Name: SurfaceShape
Type: Extrusion
L    3.1600  -23.0000  3.1600  -23.3000
A    3.1600  -23.3000  0.0000  -23.6607   0.0000   -9.6387  S
A    0.0000  -23.6607 -3.1600  -23.3000   0.0000   -9.6387  S
L   -3.1600  -23.3000 -3.1600  -23.0000
L   -3.1600  -23.0000  3.1600  -23.0000
End
Fab: 6.50
Rotate: 90.000  0.000  0.000
Surface Region Cathode
Coat Cathode Emit
END

This week we started a complete overhaul of the example libraries. We are making the following improvements:

1. Elimination of redundant or non-essential entries.
2. Complete retesting with the latest program versions and conversion to a consistent format.
3. Creation of an example index for each program with short descriptions of the techniques employed.
4. Production of a PNG illustration for each example. Using an image viewer, a user can quickly get a sense of the nature of the calculation.

With regard to last item, I highly recommend installing the FastStone Image Viewer, available at

http://www.faststone.org/index.htm

Finally, we appreciate any application examples you would like to contribute, and we welcome suggestions for useful examples.

I feel the main challenge to new users of technical software is the gap between buying the program and comfortably using it. Potential customers have two understandable apprehensions:

• Is it possible for a normal person to learn the program?
• After the investment of time and money, will the program handle the application.

I am experimenting with a new support option that hopefully resolves both issues. It involves a three-step process:

1.  To begin, I correspond with users to understand their application and to define a clear set of simulation objectives. I can then tell them exactly what the software can accomplish and give a fixed-price quotation for a complete package.
2. If they decide to proceed, I prepare a set of input files for an application calculation.
3. I then set up an interactive Web meeting where we can walk through the solution. I can demonstrate how the programs work and discuss the reasons for my decisions on mesh generation and run parameters.

The procedure gives users the advantage of my experience with electromagnetics and knowledge of the codes while minimizing consulting and travel costs. It is beneficial to me in two ways: 1) I enjoy solving real-world problems and 2) the direct interactions help identify code problems and suggest new features.

For the Web meeting component, I am testing the new DimDim service. Despite the unfortunate name, it is technically advanced (e.g., built in two-way audio, desktop sharing,…) and steadily improving. They have free and low-cost professional plans, and they are surprisingly responsive to tech help requests. Most important, it isn’t necessary for users to sign up for a program or to install software. Here’s a link:

http://www.dimdim.com/