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If you click with the left mouse button at the system menu or into the black canvas of the envelope display window, then a dialog box pops up which offers you either to print the screen display to a postscript file or to copy it to the clipboard. Both actions are now performed with color support. (The default printer has to be a color ps printer.) In order to use these copies e.g. in reports or presentations, the canvas is kept white instead of black (black and white are reversed compared to the screen output.) Also for ellipse displays you have this possibility, but only via the system menu of the graphic ellipse display window. Hint #1: If you do not have a postscript color printer at hand, then you may additionally install the Generic 'MS Publisher Color Printer' with FILE: as local port and declare this one temporarily as your default printer. Hint #2: If you have GSview 4.9 installed on your computer, you may convert the generated ps files to other formats like e.g. pdf, tiff or jpg.
It is now possible to observe graphically the bunch length (dimension 5 on the beam card) of a bunched beam along a beam line. This may be helpful for beam lines where space charge or/and bunchers play an important role. In order to see this additional 'envelope' you have to switch on its display in the 'display parameters' dialog box (last entry named 'Disp bunch length'). The dimension has to be either MM or CM. (You may have MM for transverse and CM for longitudinal or vice versa or both the same.) This is controlled by appropriate type code 15 entries at the beginning of the Transport input file. If there are some Sigma (Beam) matrix constraints for the longitudinal beam extent ( (i,j) = (5,5) ), then each fitted longitudinal beam extent is shown in the envelope display similar to fitted horizontal beam extents.
When trying to run Transport including space charge computation with heavy particles (e.g. m=210 amu) and very low momentum (e.g. p < 69 MeV/c) then the program was crashing with a misleading error message. This has been caused by the fact that for these particles gamma becomes 1.0 in single precision and therefore beta equal zero. This condition has now been corrected by computing these 2 parameters locally in double precision.
In early versions of Transport of 1985 or before the 2nd order matrix elements T556 and T566 for a drift space are incorrect and do not correspond to those of the FNAL Transport version 1.6. This bug has been reported by George Gillespie and has been repaired now.
The magnet settings (if selected in the 'Display Parameters' list) were not shown in red or blue like the corresponding labels and apertures. For solenoids the color of the label was not always drawn in red. It was depending on the first letter of its text. Both inconsistencies have been corrected and are now like in the Windows version.
Recently there was some interest in looking at the (x,y)- and (x',y')-ellipses with Transport. Because of the x-y-coupling of the particle movement in solenoids the correlation coefficients r(31) and r(42) [see CERN 80-04, page 33] are not always zero which means, that the (x,y)- and (x',y')-ellipses are not always upright. There are now 3 menu items for the ellipse display with Windows: 'Graphic' -> 'Ellipses (x,x' and y,y')'. 'Graphic' -> 'Ellipse (dl,dp/p)'. 'Graphic' -> 'Ellipses (x,y and x',y')'. All 3 ellipse displays may be shown simultaneously. The Ellipse Display control dialog bars are cascaded at fixed positions at the upper left of the screen but each window containing an ellipse display may be moved to arbitrary positions and/or rescaled. See screen shot [71 kB]. For Linux and Mac OSX-X11 three new sub-menus for each ellipse display has been created: 'Beam Ellipses' -> 'Display (x,x' and y,y') beam ellipses' or 'Display (dl,dp/p) beam ellipse' or 'Display (x,y and x',y') beam ellipses'. All 3 ellipse displays may be shown simultaneously. For the new menus (Mac OSX Panther) see screen shot [66 kB]. The Linux menus (besides some style details) are identical.
10 menu items for tabulated data and parameters computed in the graphic mode of Transport are now selectable with a more user-friendly Tcl/Tk sub-menu. For each menu item the output is given in an own xterm window. The windows are kept open until the 'Return' key is pressed. By adding a P or F key the data are either printed ore stored on a file. The old version may still be used by selecting the menu item 'Command Shell...' and entering there the command ./dispo or simply ./o . Recently there has been observed some growing interest in studying longitudinal projected phase space effects with Transport. In order to visualize graphically the propagation of dl and dp/p along a beam line a new menu item has been created for having displayed the projected phase space for the coordinates 5 (dl) and 6 (dp/p): For Windows the menu item: 'Graphic' -> 'Ellipse (longitudinal)'. For Linux and Mac the menu item: 'Display longitudinal beam ellipse'. Ellipses of projected transversal and longitudinal phase spaces may be displayed simultaneously. Longitudinal phase space effects are specially interesting with type code 11 (electrostatic accelerator, einzel lens), type code 22 (space charge) and type code 23 (RF-buncher).
The focal-length expression f in the used formula for computing the transfer matrix elements for the electrostatic accelerator was changed from the non-relativistic to the relativistic expression {f = -2*p0*v0/(E1-E0), was -4*T0/(E1-E0) , see Compendium of Transport Enhancements}. The matrix element R56 was not correctly computed in case the space charge feature (type code 22) was not turned on. Instead of the expression given in the 'Compendium of Transport Enhancements' an additional term L/gamma**2 was added to R56 for each segment (L=segment length). This bug has now been corrected. In the Compendiums's example 1, space charge is turned on (I=15 mA) for the accelerator tube, but for example 2 no space charge is present for the Einzel lens. (The longitudinal bunch length was not intended to be an issue for these 2 examples.) Up to now, when resizing the window of the envelopes or ellipses the window's content did not get resized. This situation has now been improved. During the resize operation the content still does not follow, but the window's new size is stored on file and for the next drawings the content will fill in the window's new dimensions. But there is a limitation: In order to see the '*4'-feature of the ellipse display properly drawn, the aspect ratio of the window has to be about 4 to 3. The rescaling of the screen display window has no effect on the printed copy (always full scale landscape format). A longtime nuisance for some users was the fact, that imported Transport input files from the Windows environment did not work under Linux/MacOSX-X11 (due to a non-feature of the GNU g77 FORTRAN compiler) without removing the CR-character (ASCII-value 13) before the LF-character at the end of each line. This problem has now been resolved by having the (Fortran-) code replacing each CR-character by a blank-character during the read-in process. Please note, that all the Transport programs (like QOI, BOI, BRHO etc.) which modify the input rewrites FOR001.DAT (only up to the 1st SENTINEL line) and FOR004.DAT without the trailing CR-characters. Some additional minor problems have also been solved.
The positioning of xterm and graphic output windows relative to the menu has been corrected. This may be useful for large multi-screen displays in control-rooms. Default values for the parameters of FOR004.DAT have been implemented so that a faulty or missing FOR004.DAT does not produce an error message. The 'Compendium of Transport Enhancements' shows in chapter 16.3 how measured beam line profile data and quadruple DAC settings may be transferred (via FOR022.DAT) into the input file (FOR001.DAT). This procedure requires a calibration file QUADS.CAL (see also Appendix C of the Compendium) for the quadrupoles in use for the beam line. Newer developments of the PSI proton accelerator control system (ACS) make QUADS.CAL partly obsolete, because ACS has its own data base for all quadrupoles in use. Instead of DAC values the I/O-displays are now using B-field values (at the pole tip) in kG (or Gauss). Therefore a new handler for a differently formatted FOR022.DAT has been built into Transport in order transfer the measured data.
new format:
line 1 to 3: 30 values for Quadrupol B-fields in Gauss, in a row (10F10.1)
line 4 to 6: 30 values for one-sided horizontal profile widths in mm (2 * Sigma), in a row (10F10.1)
line 5 to 9: 30 values for one-sided vertical profile widths in mm (2 * Sigma), in a row (10F10.1)
example:
-768.0 -72.0 -207.0 -33.0 1236.0 -1466.0 -2882.0 2215.0 1344.0 -523.0
-3127.0 3327.0 -2095.0 3416.0 -1937.0 1290.0 -3046.0 2185.0 0.0 0.0
0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
4.4 8.7 9.9 10.0 5.0 4.4 4.7 9.7 3.9 11.6
5.4 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
3.0 1.8 -3.5 5.2 7.5 4.9 2.0 2.2 4.2 5.9
3.1 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
-> a negative or zero profile width means that the measured value gets an accuracy of +-999.9 mm
(zero weight for fitting).
Transport Framework for Windows menu entry: O->I Func | FxyGauss (FOR022.DAT)Tpmenu for Linux and Mac OSX-X11 menu entry: Insert Quad- and Profile-Data (new) The old handler for DAC values is still working if an adequate QUADS.CAL is present: Transport Framework for Windows menu entry: O->I Func | FxyDac (FOR022.DAT) Tpmenu for Linux and Mac OSX-X11 menu entry: Insert Quad- and Profile-Data (old) When entering PX at the envelope display's prompt (L: Lasercopy,<CR>:red cursor), then a column containing the initial beam data and the B-field values (in Gauss) of all quadrupoles is added to the print-out at the right side of the plot. When entering PD instead of PX, then the quadrupole's DAC values instead of the B-field values are displayed. The conversion of B-field values (in kG) to set-point values is done with the help of the conversion table QUADS.CAL. For a quadrupole, whose data do not match to any of the table's data, its B-field value multiplied with 1000 and truncated to the nearest integer is displayed (B-field value in Gauss instead of set-point value in DAC-units).
The 'Floor Layout coordinates' table contained wrong values for the angle theta in case the angle phi was unequal 0. This bug has been fixed. The hint came from Phil Pile (BNL).
This port is 99.9% compatible with the Linux-version. So all features, which are running under Linux are also running on the Mac. It has been tested with Mac OSX Version 10.3.2 and X11 1.0 - XFree86 4.3.0. Besides X11 (from Apple) tcltk and xemacs (e.g. from http:// fink.sourceforge.net/index.php) are needed for fully functioning.
It has been observed, that the coding of the floor-layout coordinates for the 3 electrostatic elements (prism, Wien-filter and accelerator) was missing (but not for the electrostatic quadrupole). This negligence has now been corrected.
The envelope display's tick-marks on the z-axis were not properly placed. The spacing between all the equally distant marks was mistakenly scaled with a factor of 0.8 and therefore the last ones near zmax were also missing. (But the corresponding spacings of the print-out of the envelope displays were correct.) This error has now been corrected. When entering PX at the envelope display's prompt (L: Lasercopy,<CR>:red cursor), then a column containing the initial beam data and the set-point values (in DAC-units) of all quadrupoles is added to the print-out at the right side of the plot. The conversion of B-field values (in kG) to set-point values is done with the help of the conversion table QUADS.CAL. For a quadrupole, whose data do not match to any of the table's data, its B-field value multiplied with 1000 and truncated to the nearest integer is displayed (B-field value in Gauss instead of set-point value in DAC-units).
During this procedure no I/O-screen was available for diagnostics output and the help feature. This has been corrected by opening an xterm-window titled 'displaw' during the whole ellipse display session. Fitting with the stochastic algorithm takes quite some time. In order to show its progress, dots are written to the xterm-window 'tpmenu'. Unfortunately they were all buffered and only sent to the screen at once at the very end of the fitting procedure. This behavior has been corrected so that the flux of dots to the screen happens continuously in real time.
When using tpmenu (Tcl/Tk shell) for running Transport, then an error in the input file FOR001.DAT prevented Transport from running even after the error in FOR001.DAT had been corrected. (Only exiting and restarting tpmenu cured this problem.) This has now been fixed by inserting the line 'set errorCode 0' at the appropriate places in tpmenu. A legacy module written in FORTRAN-77 for inverting the position of elements along a beam line has been recompiled and included into the Transport Framework. There are several limitations, because the method is rather crude and not all input codes (FOR001.DAT) can be treated correctly. Each Transport input file may be divided into 3 sections: 1.) Top of the file down to the beam definition (type code 1., 12. and 14.) including type codes 13., 15., some 16. and some eventual comment in parenthesis. 2.) All elements with physical length and some intervening parameter definitions, i/o-controls and fit constraints. 3.) Fit sequences (starting with an {empty} title and ending with SENTINEL). The inversion algorithm tries to find the separation lines between these 3 sections and leaves section 1 untouched, reverses the order of the elements in section 2 and deletes section 3. In section 2 some special features like label shifting for drift elements or shifting type-code 16. and type code 20. elements belonging to bending magnets are performed. Type codes 6. (if its meaning is Update and not Slit) and 8. are deleted. The initial beam parameters have to be altered manually by e. g. extracting the final beam parameters before inverting the beam line and using these as initial beam parameters for the inverted beam line.
The menu and the task bar of the Transport Framework for Windows have a built-in copy tool, which allows saving e.g. Transport input files (for001.dat) under xyz.dat. If the destination path already exists, then the content of the file being overwritten is now saved under the same name but with the extension dat2 instead of dat. When using the copy tool, the file selection boxes show now also all existing files with a dat2 extension.
The to small font size and the to small left margin of text printout have been corrected. The empty trailing page has been removed. Note: Printing of the content of text windows may be started from its system menu. The Info text of the GUI-editor (help file) may now also be printed via its system menu.
In 2 tables of the 'Tables' menu items, the 1/R-value of the entrance fringe field of all but the first bending magnets was the same as for the exit fringe field. This bug has been fixed now.
The capability to apply constraints to floor layout coordinates (activated with code 13. 12. ;) while fitting with the stochastic solver (activated with code 16. 31. ; ) has been added to this version of Transport. (Using the standard gradient search solver for fitting with these types of constraints will not work.) In the 'Tables' menu an additional item for inspecting the floor layout coordinates in a separate window has also been added. (The capability to produce some graphic output of the layout will eventually be added sooner or later.) Example: /Simple sample code for fitting floor coordinates/ 0 16. 16. -2.423 /X0/ ; (Initial beam line position) 16. 17. 0. /Y0/ ; 16. 18. 7.969 /Z0/ ; 16. 19. 150. /THE0/ ; (Initial beam line direction) 16. 20. 0. /PHI0/ ; 13. 12. ; (Output is beam line layout in global coordinates) 1. 0.116 9.854 0.160 12.525 4.900 0.500 0.69556 /BEAM/ ; 12. 0.142 0. 0. 0. 0. -0.770 0. 0. 0. 0. 0. 0. 0. 0. 0. /CORR/ ; 13. 6. ; (automatic printing of transfer Mx R1 is cancelled) 16. 31. 0. ; (use stochastic solver) 16. 22. 50. ; (50 steps at maximum) 50. 1.0 -20.0 -1.0 ; (limit B-field inside -20 and -1 kG) 3. 0.0 /ZERO/ ; 3. 0.223 ; 5. 0.1475 5.21810 3.25 /Q1A/; 5. 0.14750 5.2181 3.25 /Q1B/; 3. 0.3546 ; 5. 0.1475 -6.9335 3.25 /Q2A/; 5. 0.1475 -6.9335 3.25 /Q2B/; 3. 0.1372 ; 5. 0.1475 4.6882 3.25 /Q3A/; 5. 0.1475 4.6882 3.25 /Q3B/; 3. 0.1691 ; 3. 0.0778 ; 3. 0.3456 ; 3. 0.2429 ; 24. 8. 1. 1. ; (Stores X floor coordinate at entrance of 1st dipole in register 1) 16. 5. 2.3 /GAP/ ; 2. -15. ; 4.0 0.7617 -14.9486 0.0 /B1/ ; 2. -15. ; 3. 0.4064 ; 2. -15. ; 4.0 0.7617 -14.9486 0.0 /B2/ ; 2. -15. ; 24. 8. 1. 2. ; (Stores X floor coordinate at exit of 2nd dipole in register 2) 25. 1. 2. 2. 3. /DIFF/ ; (Register 1, Register 2, Subtraction [code 2], Store in register 3) -10. 9. 3. 0. 0.001 /FIT/ ; (Fits the content of register 3 to value 0. with accuracy 0.001) -10. 8. 1. -1.1 .001 /FIT2/ ; (Fits x-floor coordinate at this position to -1.1 m) 3. 0.2866 ; SENTINEL // -1 10. /FIT2/ ; 4.02 /B1/ ; 4.02 /B2/ ; SENTINEL /*PLOT*/ -1 -10. /FIT2/ ; 10. /FIT/ ; 4.02 /B1/ ; 4.02 /B2/ ; SENTINEL SENTINEL
In case the Transport input file contains an error and you run Transport with it, then a message 'Error in FOR001.DAT' shows up. Newly added is the feature, that after clicking at the OK-button (DLL-version) or depressing the Enter-key (EXE-version) a window containing the corresponding Transport output is popping up. In this formatted Transport output you may usually find all information about faulty lines (e.g. SCANNING STOPS DUE TO ERROR AT POSITION SHOWN BELOW) or missing data (e.g. PARTICLE MASS, IN ELECTRON UNITS, MUST BE GIVEN...).
To avoid white flares showing up while resizing the envelope or ellipse display windows, the background is not erased anymore by returning FALSE when processing WM_ERASEBKGND messages. In addition, during the resizing process more care is provided to keep control over the number of selected GDI objects (fonts and pens) in order to avoid a possible local heap overflow.
Because of the limited local heap memory available for Windows 9x, the default computation mode is now the 32bit-DLL. For Windows NT/2000 it is still the 32bit-EXE. The matrix elements R21 and R43 were too large by a factor of 2. This error has now been corrected. See first the modifications being implemented in February 2001. The data file containing the Display Parameters (FOR004.DAT) has been forgotten to be redirected in February. This has now been corrected.
In order to make the installation of Transport for Windows easier and more transparent, the self extracting file (trawin32.exe) has been compressed with PKZIP's PKSFX option, which allows it to specify the unpacking directory and to start setup.exe in a dialog window. In order to be able to display the envelopes and a shifted trajectory (ray) simultaneously, an additional pair of radio buttons named 'Envelopes' has been added to the 'Display Parameters' dialog box. This new feature may be switched on or off while 'x-Ray' and/or 'y-Ray' are switched on. In order to avoid compatibility problems with the FOR004.DAT files (where the actual values of the display parameters are saved) no additional entry in this file is used. Instead this new feature has been added by extending the meaning of the 'x-Ray' and 'y-Ray' entries (0 for envelopes only, 1 for rays only and 2 for both together).
You have now the possibility to get connected to the PSI Transport home page via the Web by either clicking at the "Help" menu item or the WWW button of the 3rd "about" box. New feature: In case the "short" button in the "View in List-box" section is pressed, then the type code 13, 15 and 16 element's functions are described in a few words depending on their meaning they have in Transport. The implementation of the electrostatic deflecting device has been done as close as possible to the corresponding magnetic device: 16. 94. ; (enable electrostatic deflection) 4. L. alpha. pq. /EPRI/ ; 16. 93. ; (back to magnetic bending)The meaning of the parameters is the following:
L = central length of prism in meters. [deflection radius re0 = (180.0 / pi) * L / alpha]
alpha = deflection angle in degrees.
pq = 0.0 for cylindrical shape.
1.0 for spherical shape.
all other values: toroidal shape with pq = re0 / Re0. [Re0 = vertical curvature radius]
(upper limit = 2.0 - beta**2)
- Only first order matrix elements are included.- No type code 2. for fringing field is available. - Fitting of parameters only with stochastic method possible. - Use 16. 5. g/2. ; for drawing vertical extent of the device. The implementation of the fringing field for electrostatic quadrupoles has been done the same way as for magnetic quadrupoles. (see Compendium of Transport Enhancements): 16. 25. I1. ; (fringe field integral I1) 16. 26. I2. ; (fringe field integral I2) 16. 27. I3. ; (fringe field integral I3) 16. 96. ; (switch to electrostatic QUADs) 2. 1000. ; (compute entrance fringe field) 5.vvv Leff. Ep. a. /EQ/ ; (Ep is the electric field [kV/cm] at the pole tip) 2. 1000. ; (compute exit fringe field) 16. 95. ; (switch back to magnetic QUADs)
Traditionally Lahey Fortran with its TNT DOS extender was used for the Windows 9x (95,98,Me) operating systems. But with the apparent limitation to only 8 char directory names it has been dropped. Now for all Fortran programs the Digital (Compac) Fortran compiler is used for all Windows operating systems. (Today there is no need anymore for using a DOS extender.) For stochastic fit runs the parameters of electrostatic accelerator elements may be varied. (Be sure not to free the 0.0 on the first card of such an array.) Probably only the device voltage of such an array of type code 11 elements makes sense to free (see 2nd example in the Compendium of Transport Enhancements. This option has been proposed by Jay Flanz (Flanz@hadron.mgh.harvard.edu). It offers the possibility in type code 11 series to turn off the focusing either in x or in y direction by setting R21 or R43 to zero. 16. 40. 1. ; (turn off focusing in x) 16. 40. 3. ; (turn off focusing in y) 16. 40. 0. ; (restore standard behavior) When you install Transport for Windows you are asked into which directory it should be installed. Then - besides some DLL's, an editor and a font - all files (executables and data files) are put there. By default all newly created data files are also stored there. If you want to change this behavior - that means you want the data file access redirected to a different location - then you have to change the 1st command line parameter with which Tpmenu32.exe (green/red/black transport icon) is called (default= C:\trans\). You may access this parameter in the properties/shortcut/target entry. By default you would find there: C:\trans\tpmenu32.exe C:\trans\ COM2: C C (program name with 4 parameters on the command line). The 1st parameter you have to replace with the new directory name. (Important: If you forget the backslash at the end of the directory name it will be added!!! but please do not choose names with blanks in it!!!). What do the other 3 parameters mean ? COM2: stands for the communication port for DAC-IO together with PSI secondary beam line hardware. (Hints how to do it at your place could be provided. TCP/IP communication is also possible.) The first C stands for colored envelope/ellipse display (nC would be for only black and white). The second C means the same for printer outputs (nC for only black and white [no dithering] printer output). Up to now this 1st parameter was only influencing file output (left-over from the RAM disk age). Now - in addition - FOR001-input and all file selector boxes have been connected to this directory name. The x-Dispersion (R16) as well as the y-Dispersion (R36) may be turned on separately to be drawn as dotted lines in the envelope displays. They should give a measure of how much 1 % (default) or 0.1 % (1 permil, turned on with 15. 6. /PM/ 0.1 ;) of momentum spread contributes to the beam size. When the momentum during acceleration via type code 11 elements increases, then R66 does not remain 1.0 (decreases with p0/pend) and therefore R16 and R36 are not anymore representing the 1 % (or 0.1 %) trajectories. Therefore this effect has been compensated by drawing R16/R66 and R36/R66 (renormalization). Note: Also space charge and bunchers are producing values for R66 unequal to 1. For low energy beam lines (Tandems, Ion Sources) it is desirable to have the possibility to include electrostatic elements instead of magnetic ones into the beam lines. The electrostatic QUAD has now been included the following way into Transport (very close to magnetic QUADS): 16. 96. ; (switch to electrostatic QUADs) 5.vvv Leff. Ep. a. /EQ/ ; (Ep is the electric field [kV/cm] at the pole tip) 16. 95. ; (switch back to magnetic QUADs)- The used formula for kQ is (see Reference [6] p.99ff): kQ = sqrt( Ep * CHARGE / (a * RiE) ) with RiE = Ekin *(gamma+1)/gamma. (Ekin=particle energy in electron volts, CHARGE=particle charge in units of electrons) The transfer matrix element R11 e.g. is computed according to the following formula: R11 = cos(kQ * Leff). - The electric field gradient E is assumed to rise linearly from 0 at the axis to Ep = 2 * (Vp / a) at the pole tip with Vp to be the voltage at the pole tip with the distance a from the axis. - All 3 parameters may be varied in fit runs. - The dimension of Ep = 2 * (Vp / a) is fixed to kV/cm and may not be changed. - At the moment fringe field computations for this type of QUAD are not available like for magnetic QUADS.
If APFAC is multiplied with -1, then the magnet apertures are drawn in "complementary mode". The positive part has still the same meaning. Try both signs to test which representation you like more ! The charge of the particle (in electron units , default = 1) may be defined. The formula given on page 42 of reference [1] should be in a more generalized form: B(0) = 33.356 * ( p / (rho0 * CHARGE) ) Example: For He++ beams the line 16. 29. 2. ; should be inserted at the place of the stripper. If you start with a He- beam, do not forget to place a 16. 29. 1. ; line after the beam-card. The following type codes are influenced by CHARGE: 2, 4, 5, 11, 18, 19 and 21. - New type code 16. 98. ; All quadrupoles subsequent to this element will be taken as having the same effect in both transverse planes. Thus, if the pole tip field is positive both planes will be focusing. If the pole tip field is negative, both planes will be defocusing. All 3 parameters may still be varied. - New type code 16. 97. ; The normal option is restored for a quadrupole element. It is now focusing in one plane and defocusing in the other. - Note: This feature may also be used to simulate an electrostatic Einzel-lens, if the parameters are adjusted so that the resulting focusing length is the same as the one of the electrostatic Einzel-lens.
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![See screen shot [71 kB].](elidisp.gif){kind=link}
![see screen shot [66 kB].](mactpmenu.jpg){kind=link}