---

2. Dipole “D6” after the Wien Filter

1. Introduction (brief description of previous series)

The program ¹⁾ called after the spectrometer “LISE” ²⁾ has been developed in GANIL (Caen, France) to calculate the transmission and yields of fragments produced and collected in an achromatic spectrometer. This code allows to simulate an experiment, beginning from the parameters of the reaction mechanism and finishing with the registration of products selected by a spectrometer. The program allows to quickly optimize the parameters of the spectrometer before or during the experiment. It also makes it possible to estimate and work in conditions of maximum output of studied reaction products and their unambiguous identification.

Wedge and Wien filter selections are also included in the program. In-built Energy loss, Time-of-Flight, Position, Angular, Charge, Cross-Section distribution plots and dE-E, dE-TOF and Z-A/Q two-dimensional plots allow to visualize the results of the program calculations.

An application of transport integral ³⁾ lies in the basis of fast calculations of the program for the estimation of temporary evolution of distributions of phase space.

Recently in the frame of the collaboration Dubna-GANIL the program has undergone a number of serious changes and has been adapted to the environment of "Windows":

• Being adapted to the 32-bit operating system “Windows” the program has received an improved interface with which the user gets all opportunities of the given operating system (work in several windows, drivers of a seal etc.);
• The concept of a “dead” layer of a target has been incorporated (that is very important for work with thick targets producing light exotic nuclei);
• There appeared an opportunity to choose the parameterization of fragmentation cross-sections ^4,5) and model the charge distributions of ions ⁶⁾;
• A number of the graphic subroutines have been changed, while some discrepancies have been corrected;
• A number of the utilities for account of optimum sizes (thickness of a target, energy of a beam, magnetic rigidity) are added at the given parameters of spectrometer;
• In-built information support helps the user quickly take possession of the program;
• In-built database of nuclides (Mass excess, Binding energy, b-decay energy, S_2n , S_2p , Q_a , S_n , S_p , T_1/2) ^7,8) has been added. It is possible to see a transmission of a given isotope, its characteristics and energy after second dipole clicking on an isotope of interest in the table of nuclides by the right button of the mouse;
• The optical parameters of the spectrometer are entered as transport matrices ⁹⁾ that are more convenient. Initial angular, spatial and energy emittances of beam are used;
• The new dipole after the Wien filter of velocities has been added (see §2. Dipole “D6).

It is possible to receive this program and the last version for MS-DOS using FTP to the address (user: anonymous):

• 192.93.218.174 (at Caen);
• 159.93.20.89 (at Dubna).

2. Dipole “D6” after the Wien Filter

The dipole “D6” is placed on the turning platform in a vertical plane behind the Wien Filter. The dipole radius is determined as R @Lm / q , where q is the angle of platform turning. Angle may be varied from 0 up to 23 degrees. This dipole (denoted as DSMW on the Fig.1) serves for the fourth selection on the mass and the charge of nucleus (A/Q). Selection by this dipole as the Filter Wien is performed in a vertical plane.

Fig.1

2.1. Angle of platform

The angle of platform turning is calculated from the optical conditions and as much as possible to compensate the filter velocity dispersion to get only A/Q dispersion at the focal point after turning dipole. The Wien filter optical structure supposes that six focalization conditions must be fulfilled to have the best matching at the detection location. With addition of the turning dipole D6 these conditions must be saved. To find the angle of turning it is necessary to solve the following equation (given by R.Anne) arising from optical conditions:

, [1]

. [2]

The image shift of nuclei in the final focus plane can be roughly determined in the following way :

, [4]

, [5]

Using equation

, [6]

[7]

. [8]

[9]

[10]

Some possible combinations are considered in the program :

• D_D6 = 0 (the dipole is absent)
• D_filter = 0 (the velocity filter is absent)
• D_D6 ¹  0, D_filter ¹  0, D_filter ¹ D_D6  (it means that the angle of platform turning is not correct)
• Br ₂ ¹ Br _D6

The image size (distribution) defined in the program LISE is a result of convolution of two distributions P_Y and P_Y’ :

, [11]

1. P_Y - The image in the vertical focal plane before the Wien filter multiplied by the vertical magnification (y/y) of the filter-dipole system.
2. P_{d /Y} - contribution of momentum distribution due to dispersion in the final focus plane which is possible to determine as

, [12]

Repeating all steps like in the previous section it is possible to conclude that the use of the "fd-system" supposes that P_d/Y vanishes because as it was metioned before the sum (equation 9) is close to 0 and the value D (A/Q) for an isotope relatively itself is equal 0. It means that the final Y-image will be narrower, thus providing a better resolution than in the simple case of the velocity filter only. Hence the second distribution is taken as the d -function in order to get  as a result of convolution.

After this consideration it is possible to compare the “fd-system” with an ordinary velocity filter (see Table 1) : application of the “fd-system” provides better results for smaller object size and wider momentum distribution.

Table 1.
 

Spectrometer	SISSI + degrader in LISE	SISSI + degrader in ALPHA	LISE	LISE2000
Y-object size, mm	0.2	0.2	1.5	1.5
magnification (Y/Y) 1	15.91	12.18	4.26	3.14
magnification (Y/Y) 2	0.43	3.44	0.43	0.60
magnification (Y/Y) Wien	1	1	1	1
Y-object size final, mm	1.37	8.37	2.76	2.83
Acceptance, %	0.5	0.5	2.5	5
Dispersion W, mm/%	3	3	3	3
Acc*DispW, mm	1.5	1.5	7.5	15
Y-image final, mm	2.0	8.5	8.0	15.3
Y-image / Y-object	1.5	1.0	2.9	5.4

2.4. Separation with the Dipole D6

The LISE standard configuration was chosen in order to compare different modes of selection. These experimental settings (beam, target, wedge, slits) are given below.

The advantage of using all 4 selections follows apparently from Table 2. In this case the purification is 30 times better than after the first selection, but the ³⁶Ar rate is lower only in 1.5 times. Figures 2 and 3 show vertical space distributions in the focal final plane for selections by the velocity filter and the “fd-system”. The contribution of momentum distribution into the vertical image due to existence of non-zero velocity dispersion in the mode only with the velocity filter (Fig.2) makes the image wider as compared to the “fd-system” that was already discussed in “§2.3. image size”.

2.5. The program “LISE” for the new spectrometer VAMOS

VAMOS ¹⁰⁾ is a collaboration to build a large acceptance spectrometer for identifying products of reactions induced by the Systeme de Production d'Ions Radioactifs et d'Acceleration en Ligne (SPIRAL) facility at the Grand Accelerateur National d'Ions Lourds (GANIL).

The QQFD-spectrometer VAMOS has the following main properties and characteristics:

• A very large geometrical acceptance, of the order of 100 msr, that is equivalent to an angular acceptance of ±160 mrad ;
• A nominal dispersion of about 2.5 cm/% at the focal plane ;
• A momentum acceptance of the order of ± 5% ;
• A velocity filter function.

Version 3.4
[general]
File = C:\LISE\config\VAMOS.lcf
Date = 12-05-1999
Time = 13:41:31
Title = VAMOS
[object]
X Slits before target = 10 (±)mm ; hor.slit width before target to collimate a beam
Y Slits before target = 10 (±)mm ; ver.slit width before target to collimate a beam
X Slits intermediate = 100 (±)mm ; hor.slit width at the dispersive focal plane
Y Slits intermediate = 10 (±)mm ; ver.slit width at the dispersive focal plane
X Slits first focus = 10 (±)mm ; hor.slit width at the first focal point /after wedge/
Y Slits first focus = 10 (±)mm ; ver.slit width at the first focal point /after wedge/
Slits second focus = 10 (±)mm ; ver.slit width at the second focal point /after Wien/
[acceptances]
Maximal momentum accept = 5 (±)% ; upper limit for the setting of the slits
Theta target acceptance = 160 (±)mrad ; angular target horiz.acceptance
Theta wedge acceptance = 200 (±)mrad ; angular wedge horiz.acceptance
Phi target acceptance = 160 (±)mrad ; angular target vert.acceptance
Phi wedge acceptance = 200 (±)mrad ; angular wedge vert.acceptance
[optics]
BX = 1.5 (±)mm ; one-half the horisontal beam extent (x)
BT = 3.3 (±)mrad ; one-half the horisontal beam divergence(x')
BY = 1.5 (±)mm ; one-half the vertical beam extent (y)
BF = 3.3 (±)mrad ; one-half the vertical beam divergence (y')
BD = 0.1 (±)% ; one-half of the momentum spread (dp/p)
Ra1 = 2.6 m ; Curvature radius of first dipole
Ra2 = 2.003 m ; Curvature radius of second dipole
L target-wedge = 0 m ; Object - DispFocPlane
L wedge-detector#1 = 0 m ; DispFocPlane-AchrFinalPlane
M1X = 1 ; X Magnification target -> wedge
D1X = 10 mm/% ; X dispersion target -> wedge
M1T = 1 ; theta magnific. target -> wedge
D1T = 0 mrad/% ; theta dispers. target -> wedge
ThX = 0.1 mrad/mm ; theta/x coef. target -> wedge
M1Y = 1 ; Y Magnification target -> wedge
PhY = 0.1 mrad/mm ; fi/y coef. target -> wedge
M1P = 1 ; fi magnificat. target -> wedge
M2X = 1 ; X Magnification wedge -> focal
D2X = -10 mm/% ; X dispersion wedge -> focal
M2T = 1 ; theta magnific. wedge -> focal
D2T = -1 mrad/% ; theta dispers. wedge -> focal
T2X = 0.1 mrad/mm ; theta/x coef. wedge -> focal
M2Y = 1 ; Y Magnification wedge -> focal
P2Y = 0.1 mrad/mm ; fi/y coef. wedge -> focal
M2P = 1 ; fi magnificat. wedge -> focal
Angle = 0 mrad ; beam respect to the spectrometer axis
[wien_filter]
Wien filter = Enabled ; Disabled & Enabled
E_F = 2000 kV/m ; electric field
B_F = 478.861416 G ; magnetic field
DiC = 1.3856e-3 mm/% ; dispersion coefficient
LenE = 1 m ; effective electric length
LenB = 1 m ; effective magnetic length
Red = 1 ; Real/Red field
Mag = 1 ; Magnification

3.1. Physical calculator

Very often it is necessary for User to perform a fast transformation of one physical value to another  while working with the program. The dialog “GOODIES” allows to get calculated correlated value only for a given Br -value obtained for a setting fragment. However, if User needs to know (for example) a range in some material for energy unconnected with given settings? The new version of the code “LISE” allows to solve this problem. The new dialog “Physical calculator” permits immediately to perform calculations of correlated values independently from calculations for a setting fragment. Clicking on any radiobutton User may choose the respective form to type a physical value in order to get other correlated values. For example, User may input the Br -value for ³⁶Ar (see Fig.4) and get all correlated values including the range in the given material and the energy loss for the chosen thickness, or typing the energy rest ²²Al after the material (Si 100 mg/cm² in Fig.4), one can recalculate initial energy of a nucleus before the material and other correlated values as shown in Fig.5.

Fig.4,5

The eight correlated values of a nucleus (which is inputted in the upper part of the dialog) are included to “Physical calculator”:

• Energy [MeV per nucleon] ;
• Br -value [Tm] (for calculations it is taken Qt - the ionic charge) ;
• TKE is the Total Kinetic Energy [MeV] ;
• Velocity [cm/ns] and beta ;
• Range in the specific material chosen by User. The Range may be inputted in mg/cm² as well as in micron form.
• Energy rest of a nucleus [MeV per nucleon] after the material defined by User. For convenience the energy loss [MeV] in the material is shown in the static window below.

3.2. Configuration file

Two types of files were used in the previous version of the program : LISE-file (extension LIZ) and Result-file (extension RES). The data settings could be recovered only from LISE-files. If User wanted to repeat old settings for a new file it was necessary first to find the corresponding LISE-file with same setup configuration and then to save it with a new name. In the new version there is an additional possibility to save and to extract settings to/from the new kind of file is called Configuration-file. User has an access to these files via the menu “File -> Configuration”. These files contain only some divisions from standard LISE-file :

• general (date of creating, description);
• object (size of all slits);
• acceptances;
• optics;
• Wien-filter.

On the base of optical matrices and physical characteristics of setups given in the Ref.^11,10), different setups for the LISE program were put to configuration files. User may find these configuration files in the distributive version “lise34.zip” :

• LISEstandard.lcf - the standard spectrometer LISE configuration. A target is placed into the LISE target box ;
• LISE2000-bis.lcf - the new project of the spectrometer LISE with large angular and momentum acceptances, maximal magnetic rigidity of the second dipole is 4.3 Tm . A target is placed into the LISE target box ;
• SISSI_AlphaDegrader_AlphaArete.lcf - a target is placed into the device SISSI, an achromatic degrader in the dispesive focal plane of the spectrometer Alpha. The final focus plane is “ARETE” (the Alpha spectrometer outlet) ;
• SISSI_AlphaDegrader_LISEd6.lcf - a target is placed into the device SISSI, an achromatic degrader in the dispesive focal plane of the spectrometer Alpha. The final focus plane is the hall “D6” of the spectrometer LISE ;
• SISSI_LISEdegrader_LISEd6.lcf - a target is placed into the device SISSI, an achromatic degrader in the dispesive focal plane of the spectrometer LISE. The final focus plane is the hall “D6” of the spectrometer LISE;
• VAMOS.lcf - this configuration has been already discussed in “§2.5. The program “LISE” for the new spectrometer VAMOS”.

3.3. Angle for Thickness

Fig.7.

Physicist may vary a target thickness changing an angle of target that is placed into the target box of the SISSI device or the LISE spectrometer. Sometimes it is necessary to calculate and input the value of the angle in the experiment. In the new version of the code User can change an angle of a target (wedge, degrader, materials). There is a possibility to calculate each of three values from the two other known ones : Effective thickness, Thickness at 0 degrees or Angle of turning (see Fig.7). For example, if User knows the effective target thickness and the thickness at 0 degrees he can simply click on the button “Calculate Angle ” to get the angle value as shown in Fig.7. User may input the material thickness using two dimensions : mg/cm² or microns.

3.4. List of recently used files

To open a document User has used recently, it is necessary to click its name at the bottom of the File menu where the list of recently used documents is placed.
 
 

3.5. Calculation of Q-ground value for binary reaction

In the new version User may see a Q-value of reaction at the bottom of the window “ Statistics ” (this window is appeared when User clicks on an isotope of interest in the table of nuclides by the right button of the mouse). Q-value is calculated from the supposition that the reaction has two nuclei as a result. The first nucleus is the nucleus chosen by User, the second one is calculated as residual from “ Projectile + Target - Fragment of Interest ”. Therefore Q-value is estimated as :

Fig.8 .

3.6. Chromatic mode (Dispersion ¹ 0)

Since its first version, the program has been adapted to operate only in the achromatic mode. The focal plane of the second section being achromatic, there is no momentum dependence of the final horizontal position (as well as vertical). In the new version the admission that the full momentum dispersion is not equal to 0 has been included. User may observe this admission on the Wedge image (X) plot in the First focal plane. This assumption is fulfilled because the selection by the velocity filter and the dipole “D6” takes place in the Y-plane. Using this new mode User may visualize the images and obtain a transmission not only for “ideal” case of an achromatic spectrometer.

The code is calculated full momentum and angular dispersions on the base of inputted in the program the two transport matrices for both parts of the spectrometer as :

,  [14]

. [15]
 

Fig.09. 

Fig.10.

Fig.11. 
 

4.1. Results file

The Results file has not been changed since its DOS-version 2.5, and consequently in versions 3.0-3.3.05 it does not reflect all parameters needed for User (“D6”-dipole parameters, applied methods of the cross-section parameterization and the ionic charge state distributions, target angle). In the new version the Results file has got more readable form, and all values needed for further work of User with this file have been included.

LISE CALCULATIONS Version 3.4
File : C:\user\OLEG\winlise\FILES\36Ar_22AlLisenodegr.liz
Date : 5/19/1999 Time : 9:13:01
Title : 22Al
Projectile : 36Ar 18+ at 94.4 MeV/u - Intensity : 1000 enA
Target : Be Thickness : 537.95 mg/cm2 (2907.84 microns)
Wedge : Be Thickness : 196.47 mg/cm2 (1062 microns)
Material(s) :
#1 : Si Thickness : 69.9 mg/cm2 (300 microns)
#2 : Si Thickness : 69.9 mg/cm2 (300 microns)
#4 : Si Thickness : 116.5 mg/cm2 (500 microns)
#5 : Si Thickness : 116.5 mg/cm2 (500 microns)
#6 : Si Thickness : 1398 mg/cm2 (6000 microns)
Settings calculated on 22Al 13+ 13+
Brho1=1.9530 Tm Brho2=1.7100 Tm (B1=0.7512 T B2=0.8537 T)
Wien filter : E=3500.0 kV/m B=331.8000 G Disp=3.184 mm/% Magn=1
D6 : B=0.5354 T Angle=13.97 deg Disp=3.185 mm/%
Mechanism: Vopt/Vbeam=1.000 Sigma0=90.0 MeV/c SigmaD=200.0 MeV/c
Methods: Cross Section=0 Charge states=0
Acceptances :
Maximum momentum acceptance : +/- 2.50 %
Target : Theta : +/- 17.45 mrad Phi : +/- 17.45 mrad
Wedge : Theta : +/- 20.26 mrad Phi : +/- 6.00 mrad
Slits :
X,Y Slits before target (Collimator) mm +/- : 15 15
X,Y Slits intermediate (Momentum sel.) mm +/- : 8.6 10
% in Brho +/- : 0.50
X,Y Slits first focus(Wedge selection) mm +/- : 7 10
Second image slits (Wien selection) mm +/- : 5
Beam emittance (+/-): 1.5 mm 3.3 mrad 1.5 mm 3.3 mrad 0.1 %
Beam angle on target : 0 mrad
OPTICS ([mm],[mrad]):
Target - DispFocalPlane(Wedge) DispFocalPlane(Wedge)-First image
-0.783 * * * 17.3 -2.5607 * * * 44.3
0.267 -1.284 * * 3.51 0.4 -0.389 * * -5.56
* * -4.26 * * * * -0.432 * *
* * -0.858 -0.273 * * * -0.32 -2.4 *

TRANSMISSION AND RATE CALCULATIONS
A Z |Qt |Qw | Ang. | Brho |Wedge |WienD6|Y&C&DT| Total | Cross | Rate | Qt | Qw
| | |Trans.|Trans.|Trans.|Trans.|Trans.| Trans.|Section| | |
| | | (%) | (%) | (%) | (%) | (%) | (%) | (mb) | (pps) | (%) | (%)
-----|---|---|------|------|------|------|------|-------|-------|-------|------|-----
23Si| | | 6.534| 4.692| 85.05| 2.641| 88.41| 0.0061|3.3e-06| 0.0025| |
22Al| | | 6.291| 10.40| 86.17| 99.78| 88.41| 0.4972|0.00049| 31| |
21Mg| | | 6.018| 4.905| 84.89| 0.921| 88.41| 0.0020| 0.029| 7.5| |
================================================================================
ALMOST : 38 pps
 

4.2. New parameterization

The code used three in-built parameterizations of cross-sections on the EPAX ⁴⁾ base. The new parameterization EPAX 2.13 has been kindly presented by B.Blank and K.Summerer for the new LISE-version. This new approximation shows very good agreement in cross-section estimation for proton rich fragments, while for the super neutron rich isotopes placed far from a beam ¹²⁾ the discrepancy appears (see Fig.12) as in the previous parameterization but from the other side.

Fig.12.

User may choose the new parameterization to perform calculations via the Menu
“Options->Production Mechanism”.

4.3. Trigonometric function of the in-built calculator

The trigonometric functions (sin, cos, tan, arcsin, arccos) have been added in the in-built calculator. User has also got an opportunity to choose units (degrees or radian) for trigonometric calculations (see Fig.13).

4.4. Three points interpolation for the energy loss and range subroutines

5. Plots

5.1. image after Wedge & D6 (one-dimensional plot) and dE - Y image (after wedge & D6)
 

Two kinds of plots have been created to visualize Y-image distribution in the final focus plane after the velocity filter and the dipole “D6”. The one-dimensional plot (left menu) has been already presented in Fig.2 and 3.  The two-dimensional plot (right menu) dE-Y (Energy Loss versus Y-image) is presented in Fig.15.

5.2. dE-dE plot

Fig.17.

5.3. dE-X plot

5.4. Plot of Q-ground values

Fig.19.

5.5. Realistic image of peaks

  Two-dimensional plots in standard mode are drawn only by one color corresponding to their intensity. The width of peak is equal to its distribution FHWM. “Realistic” mode for peak drawing uses some colors depending on a distance between the peak center and given point inside the peak (width ±  2s ). Example of the plot drawn in the “realistic” mode is presented in Fig.17.

5.6. Gray and Color Palettes for two-dimensional plots

  User does not always have a possibility to print two-dimensional plots on color printers. Therefore the button has been added to switch the palettes of plot to reproduce intensity of peak for printing.

6.1. The thickness dialog - density

Before it was impossible to input a float value into the density window of the thickness dialog. This has been corrected.

6.2. The dialog “Calibrations”

After inputting new nucleus in the calibrations dialog the range was not recalculated. This has been corrected.

6.3. Adaptation the code to the PC emulator on Mac

Cross-section calculations were performed incorrectly on Mac under the PC-emulator due to some discrepancy in the C function “pow(x,y)” between these system platforms (?). The function pow(x,y) has been changed in the code by redefinition #define pow(x,y)  exp((y) log(x))

6.4. Negative dispersion

The negative momentum dispersion provoked a crash of the program. This has been corrected and User may use the negative momentum dispersion.

6.5. After reading of a LISE-file the program did not calculate magnetic field

The conjugate values (Br and B) are immediately recalculated when User changes the Br-values or the B(magnetic field)-values using the dipoles dialog or when the program calculates these values. When User read a LISE-file, the Br-values were inputted into the code but without recalculation of the magnetic field. This has been corrected.

6.6 Distributions

Some bugs provoking crash of the program have been corrected.