3.2 Experimental Setup and Simulation Geometry
3.2.1 Simulation with MOCADI
For a beam dynamic simulation of the resonance reaction of 33Cl(p, γ)34Arand 34mCl(p, γ)35Ar the Monte Carlo simulation tool MOCADI was used. It is capable of ion-optical transport with higher-order image aberrations. It was developed in the late 1980’s by T. Schwab, H. Geissel, and A. Magel on IBM computers with PL/I language. MOCADI has been used for design studies of the fragment
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20 CHAPTER 3. EXPERIMENTAL FACILITY AND ION OPTICS SIMULATION separator (FRS) at GSI and is used for preparation and analysis of experimental programs at the FRS.
Iwasa et al [33] translated MOCADI into C-language on LINUX and improved its input and output format. CERN-standard one- and two-dimensional histograms (HBOOK) and list-mode output as well as NTUPLE and ROOT Trees are available [34].
Event Generation
In MOCADI the event generation is provided through the functionBEAM.Nions of the primary beam with atmoicnumber, mass, and chargestate are produced with initial position distribution(X, Y), angular distribution(A, B), energy distributionEand time distributionT. More detailed information can be found in the manual (http://web-docs.gsi.de/~weick/mocadi/mocadi-manual.html). The comment sign is *.
Listing 3.1: Event generator for initial beam and modifier in MOCADI
∗BEAM
∗N
∗E0 , T0 , mass , c h a r g e , e l e c t r o n
∗modeXA
∗maxX , maxA , rXA , X0 , A0
∗modeYB
∗maxY , maxB , rYB , Y0 , B0
∗modeET
∗maxE , maxT , rET , E1 , T1 BEAM
1000000
0 . 1 1 2 3 8 3 7 , 0 , 3 3 . 9 7 3 7 6 2 4 8 5 , 1 7 , 0 , 0 , 0 , 180 4
0 . 1 , 0 . 5 4
0 . 1 , 0 . 5 2
0 . 0 0 1 , 0 , 0 , 0 , 0
∗param [ 0 ] = mass t o change t h e beam t o i n [ u ]
CALL / mocadi_sim / c u s t o m _ f u n c t i o n / r e a c t i o n . s o isomeric_beam 3 3 . 9 7 3 9 1 9 6 1 ∗change t o i s o m e r i c mass beam
p a r a m e t e r s
MATRIX ’ i n i t i a l d i s p e r s i o n ’ CRYRING000 .MAT
3 3 . 9 7 3 9 1 9 6 1 , 1 7 , 0 . 1 1 2 3 8 3 7 1 , 1
In listing3.1one can see the code for the event generation that was used for the first resonance energy (110 keV, seen in Table 1.1) of the 34mCl(p, γ)35Ar reaction. This reaction involves proton capture onto 34Cl in its isomeric state; this means that the mass for 34Cl is not the ground state mass, but must be modified according to the excitation energy of the isomeric state. With CALL a custom function is being called. This is needed because the commandBEAM samples according to its given massparameter from the AME2012 table [35]. But this table does not have an entry for the mass of the isomeric state of 34Cl. Therefore, to create the correct mass for the isomeric state in the event generator, it is changed after generation to the right value with the functionisomeric_beaminside the file reaction.c (see listingB.2in appendix for the whole file). The CRYRING has a small amount of
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3.2. EXPERIMENTAL SETUP AND SIMULATION GEOMETRY 21 dispersion. To account for that, the matrix ’initial dispersion’ on the end sets the beam to the correct dispersion of the ring.
The energy and initial position distributions are also set with the commandBEAM. These represent the emittance of the incoming beam. It is set to a low setting to obtain results that are independent of the emittance. It has been adjusted later to the real measured values for more realism. In listing 3.2are the values shown for the calculation with emittance.
Listing 3.2: Event generator for initial beam and modifier in MOCADI with emittance BEAM
1000000
0 . 1 1 2 3 8 3 7 , 0 , 3 3 . 9 7 3 7 6 2 4 8 5 , 1 7 , 0 , 0 , 0 , 180 4
0 . 9 7 3 3 , 5 . 1 3 6 9 4
1 . 1 2 3 8 , 4 . 4 4 9 1 1
1 . 0 0 0 , 0 , 0 , 0 , 0
The ion beam transport matrices (for calculation method see section2.4) are setup with the parameters mass,chargeandE0to set the system to the beam one wants to carry through. They also need up to which order they were computed within GICOSY (an ion optics program). Listing3.3 shows the implementation of a dipole.
Listing 3.3: Dipole magnet and collimators in MOCADI DRIFT
1 9 6 . 2 5 0 0 0 0
MATRIX ’ f f ’
CRYRING001 .MAT
3 3 . 9 7 3 9 1 9 6 1 , 1 7 , 0 . 1 1 2 3 8 3 7 3 , 3
COLL
1 , 0 , 0 , 2 0 . 0 0 0 , 4 . 0 0 0 , 0
MATRIX ’ d i p o l e ’
CRYRING002 .MAT
3 3 . 9 7 3 9 1 9 6 1 , 1 7 , 0 . 1 1 2 3 8 3 7 3 , 3
COLL
1 , 0 , 0 , 2 0 . 0 0 0 , 4 . 0 0 0 , 0
MATRIX ’ f f ’
CRYRING003 .MAT
3 3 . 9 7 3 9 1 9 6 1 , 1 7 , 0 . 1 1 2 3 8 3 7 3 , 3
The entire dipole field is represented by three matrices. Two marked as ff (fringe field) are for corrections and the main field is done with the remaining one. Drifts to another matrix or function are accomplished with the commandDRIFT. It only needs the distance incm.
The functionCOLLis representing a collimator to account for the real size of the beam pipe. All events that are not with in the area, computed according to the wanted shape withX andY parameter, will not be carried further.
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22 CHAPTER 3. EXPERIMENTAL FACILITY AND ION OPTICS SIMULATION Target
MOCADI does have a built in function for a target representation, but it does not support binary reac-tion kinematics. Therefore it is implemented with a custom funcreac-tion. In listing3.4the implementation of the target is shown for the example of a(p, γ)reaction.
Listing 3.4: Target as a custom function in MOCADI
∗ t h i n H g a s j e t t a r g e t
∗ param [ 0 ] = mass t a r g e t n u c l e u s [ u ] ,
∗ param [ 1 ] = mass p r o j e c t i l e r e c o i l [ u ] ,
∗ param [ 2 ] = mass t a r g e t r e c o i l [ u ] ,
∗ param [ 3 ] = s w i t c h which r e c o i l t o l o o k a t (1= t a r g e t , o t h e r s=beam )
∗ param [ 4 ] = c h a r g e p r o j e c t i l e r e c o i l [ e ] ,
∗ more p a r a m e t e r s a r e o p t i o n a l t o l i m i t a n g u l a r r a n g e i n CM
∗ param [ 5 ] = theta_min [ deg ] , param [ 6 ] = theta_max [ deg ] CALL / mocadi_sim / c u s t o m _ f u n c t i o n / r e a c t i o n . s o ext_beam
∗1 . 0 0 7 8 2 5 0 3 2 2 3 3 3 . 9 7 3 9 1 9 6 1 1 . 0 0 7 8 2 5 0 3 2 2 3 0 17 0 180 ∗pp 1 . 0 0 7 8 2 5 0 3 2 2 3 3 4 . 9 7 5 2 5 7 5 8 6 0 0 18 0 180 ∗pg
p a r a m e t e r s
In the function ext_beam all incoming particles will be converted into the selected product. Each reaction channel has to be treated individually. MOCADI can only track thereby one channel at once.
The different branching ratios and cross sections are not taken into account with this method.
The functionext_beam(see listingB.2in appendix) sets the new mass according to the input and also will compute the new momentum vector of the particle. The center of mass angular distribution forθ andφ, needed to generate the x,y andzcomponents of the incident momentum vector, are sampled from an isotropic angular distribution. How to compensate for the Rutherford scattering when elastic scattering occurs is shown in section3.2.2.
The target function as well as the beam generation needs the right beam energy in the laboratory frame coordinate system. Since the tables for the nuclear levels are all in the center of mass frame, they have to be convert. This can be achieved as follows
ELAB= mtarget+mprojectile mtarget
ECMS (3.1)
For the produced fusion product γ-cascading is not taken into account. Only one γ emission to the ground state is considered.
The energy loss inside the target was computed with SRIM software [36]. With a target density of ρt= 5.9·1017atmos/cm3 and varying beam energies the calculated values for dEdx are shown in Table 3.1.
The energy loss is even for the lowest resonance at110 keV negligible.
The input file used to do the MOCADI simulation for the lowest resonance reaction in34mCl(p, γ)35Ar can be seen in the appendix (listingB.1).
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3.2. EXPERIMENTAL SETUP AND SIMULATION GEOMETRY 23 Table 3.1: SRIM calculation stopping power output for a34Cl passing through a hydrogen gas target with a target density ofρt= 5.9·1017atmos/cm3at different beam energies
Ion energy [MeV] dEdx [10−15·eVcm2]
3.25 58.23
3.5 62.01
6 100.5
6.5 107.3
7 113.6
17 170.9
18 172.4
22.5 174.9
25 174.2
27.5 172.4
30 169.9
32.5 166.9
35 163.6
Output
In MOCADI only anin situ image of the beam particles is possible. Such an image is provided with setting a save point with the commandSAVE. The save point can be imagined as a plane orthogonal to the beam. Such a point is shown in listing3.5.
Listing 3.5: SAVE command inside MOCADI input code
∗−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−
SAVE #1
∗−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−
This save point will store all the data of all particles inside the simulation at the point. The data is stored within a ROOT Tree as an array. Following properties are saved as floats:
• y andxcoordinates
• corresponding momentum as angles to beam axis (aandb)
• the beam energy
• simulation time
• mass, charge and number of electrons of the particle
• scattering anglesφandθ
• additional beam optics properties