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GSI » FRS » Technical » FRS data acquisition » FRS stand-alone system » FRS algorithms
Algorithms to convert raw data to physical quantities Time stamp information The TITRIS module delivers timing information in the form of a 48-bit (3 words) time stamp with 20 ns resolution. Time "zero" refers to the moment when the the master timing module was last reset. When the time reaches the maximum (ca 5.63E+06 s, or 65.16 days) it wraps around and starts again from zero. Since the time stamp information is "absolute" with reference to the last reset time, the time interval between different events can be deduced simply by their difference in time stamp. Scalers The FRS VME scalers deliver 32-bit (2 words) information for each channel. When the counter reaches maximum (x*10^y) it wraps around and starts again from zero. Pattern unit The FRS VME pattern unit currently delivers two 16-bit data items: a pattern register and a so-called multiplicity register. (Both channels are cleared after each read.) Refer to the module manual for more information. Multi-wire detector signals Each multi-wire detector delivers five signals: one anode time and four cathode times, measured with a TDC relative to a common start (normally the accepted trigger). Using known properties of the MW delay lines, the times can be related to position of the interaction in the detector.
Sum conditions
In order to select
"good" events, a condition placed on the respective sums of the x and y cathode times
should be fulfilled. To make these sums independent of trigger timing, the anode
times are subtracted:
Position determination
From the cathode time differences, the "relative" x and y positions in MW detector number i can then be determined
for those events fulfilling the sum conditions:
Finally, absolute calibrated positions are obtained by taking into account
the known properties of the MW delay lines as well as potential offsets
(e.g. due to the center of the detectors not being aligned with the
central beam axis): Particle 'tracking' At any given focus equipped with two (or more) position-sensitive detectors, the trajectory of each beam particle can be extrapolated, or 'tracked'. This is extremely useful, e.g. for determining the width of the particle position distributions at the intended focal planes and/or at the location of other detectors. As an example, we consider the determination of particle x-position tracked to the nominal focal plane location at S2 using information from MW21 and MW22.
The distances involved, i.e. between
the MW detectors themselves (needed for angle determination) and between
MW22 and the nominal focus, are normally determined as differences between
positions defined relative to the exit of the TS3QT33 quadrupole magnet.
If the MW x-sum conditions were fulfilled for both MWs, we then calculate
the angle (in radians, using the "small angle Ansatz") of the heavy ion traversing the detectors:
The trajectory can now easily be extrapolated from MW22 to the nominal S2 focal plane: A corresponding procedure can of course be applied to obtain y_FocS2. At S4 and at S8, positions are normally defined relative to the exits of the HFSQT13 and TH4xxx quadrupoles, respectively. MUSIC information The MUSIC detectors consist of a number of independent anodes which deliver energy loss (and time) information. Two different MUSIC detectors are in use at the FRS: the 'old' type with 4 anodes and the 'new' Munich design with 8 anodes.
'Raw' energy loss
In any case, the raw ADC signals should be corrected
for the pedestal values - referred to in the following as offsets: These anode values can now be used to form pairwise products which are combined to "truncated" mean values - this procedure results in better resolution than simple averaging.
In the case of 4 anodes we have:
Correspondingly, in the case of 8 anodes: Note the 'numerical trick' of dividing up the calculation! Position-corrected energy loss The 'raw' MUSIC energy loss is dependent on particle velocity, an effect which is described in the 'particle identification' section below. In addition, corrections should in principle also be made for the dependence on interaction point x-position and (to a certain degree) the x-angle of the particle trajectory. The position dependence is mapped out by simultaneously illuminating the MUSIC detector and calibrated position-sensitive detectors (such as MWs) with (defocussed) primary beam - the coefficients of the correction polynomial are determined by fitting the dependence of MUSIC_energy on the x-position of the interaction point. The latter is most often determined using tracking with the MW detectors, but in certain cases (see below), the MUSIC can itself provide x-position information.
Assuming the MUSIC is located at S4, where dist(MW42->MUSIC would be the
distance between MW42 and the center of the MUSIC detector, we have:
Now plot MUSIC_energy as function of this position, and fit the dependence with
a polynomial of at least 2nd order (coefficients C0, C1,...):
Apply the correction as follows to remove the position dependence: NOTE that this is not just a calibration - the detectors chosen to deliver position information for the correction must be inserted in the beam and be operational during the entire production beamtime! 'Self-correction of position' As the drift voltage in the 'old' MUSIC chambers is applied horizontally, perpendicular to the beam axis, a measurement of the anode time (relative to a common start taken as the accepted trigger) can be used to determine x-position of the interaction. In the 'new' Munich MUSIC chambers, the drift voltage is applied vertically, and the drift times could thus in principle be used to extract y-positions. However, this is of less interest and thus the time signals from these detectors are not normally recorded. The conversion of anode time to absolute position can be easily calibrated by comparison with MW detector information (see section on 'tracking'). The correction polynomial should in this case be evaluated as a function of the average position determined from the MUSIC chamber itself. Scintillators The FRS standard scintillators, most of which are read out simultaneously by a pair of photo-multiplier tubes, give energy loss and timing information. Energy loss
The scintillator energy loss information, which is collected using a QDC,
does not have very high resolution, but can nevertheless be useful,
i.e. for vetoing secondary reaction products.
For scintillators with two PMTs (left and right sides), the energy loss is
estimated by taking the square root of the product of the two individual
QDC signals (after subtracting the corresponding pedestal offsets):
Position information Position information is obtained by using TACs to accurately measure the time difference between the right and left PMT signals. The conversion of left-right time difference into absolute position is calibrated by simultaneously illuminating the SCI detector and a pair of e.g. MWs with (defocussed) primary beam - the coefficients of the calibration polynomial are determined by fitting the dependence of the tracked x-position on the time difference. (Some scintillators, like SC41, may provide y-position information in the form of an up-down time difference. This is treated in a corresponding fashion.)
For SC21, where dist(MW22->SC21 is the distance between MW22 and SC21, we have: Now plot x_SC21 as a function of SCI_lr_time(SC21) and fit the dependence with a polynomial of at least 2nd order (coefficients C0, C1,...).
The absolute x-position, as determined by SC21 itself, then is: Time-of-flight (TOF) The time-of-flight of particles through the FRS is determined by measuring and averaging time differences between two scintillators, both with simultaneous readout of the right and left sides, placed at different focal planes. In order to partially compensate for differences in path length for particles that deviate from the ideal trajectory, the right-right and left-left time differences are averaged.
As an example, we consider the time-of-flight between S2 and S4: Because the respective TACs have been calibrated (in picoseconds/channel), the parameter SCI_tof_21-41 is given in the proper time unit, but it is the sum of the actual 'absolute' time-of-flight and an experiment-specific TOF offset. The offset is determined in the FRS primary beam calibration procedure.
For 3-4 primary beam energies, corresponding to specific
relativistic velocity parameters Beta_primary, SCI_tof_21-41is determined experimentally.
Then the product SCI_tof_21-41* Beta_primary is plotted as function of Beta_primary and
fitted with a linear equation:
The coefficients C0 and C1 have special physical meaning. The absolute value of C0 * light_velocity is
equal to the average flight path, while C1 represents the TOF offset mentioned above. These parameters
are used later for the calculation of A/q, and for this reason, we give them special names : Basic particle identification Once basic information on time-of-flight and energy loss are available, the proton number Z and the mass-to-charge ratio A/q can be calculated.
Mass-to-charge ratio A/q Several "basic" properties of the FRS and its beam optics enter into the calculation of A/q, including the effective average dipole radii of the 1st and 2nd halves of the separator as well as magnification and dispersion parameters. These values are obtained from the FRS primary beam calibration measurements and the beam optics calculations, respectively. Apart from these and other 'constants', which remain the same for all particles that are transmitted at a specific FRS setting, data on the measured time-of-flight and x-positions for each heavy ion at the two focii S2 and S4 are needed in order to calculate the relativistic velocity. Normally, X_S2 is determined from SC21 and X_S4 using MW tracking, but the latter position can also be obtained from SC41. To start with, the average Brho values are determined, using optics parameters, radii and B-field values. (The dispersion is given in units of m/%)
For S2-S4 we obtain:
The relativistic velocity parameters Beta and Gamma of the heavy ion are now given by
Now we can finally determine the mass-to-charge ratio: Note: especially for fission fragments, it may be necessary to correct the thus obtained A/q values for e.g. S4 x-position (and x-angle) in order to improve the resolution of the calculated mass-to-charge ratio. Proton number Z The fragment proton number Z_fragment is normally calculated as the product between the primary beam proton number Z_primary and a velocity-dependent correction factor. The latter is obtained as the ratio of the measured MUSIC energy loss of the fragment and that of a primary beam ion having the same velocity as the fragment.
The primary beam MUSIC energy loss as function of the relativistic velocity parameter Beta is
determined in the standard FRS calibration procedure, where the response of the MUSIC
chamber to primary beam particles at varying energies is mapped out. Typically it
is expressed as a 3rd order polynomial, obtained by fitting (position-corrected)
MUSIC_energy as a function of Beta:
The Z of a particle with measured velocity Beta and energy loss MUSIC_energy can then
be expressed as
In order to accurately calculate Z over a range of elements, it may be necessary to 'renormalize' this
value; this can in most cases be done by applying a simple linear or quadratic correction: Energy loss at S2 It can sometimes be quite useful to estimate the energy loss that the fragments undergo at S2, e.g. by interactions in the scintillator, the degrader and/or in other layers of matter. This energy loss could be directly calculated from the difference of velocities before and after S2, but in the standard case, we only measure the S2-S4 velocity. The TA-S2 velocity can, however, be estimated with the help of some basic assumptions.
We can estimate the rigidity of the particle TA-S2 as:
By setting ID_Aoq_TA-S2 = ID_Aoq_S2-S4 (it is after all the same ion!), we then obtain:
The total energy loss of the ion in the layers of matter at S2 is then |
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