investigations of the isomax tracking detector employing a...

Investigations of the ISOMAXtracking detector employing a

new low power time acquisitionread-out system

Diplomarbeitzur Erlangung des akademischen Grades

Diplom-Physiker

dem Fachbereich Physik derUniversität-Gesamthochschule Siegen

vorgelegt vonDragos Vasilas

Juni 2000

Contents

1 Introduction ........................................................................1

2 ISOMAX. Principles and Experimental Setup ..............3

3 The Tracking Detector .......................................................7

3.1 The Drift Chambers ......................................................................7 3.1.1 Functioning Principle .......................................................7 3.1.2 Description .........................................................................8

3.2 The Read-Out System .................................................................11 3.2.1 System Presentation .........................................................11 3.2.2 Measurement Proccess .....................................................14

4 Linearity and Temperature Test ....................................17

4.1 Tests at Room Temperature ........................................................18 4.1.1 Experimental Setup ..........................................................18 4.1.2 Linearity and Time Resolution Measurements ................21 4.2 Temperature Tests .......................................................................30 4.2.1 Experimental Setup ..........................................................30

4.2.2 Linearity and Calibration Tests ........................................31

5 The Spatial Resolution ...................................................35

5.1 Offset Determination ..................................................................35 5.2 Drift Time - to - Path Relation (DPR) ........................................41 5.3 Residuals Scatter Plot and the Spatial Resolution ......................46 5.4 The Angle Correction ..................................................................49 5.5 3σ Correction ..............................................................................54

6 Conclusions .......................................................................57

Bibliography ...............................................................................59

1. Introduction 1

Chapter 1

Introduction

Studies of energetic particles from distant regions of the galaxy andthe universe bring us information about the processes in which the particlesare accelerated to relativistic energies, about the role of the particles andtheir accelerators in driving dynamical processes in our galaxy and beyond,and about the distribution of matter and fields in interstellar space.

One important experimental mean in answering such questions is theisotopic and elemental composition measurement of cosmic rays. Someisotopes (e.g. 10Be, 26Al) are unstable radioactive clocks whose decaylifetime is of a magnitude which allows them to be sensitive to cosmic raypropagation lifetimes and matter densities encountered. All of the existingsatellite measurements, while consistent, are in the 100 MeV/nucleonenergy range. Because these measurements are too low to distinguishbetween the nowadays competing propagation models, it is of greatinterest to measure accurately the abundance of the beryllium isotopes10Be/9Be over an extended energy range [Streitmatter 92]. Suchmeasurements will minimise the effects of solar modulation, test theviability of the several cosmic rays propagation models and constrain theparameters of those that are viable.

ISOMAX (Isotope Magnet Experiment), whose goal is to carry outthis type of measurements, is a collaboration project among Goddard SpaceFlight Center, California Institute of Technology and the University ofSiegen. This instrument is a balloon-borne mass spectrometer utilising a

1. Introduction 2

superconducting magnet in combination with a drift chamber trackingsystem, a time-of-flight system and two aerogel Cherenkov detectors.Siegen‘s main contribution to this project, the tracking system, consists ofthree wire drift chambers using a hexagonal drift-cell structure, filled withpure CO2 gas. Final production and integration of low power preamplifiersand TDCs for drift chamber readout is also a responsibility part ofUniversity of Siegen.

On August 4th 1998 the first flight of ISOMAX took place from LynnLake, Manitoba, Canada. This successful flight lasted 29 hours with 16hours at float altitudes greater than 36 km. The data analysis is not yetcompletely finished but preliminary results show very good performancesin resolving isotopes of light nuclei with a mass resolution better than 0.25amu for 10Be at 1 GeV/nucleon [Göbel 2000].

In order to improve the general statistics and to extend the domain ofenergy measurements to 3 GeV/nucleon, a second flight with a duration ofthree days is planned for the summer of 2000. To perform such a flight, lowpower data acquisition and trigger electronics must be incorporated in theinstrument. Hence, a new drift chamber read-out system was developed atSiegen, a system that reduces the power consumption by more than a factorof four, has new facilities and an improved time resolution.

Its full capabilities were in the last few years intensively tested,although from practical reasons the whole series of tests were performedonly at ground level and without magnet. Before the final drift chambersintegration in the whole instrument at Goddard, the new electronics weretested against extreme temperature variation to prevent unexpectedbehaviour of the system in flight. This required appropriate experimentalsettings together with specific software for data analysis. The test analysistogether with a description of the new read-out system electronics andmeasurement techniques are included in the present work.

The measurement precision of particles tracks is the most importantperformance parameter that characterises this type of detector since itaffects directly the overall mass resolution. During ground tests withmagnet off at Goddard, a data set aimed to the calculus of the positionresolution was recorded. The results are presented in this thesis and alsothe applied procedure is described in detail. Although the data analysissoftware is similar to the old one, some routines had to be added oradapted according to the present features of the new electronics.

2. ISOMAX. Principles and Experimental Setup 3

Chapter 2

ISOMAXPrinciples and Experimental Setup

ISOMAX observes cosmic rays isotopes from He to O (2 ≤ Z ≤ 8) overthe energy range from 0.2 MeV/nucleon to more than 3 GeV/nucleon(multiple flights), with emphasis on the isotopes of beryllium, whichinclude the radioactive clock 10Be. In other words, for such an analysis oneneeds to know three features of a subject nucleus: energy, charge and mass.

The measurement technique relies on the fact that the curvatureradius r of a nucleus track in magnetic field is expressed by the relation:

rp

Z e BZA

=⋅

⋅ sinθ (2.1)

Here B is the magnetic field, θ the angle between the field and the initialvelocity, Ze the nucleus charge and Z

A p is the nucleus momentum. The firstratio in the right hand side, proper to each type of particle, is commonlydenoted as rigidity R since it is a measure of how much rigid will be thetrack in a given magnetic field:

ZA Z

A

Rp

Z e=

⋅ (2.2)

Once the particle track and the magnetic field are known, the rigiditycan be calculated.


If we replace the momentum and present the result in terms of massM then we get:

MR Z e

c= ⋅ ⋅

⋅−

ββ1 2 (2.3)

Therefore a simultaneous measurement of rigidity, charge and velocityassures the determination of mass. The energy of particles is thereaftereasily inferred once that the mass and the velocity are known.

The rigidity is provided by measuring the track of particles as theyare detected in a system of three drift chambers. The velocity is measuredwith a time-of-flight system composed of plastic scintillators andphotomultipliers. Two Cherenkov counters complement and extend theenergy range covered by the TOF. From the energy loss of the passingparticle in the scintillators, the charge can also be determined.

The ISOMAX instrument is shown schematically in Figure 2.1.

.


Since the drift chambers are discussed in detail in the next chapter Iwill start presenting other components of the ISOMAX instrument.

The magnet is designed to operate at a maximum current of 200A,which corresponds to an average magnetic field integral of 0.91 Tm. Thedistance between the two magnetic coils is almost equal with its diametersand thus a relative homogeneous field is produced in the middle chamber.Those coils, which consists of filamentary NbTi embedded in a Cu matrix,are placed in liquid helium dewars and thus kept in a superconductingstate. The magnetic field lines inside the drift chambers are represented inFigure 2.2:

Figure 2.2 Magnetic field lines of the magnet and location of drift chambers seenfrom the non-bending plane.


The ISOMAX TOF system is made up of three layers of fast BicronBC240 1 cm thick plastic scintillator with a fluorescence rise-time of 500 ps.The top and bottom layers consist of five paddles of 20 cm × 100 cm whilethe intermediate one is made from three paddles of 23 cm × 69 cm. Bothends of each paddle are connected to light-pipes and attached throughtransition pieces to Hamamatsu R2083 photomultiplier tubes. Single paddletime resolutions better than 50 ps can be achieved, depending on particlespecies and corrections [Geier 99]. This system is also used to measure thecharge and acts as the trigger on a two level-basis for the whole instrument.

At energies higher than 1 GeV/nucleon, ISOMAX measures particlevelocities using a pair of high resolution Cherenkov detectors with silica-aerogel radiators. They consist of two large-area diffusive-light-integrationcounters (88 × 88 × 14 cm3). Each counter contains two layers of silica-aerogel radiator blocks with an average index of refraction n = 1.14 for the1998 flight and thus covering the energy range from 1.08 GeV/nucleon toabout 1.7 GeV/nucleon [de Nolfo 99]. Light is collected with 16Hamamatsu R 1848 3-inch phootmultiplier tubes per counter resulting atotal of about 22 photoelectrons for relativistic singly-charged particles. Thesignals from the Cherenkov photomultipliers are amplified using charge-sensitive preamplifiers and subsequently digitised using LeCroy 2259 ADCmodules.

ISOMAX incorporates commendable on-board calibration for thedrift chamber, Cherenkov and TOF electronics. The high-voltages andthresholds for all detectors are fully commendable and continuouslymonitored. As configured for its first flight, the ISOMAX electronics used1000 W of power whereas the drift chambers contribution was 197 W. Thedrift chambers will require even less power consumption in the 2000 flightsince use of the new read-out system implies only 53 W of power.

3. The Tracking Detector 7

Chapter 3

The Tracking Detector

3.1 The Drift Chambers

3.1.1 Functioning principle

The passage of energetic charged particles, such as electrons, protonsor heavy nuclei, through a gas, which is electrically neutral, makes possiblethe ionisation of the gas molecules. If the kinetic energy of the particles islarger than the ionisation energy of the molecule, the electric fields of thesecharged particles pull electrons out from molecules near their path,producing what is called an ion pair: an electron and the rest of themolecule, positively charged. It will be thus formed in a gas along theionising particle track a “mirror“ track consisting of electrons and chargedmolecules, making the problem of particle track detection equivalent withobtaining an “image“ of such a electrically charged band in gas.

When gas molecule are ionised, they tend to recombine, returning tothe neutral state and consequently after a short time these types of trackswill vanish. To prevent this, the gas could be placed between an anode anda cathode, which can collect the charges before they will recombine. If thedrift time of the electrons from the place of their creation until the arrival atthe anode is known then one can draw conclusions about the distance they


have travelled in the gas and points from the track can be calculated. Thisis the principle followed by the tracking detector in ISOMAX.

3.1.2 Description

The gas used in this detector, CO2 of 99,995% purity, fills threechambers that are traversed by a regular grid of anodes and cathodes as inthe figure 3.1. This gas was chosen because the liberated electrons driftslowly compared to common chamber drift gases [Sauli 84], so that Lorentzforces remain small in the presence of magnetic fields. In addition, CO2 hasthe advantage of being a non-flammable gas. To maintain this purity and asuitable working pressure a special control gas system was developed inSiegen, thoroughly depicted in [Hams 96].

Figure 3.1 The drift chambers system of the ISOMAX instrument.


All three drift chambers lateral walls are constructed from 10 mmepoxy plates while its upper and lower parts are 125 µm Mylar foilslaminated on 35 µm copper foils. Between the chambers there are 2 spacersgiving a total height of the tracking system of 150 cm. A detaileddescription of mechanical structure of the chambers can be found in[Bremerich 97].

The inner space of the chambers is divided in small hexagonal driftcells, made up from an anode wire in the centre and cathode wires in eachcorner of a hexagon. Such a drift cell structure is illustrated in the figurebelow:

Figure 3.2 The drift cell structure.

The wires consist of gold-plated tungsten of 30 µm diameter for theanode wire and 100 µm the cathodes. The reason for the hexagonal cell isdue to the fact that one needs to obtain an electric field as symmetric aspossible and consequently, to have the curves of equal drift times as closeas possible to circles. The introduction of additional potential wires has therole of increasing the symmetry of the field [Bremerich 92]. The guardwiresare added between the adjacent X and Y layers and between the outerlayers and the frame to prevent distortions of the electric field in the cells.

Guard wires (1.1 kV)

Anode wires (4,6 kV)

Cathode wires (grounded)

Potential wires (570 V)


a) b) c)

Figure 3.3 a) Electric field lines inside a drift cell b) Equipotential lines c) Lines of equal drift times

Due to its strong internal electric field, the cells collect those electronswhich were created inside its active volume. In principle, as soon as aparticle has passed a cell, a track point can be calculated, more hit cellsmeaning more known points of the track.

Hence, the distribution of the cells is similar to that of a honeycombto assure an optimal covering of the chamber inner space. In the bendingdirection, denoted as X, there are 16 layers of cells while in the non-bendingY direction 8 are present. Calculating track points in two perpendicularplanes assures that the track can be known in a 3D representation.

Each anode signal is fed in preamplifiers through a coupling circuitryas can be seen in the figure 3.4. It is essentially a high frequency by-passfilter where the high voltage for the anodes is delivered through a 10MΩresistance and the connection to the preamplifiers is done using a 1nFcapacitor. A voltage divider with two 5MΩ resistances is used to obtainboth the voltage for the guard and potential wires.

Figure 3.4 The coupling c

1

Preamplifier

ircu

nF Capacitor

itry of anode w

10 MΩ Resistor

Anode wire
Cathode wire
ires to preamplifiers.


3.2 The Read-Out System

To be able to measure the drift time of the electrons from the point ofcreation until the arriving at the anode we need in principle two referencesignals, denoted as the start signal (trigger signal) and the stop signaltogether with an appropriate clock. In the first approach the trigger signalfrom TOF scintillators and the anode signal can be considered as start andstop signals. The role of the two signals will be however reversed to fit thefunctioning features of the used “clock“ in this experiment.

In contrast with the ISOMAX‘s 1998 flight when as “clock“ it wasused an ensemble of LeCroy 4291B TDCs, in the 2000 flight this role isplayed by a new read-out system with improved qualities, called AK8092and developed by a company in Siegen called Scholl Physical-TechnicalDevelopments.

3.2.1 System presentation

As I already mentioned, there were many reasons why a new read-out system for the drift chambers was developed: reduced powerconsumption, better time resolution, reduced weight for a balloon flightand complete automatization of the parameter settings. The new systemconsumes only about 140 mW/channel accomplishing thus a total powerconsumption with four times less than the LeCroy‘s one. The timeresolution was improved from 3 ns to 1 ns. Among other parameters, whichwill be described below, the threshold of discriminators and the internaldelay of Control Unit, can be now adjusted through software commands.

The AK8092 time measurement is divided in two physical domains.One domain consists of mainboards mounted directly on the drift chamberswhile the other is denoted as Control Unit. One mainboard is presentedschematically in the following figure.

Figure 3.5 Mainboard with its additional electronic

BVoltage Connection

Preamplifier

Time Acquisition Card

Logic Module
us Connection
devices.


On each mainboard the anode wires are connected to thePreamplifiers (PA-M71031) and the Time-Acquisition Cards (TAC-M71032)located on it. Each TAC and PA card can handle four anode signals. Thepreamplifier card contains in addition a discriminator with an externaladjustable threshold and a pulse shaper. The four outputs of thepreamplifier are connected to the inputs of one TAC card where a so-calledstart time stamp is created. The start time stamps are transmitted to theother measurement domain, the Control Unit, where are initiated the mostimportant operations in getting the measured times.

Figure 3.6 Logic Module Layout


The on-board Logic Module (LM90616) handles the communicationbetween TACs and Control Unit. In addition, it supplies the preamplifiercards with the threshold for discriminators, which can be individually setfor each LM through software commands. One Logic Module can controlup to 32 Preamplifiers and TACs. In the present configuration there are 14Logic Modules and consequently 14 mainboards. They correspond tocertain groups of anode wires as presented in the Figure 3.6. The encirclednumbers show also the physical place where a Logic Module is located onthe Mainboard.

The Control Unit consists of one Control Module and up to eight BusControllers (Bus Extension Module). The Bus Controller enables theconnection through a 34-pole ribbon cable between a maximum of 16 LogicModules and the Control Module. In this way a total of 16384 channels canbe controlled. In the Control Module the actual measured times arecomputed and using a PC the control of the whole system is achieved.

To communicate with a computer it also requires one PC/104Interface Card, mounted on the PC. The internal delay in the ControlModule can be adjusted manually, by sending software commands or byusing the set screw from its front panel. Further useful features areavailable especially for tests such as “Test Output“, which produces a testsignal playing the role of an anode signal or the input “Set ready formeasurement“, which deletes the last event and prepares the system for anew measurement. The 50-pole male Berg cable connector from the frontpanel makes the connection with the I/O card. The whole read-out systemis shown in Figure 3.7.

Trigger Input

Bus Cable:34 pole flatribbon cable Readout PC

Bus Controller Control Module

Interface Cable50 pole flatribbon cable

Trigger Logic

Data Interface& IO Card

Drift Camber

Main Board

Bus Termination

Preamps &Time-Acquisition

Logic Module

Control Unit

Trigger Veto (TTL)

Trigger (NIM)

Trigger Veto

Trigger (TTL)

Figure 3.7 The AK8092 read-out system.


3.2.2 Measurement Process

The AK8092 instrument is a hybrid system, in the sense that the timemeasurement is done both digital and analogue. This concept was usedbecause of demands that this system should be able to measure times up to3 µs with a resolution of 1 ns and with relatively low power consumption.The main clock of the system is achieved digitally with a period of 32 nswith the help of two added sinus-like signals like in the figure 3.8.

Figure 3.8 The general clock signals of AK8092.

This main beat is common for the whole system and it is generatedfrom the Control Module. Between two pulses, separated in time by 32 ns,in each TAC and in Control Module can be generated an analogue signalevolving in time in a linear fashion, therefore called ramp. The starting ofthis ramp is conditioned by the existence of an anode signal with theappropiate features, able to pass the discriminator.


The coincused at thwill starpermaneincludingmeasuremsignal ar(correspocomputa

At started bsignal is the outpuThis one incomingtM) and ththe TAC ramp val

In 3 µs, a svalues in

Main beat

Trigger Signal (from scintillators) Stop Signal

e

S

Ram

Ramp in Control Modul

tart Signal (from anode wire)

Figure 3.9 The measurement principle

idence signal of the TOF scintillators produces the trigger signale “Trigger input“ in the Control Module. The arrival of this signalt the above mentioned ramp, whose value will increase

ntly until the next beat of the clock will occur. Since all TACs, the ramp from the Control Module, are calibrated prior to theents, the voltage value will correspond to the time tT when this

rives between two consecutive beats. Both the ramp valuending to the time tT) and the beat number nT are saved for further

tion.the anodes, the TAC ramps corresponding to each hit cell will bey the anode signal after a time equal with the drift time. The rawpreamplified and selected with the help of the discriminator. Att a TTL signal of 3 µs will be available, denoted as start signal.is fed into the TAC and thus the ramp will be started. With the of the next clock beat the ramp value (corresponding to the timee beat number nM are saved internally in TAC. During these 3 µs

is not anymore sensitive to other anode signals, meaning that theue and the beat number cannot be overwritten.the Control Module, after a delay equal with nV beats but less thantop signal will be generated. This will cause the ramp and time the activated TACs to be saved, otherwise these would have been

p in TAC


reset. The Control Module checks further if there are hit cells in the systemand in the affirmative case the previously saved values are gathered overthe data bus with the help of the logic modules. At the point when thesaved ramp values are to be transferred to logic module the voltages aretransformed in time units through an ADC implemented in each TAC.

The measured times tD are computed in the Control Module inCommon Stop Mode with the following relation:

( ) TMVTMD ns32 tnnntt −⋅−++=

where the involved times are described in the previous paragraphs. Thiscalculus is done for each hit wire. The data transferred to the PC containsessentially two data words per hit wire, one being the address of the wireand the other the measured time. A detailed presentation ofcommunication with AK8092, the control commands and data format isdone in [Hams 96].

4. Linearity and Temperature Test 17

Chapter 4

Linearity and Temperature Test

The capabilities of AK8092 read-out electronics were intensivelytested in Siegen over the past few years [Hams 96]. Since the ISOMAXinstrument was configured for the first flight with a different read-outsystem, the complete integration of the new electronics was notpossible. Therefore an outer spare drift chamber, also built in Siegen, onwhich this new read-out system was implemented, served as testinstrument.

The most important characteristic of AK8092, also the mostinvestigated one, is the spatial resolution. This analysis will bediscussed in the next chapter, being related to the way the DCs areconstructed. In the present section properties related intrinsically to theelectronics are examined. The data analysis software for the spatialresolution uses the fact that the dependence measured time/theoreticaltime for large time domains is linear with the slope equal to one. Thiscalibration line is to be found out in the present chapter. Furthermore itis important to verify how accurate the system measures times and howclose they are to the estimated resolution of 1 ns.

Another issue to investigate is the behaviour of the read-outsystem during temperature variations. Balloon payloads are subject toextremes of hot and cold. Under these circumstances, a careful thermalanalysis, including the effects of ascent through the atmosphere, isnecessary in order to configure the payload insulation and thermalsurfaces so as to avoid either overheating or overcooling. However, in


the 1998 flight the chosen payload insulation corresponded to antemperature interval from –10°C to 25°C, which in principle is not beinconvenient for the read-out electronic devices. To prevent electronicfailures during the 2000 flight, the system behaviour at temperatureswell different from the working ones has to be tested. It is alsoimportant to know if temperature variations induce a change ofmeasurement performances described in the beginning of this chapter.

Those tests are conducted regardless of the presence of DriftChambers. Known time intervals, generated by devices like PulseGenerators, are measured and analysed with the AK8092 system.Therefore there is no trigger signal along those investigationsproceeding from coincidence scintillators. The choice of trigger givesthe opportunity to investigate two aspects of the read-out system. Usinga signal generated by the system components as trigger, one caninvestigate its intrinsic properties (internal trigger). An external trigger,such as the one generated by a Pulse Generator for example, modelssomewhat better the real situation but introduces its own imprecision.

4.1 Tests at room temperature

4.1.1 Experimental Setup

The main purpose of the first series of tests was to test theintrinsic properties of AK8092 system. As samples, there were chosen 48channels, namely 12 TACs, copies of the ones integrated in theinstrument‘s DCs at Goddard. One Logic Module was responsible forall channels and the communication with the Control Module was donethrough a solely Bus Extension Module. In the case of internal trigger astest signal it was used the feature “Test Output“ of the Control Module,see figure below (coloured in red). This is emitted simultaneously withthe clock beats and with the internal trigger meaning that the ramp inthe Control Module will always be precisely zero. A Stop Signalsimultaneous with the clock beat will be generated after a desired timeinterval. Consequently, the error of time measurement with this kind oftrigger is largely caused by the ramp error in TAC.


Control UnitOn-Board PCInterface

I/O CardTTL

Pulse Generator

ConveTTL-N

Control Module

M

Figure 4.1 Experimental setup

In the case of external are used both as trigger for CoThose TTL pulses are aboumilliseconds domain. There described in sub-section 3.2.1,when the system is ready for Philips PM5786 works in the the input into an appropriatesignal a TTL-NIM Convertenecessary. During all measurevalue of 1.5 V to reject a possib

Figure 4.2 shows the sigboth at the “Trigger Input“ experimental configuration thmean that the ramp in Contrthis time.

50 pole flat cable

rterIM

Logic FanIn/Out

Test Output

Bus Controller

Trigger InputNIM

PreamplifierCard (PA)

Time -AcquisitionCard

T

NI

Mainboa

with external (blu

trigger the emitntrol Module a

t 3 µs long ais no need for since the I/O Ca new measuretriggered regim test signal. For and a Logiments the threle noise backgr

nals prior to theand Preamplif

ere is a delay ofol Module wou

TL

rd Logic Module

e) and internal trigger (red).

ted pulses from I/O Cardnd as test signal for TACs.nd have a periodicity invetoing trigger signals asard is the one that decides

ment. The Pulse Generatore and it was used to shaper getting the right triggerc Fan In/Out were alsoshold was maintained at aound. start of the measurement,ier input. Because of the about 33 ns, which wouldld be started earlier with


a) b)

Figure 4.2 Signals at Trigger Input (channel 1) and Preamplifier Input(channel 2) presented at different time scales: 1 µs (a) and 25 ns (b).

The signal processing inside the Preamplifier Card takes about 40 ns as one can see in the next figure. There is represented the signalbefore the PA Card (channel one) and before TAC Card (channel two).One can also notice that for 3 µs (2.92 µs on the figure) the ramp valuein TAC is not overwritten by other events, being the reason why theinternal delay in the Control Module is always smaller than that.

a) b)

Figure 4.3 Signals before the Preamplifier (channel 1) and before itscorresponding TAC (channel 2) at different time scales: 1 µs (a) and 50 ns (b).


4.1.2 Linearity and Time Resolution Measurements

The internal trigger was used to infer the time resolution properto the TAC ramp. 1000 test pulses were emitted and the stop signal wasdelayed in turn with several values, in order to span larger timedomains. With each internal delay value a data set was recorded. Atypical time distribution for all 48 channels is represented in the nextfigure. The internal delay value in Control Module for this data was setto 2240 ns (70*32 ns).

Figure 4.4 Data set with internal trigger for 48 channels.

The fact that the width of the distribution is large consists in thedifferences of the TACs electronic components and the physical placewhere they are located on the mainboard. This shows another reasonwhy a further data analysis is ideal to be made in turn for each channeland not for each Logic Module. By representing, from the above graph,only the first channel, one can get a typical distribution for themeasured times of a single channel.

Figure 4.5 Typical time distribution for a single channel with internal trigger.

Time (ns)

Time (ns)


The measured times for a single channel form a sample takenfrom a population specific to each channel. The interest is to find outthe mean value and the standard deviation of each channel‘spopulation. Those can be inferred using the method of estimators.

If one calculates from the above data the sample mean x_

and the

sample variance ∑ −−

=i

i xxn

s 2_

2 )(1

1 for each channel, then x_

estimates

the mean value of population and s2 estimates its standard deviation.The errors on estimators are 10-5 % for mean value and 10-2 % forstandard deviation due to the number of events (103). Special FORTANroutines and PAW kumac files were written to read and organise thedata format and to compute in an automatic fashion the aboveestimators. For the channel represented in Figure 4.5 the computedvalues are 2267.97 ns for the mean value and 0.5 ns for the standarddeviation.

The sample mean values of the 48 populations (further calledmeasured times) are represented against channel number for an internaldelay 2240 ns. The last will be further denoted as theoretical time sincethe objective of the experimental setup was to measure times equal withit. The plots for other values of internal delays are similar and thereforenot any more presented.

Figure 4.6 Measured times for all channels in both internal and externaltrigger case (theoretical time 2240 ns).

-4 0 4 8 12 16 20 24 28 32 36 40 44 48 52

2260

2262

2264

2266

2268

2270 internal trigger external trigger

Channel number

Tim

e (

ns)


The measured times are in the both cases greater than thetheoretical 2240 ns, although from previous considerations one couldhave been said the contrary. A measured time longer than the internaldelay can be explained assuming that in the present configuration theramp in TAC is started prior to the one in Control Module with about25 ns. Considering the 33 ns and 40 ns delays presented before, one canestimate a difference in the answer times of the two electronic circuitsresponsible for the time measurement: the TAC ramp and the ControlModule ramp. For an ideal situation when the test signal and the triggerare simultaneously, one winds up with a difference of about 98 ns.

The processing of the external trigger signal seems to take alonger time than in the internal case (app. 1 ns), explaining why themeasured times are greater in the first case. Finally, one can be noticedthat the outer channels in each TAC (channels 4, 8, 12…) measure largertimes than the inner ones, which can be explained through the fact thatthe ramps in those channels are started faster.

The time resolutions were calculated with internal trigger forintermediate values of the internal delay ranging from 512 ns to 2240 ns.In Figure 4.7 there are presented the ones calculated for 512 ns, 640 nsand 2240 ns, respectively. The typical observed resolutions were inaverage between 0.3 ns and 0.5 ns for all channels. There are alsoisolated exceptions such as the resolution for channel 10, which is about1 ns in some cases. This can be explained only through the differencesin the electronic components of this specific channel. One can noticethat in the case of internal trigger, when the error of the measurement iscaused by the ramp in TAC, the accuracy is better than the estimated

1 ns, showing a good quality of the system. Those values agreevery well with the results from a similar series of tests performed a fewyears ago [Hams 96].

a)

0 4 8 12 16 20 24 28 32 36 40 44 48

0.0

0.2

0.4

0.6

0.8

1.0

1.2

Channel number

Tim

e r

esol

utio

n σ

(ns

)


-4 0 4 8 12 16 20 24 28 32 36 40 44 48 52

0.0

0.2

0.4

0.6

0.8

1.0

Channel number

Tim

e r

eso

lutio

n σ

(ns)

b)

c)

Figure 4.7 Time resolution for all channels, measured at three different timeswith the internal trigger: 512 ns (a), 640 ns (b) and 2240 ns (c).

The same measurement procedures were applied for the externaltrigger from the I/O Card. In Figure 4.8 there are compared the timeresolutions with both types of trigger in the case of an internal delay of2240 ns. As expected, in the case of external trigger, the average timeresolution 0.71 ns lies above the one from the previous case, because ofan additional error in the ramp of the Control Module. Since the case ofan external trigger can be considered as a model of the real situation,this resolution shows how accurate the drift times are measured withthe AK8092 read-out system.

-4 0 4 8 12 16 20 24 28 32 36 40 44 48 520.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

Tim

e re

solu

tion

σ (n

s)

Channel number


Figure 4.8 Time resolution in the both cases : internal and external trigger.

The next problem to investigate is the calibration line proper tothis read-out system. This could be accomplished by making knownvariations of the time interval between the trigger signal and the testsignal and by representing the measured time versus the theoreticalone. As the studied time range spans over 2000 ns, one needs for thispurpose devices that are very accurate in obtaining those delays.

An accurate difference between the trigger and the test signal canbe achieved in two different ways. One way would be the use of themethod from the time resolution measurements. While the timedifference between the trigger and the test signal remains constant asbefore (73 ns), one varies the internal delay of the Control Module. Sincethis variation is done in steps of 32 ns clock beats, the time resolutionmeasured in this fashion will be as good as before. This method waseasily put into practice because it did not required a highly performantPulse Generator and the internal trigger can be used. The analysis wasconducted for several channels but as the results are similar only thefirst channel is presented. It was used the built-in feature of the ControlModule to set the internal delay after each emitted test pulse. Theinternal delays decreases in steps of 150 ns from 2240 ns until 890 ns,corresponding to ten emitted test pulses and thereafter the procedure is

-4 0 4 8 12 16 20 24 28 32 36 40 44 48 520.0

0.1

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Channel number

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800 1000 1200 1400 1600 1800 2000 2200 24000.48

0.50

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e re

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tion

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s)

Time (ns)

resumed. There were 21000 pulses emitted in total. The timedistribution is presented in Figure 4.9 :

Figure 4.9 Time distribution for channel one in the case of internal trigger.

The width of the 10 peaks were calculated as before and show forchannel one a good stability of the resolution at various times, aspresented in Figure 4.10 :

Figure 4.10 Time resolutions for channel 1 calculated at various time values.

Time (ns)


800 1000 1200 1400 1600 1800 2000 2200 2400800

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Expected time (ns)

Mea

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me

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The estimators for the mean values are calculated, correspondingto each peak. By representing those times versus the internal delays thefollowing line is obtained:

Figure 4.11 Calibration line in the case of internal trigger.

Assuming a linear relation one can get for the value of the slope0.996±0.007 and under this assumption a χ2 equal to 97. This high valueof the χ2 is explained by the inaccuracy of the Control Module’s internaldelay when it is used at such a test method. Since the method of varyingthe internal delay is not being in usage during normal operation mode,the exact shape of the calibration line is not that important at this point.This method was chosen because the required Pulse Generator was notavailable in Siegen and further tests were not conducted because ofschedule reasons. From these considerations, the same method withinternal trigger will be applied to observe the calibration line behaviourduring the thermal tests presented in the next sub-section. Therefore atthis point only a general trend of the calibration line is to beconsidered, as the slope for example. A more precise measurementmethod, described below, which models the real situation of theexperiment could become possible only recently at Goddard [Hams2000].

The second way to obtain the calibration line is to maintain fixedthe internal delay in Control Module and to vary the time intervalbetween trigger and test signal. This variation could be done with aPulse Generator, which emits two different pulses at differentprogrammable times. Such an instrument, a Phillips Charge/TimeGenerator 7120, was recently available at Goddard Space Flight Center,where the ISOMAX detector is located [Hams 2000]. Logic Module 10


0 500 1000 1500 2000 25000.72

0.74

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Delay 0 ns Delay 416 ns Delay 832 ns Delay 1248 ns Delay 1664 ns

Tim

e r

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was studied and only the results for the channel 306 are presented here.The measurements now cover almost all the active time range, from 20ns upto 2300 ns. The Pulse Generator emits both the trigger and the testsignals. The delay between those two signals can be adjusted to thedesired value. This was accomplished in multiples of 35 ns, beingpossible to make measurements at 67 intermediate times. As could beassumed, the time resolutions will be poorer this time because of twofactors: the external trigger and the internal delay of the PulseGenerator. Figure 4.12 shows the measured time resolutions. Theobserved periodicity is related to the way the Pulser generates the testsignal and it is not proper to the read-out system. The patterndisappeared when a new data set was recorded, using a 512 ns full scale(FS) instead of 10 µs FS as in the first case. The internal delay was variednow in multiples of 416 ns and the Pulser FS delay was divided in 16equal steps of 32 ns.

a)

b)

Figure 4.12 Time resolutions in the case of trigger from Pulse Generator fortwo different working modes: a) 10 µm FS and b) 512 ns FS.

0 500 1000 1500 2000 25000.95

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The calibration line obtained in this case is presented in Figure4.13. The slope was found 1.00069 ± 9*10-4 and χ2=0.2. As this situationmodels the experiment more accurately than the case of internal trigger,this value of χ2 has a full meaning in comparison with the one obtainedfrom Figure 4.11. One can remark that the assumption of consideringthe calibration curve of the read-out system a straight line with theslope one, describes very accurate the reality.

Figure 4.13 Calibration line in the case of trigger from Pulse Generator.

0 500 1000 1500 2000 2500

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4.2 Temperature Tests

4.2.1 Experimental Setup

The basic idea behind this type of tests is to try to repeat theabove measurements at temperatures well different from the roomtemperature and to observe the effects that such variations bring to thesystem parameters. It is therefore needed a device both capable ofcooling and warming in a range from -20°C to 40°C. Such an apparatuswas available in Siegen but its main disadvantage was that the interiorwas too small to host the test mainboard and the Control Module.Therefore changes to the first experimental setup must be made toenable the measurements. A digital thermometer was used to measureprecisely the temperature inside the thermal controlled compartment.

Since one wants to make a representative test for the wholesystem, a copy at smaller scale will be sufficient to achieve therequirements. The task was to build a new mainboard which shouldcontain only one TAC (4 channels) and a Logic Module. This smallermainboard was placed on the top of the Control Module, forming thus acompact ensemble that fit perfectly inside the thermal controlledcompartment, as shown in Figure 4.14.

Figure 4.14 Experimental setup for the temperature tests.

The first attempts to cool down the system were not successfulbecause at approximately 2°C the Control Unit became unstable. The


reason for that was the solderings of the electronic components. Oncethe problem was solved low temperatures did not harm the systemanymore. Cold tests for the instrument electronics at Goddard willforestall such accidents during the flight.

4.2.2 Linearity and Calibration Tests

To test the variation of the measured time against thetemperature, the external trigger from the I/O card was used. A dataset with 1000 pulses was recorded at each degree Celsius from –20°Cupto 20°, and then each five degrees up to 40°C. Before each recordingan internal calibration of the system ramps was done (see sub-section3.2.2). The internal delay of the Control Module was set to 70*32 ns(2240 ns).

All four channels had similar behaviour, therefore only thechannel 45 is shown in Figure 4.15. Along the 60°C variation, themeasured times increased by 1.7 ns, resulting in an average of 0.028ns/°C. This result can be explained either assuming that the periodicityof the quartz clock or the answer time of the Control Module areaffected by temperature. It is remarkable that over a large spectrum oftemperatures, a system destined to measure times up to thousands ofnanoseconds, has such a small offset.

Figure 4.15 Offset behaviour against temperature variations.

-20 -10 0 10 20 30 40

2256.6

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The time resolution over this temperature range is presented inFigure 4.16. As can be noticed the resolution is preserved in the samedomains as in the case of room temperature tests (average 0.65 ns) andthere is no temperature dependence. This clearly demonstrates that thetime resolution is not affected by temperature variations.

Figure 4.16 Time resolutions over a wide temperature range.

The next issue is to test the linearity of the calibration at differenttemperatures. The internal trigger was used just as in the case of theroom temperature test. There were recorded three data sets at –20°C,10°C and 40°C respectively. In Figure 4.17 the calibration lines ofchannel 45 at the three measured temperatures are presented. Theslopes are at the same value as before, 0.996, as well as the chi-squareχ2=97. The temperature variation does not affect the calibration line ofthis channel.

The same measurements are used in Figure 4.18 to show that thetime resolution over the whole studied time range is not affected by thetemperature and remains at the same values as before.


Figure 4.17 Calibration lines at different temperatures for channel 45.

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Figure 4.18 Time resolutions of channel 45 at three different temperatures.

The same stability of time resolution against temperaturevariations is present if the same measurements are done only with asingle internal calibration of the ramps at –20°C. The results arepresented in the next table.

Channel

Temp(°C)

45 46 47 48

Measured time (ns) 2258.6 2259.2 2258.3 2259.9-20Time resolution (ns) 0.62 0.75 0.73 0.86Measured time (ns) 2259.2 2259.6 2258.8 2260.50Time resolution (ns) 0.61 0.8 0.77 0.95Measured time (ns) 2260.3 2260.9 2259.9 2262.140Time resolution (ns) 0.63 0.81 0.81 0.84

It is worth mentioning that in the case of no calibration, themeasured times behaved as in the case when the calibration was done.One can see that the differences of the measured times for channel 45 isexactly 1.7 ns for 60°C, as in the previous situation, showing a relativesmall influence of the calibration on the offsets.

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5. The Spatial Resolution 35

Chapter 5

The Spatial Resolution

In this chapter it will be presented the calculus procedure whichleads to the spatial resolution of straight muons tracks as recorded withthe tracking detector of the ISOMAX instrument (magnet off). To analysethe drift chamber performance I used a software package, which has beendeveloped in Siegen during the past years and applied alreadysuccessfully at other balloon flights as: IMAX, Caprice and ISOMAX [Hof94].

The read-out system AK8092, previously described, was used at thedata recording, which took place on 25th of October 1999 at Goddard SpaceFlight Center. From technical reasons, only the middle and the bottomchamber could be part of the test. The data recording lasted for 8 hoursand contained 22000 events. The threshold in the discriminators was set to0.7 V and the anode voltage was 4.6 kV.

5.1 Offset Determination

The collected data from the time measurement are not yet the drifttimes but they contain the key information leading to this goal. In contrastwith the situation from the temperature tests, the measured times are nowcomplementary to the drift times, and therefore drift time dependent. As a


consequence, smaller drift times correspond now to large measured timesand vice versa.

The first graph representation would be naturally the histogram ofthe measured times, further called (MTH). The presented MTH are theoriginal data as they were recorded, but they were subtracted from 2750 ns(Figure 5.1) in order to present them in Common Stop mode.

Tdrift tiinstrumthe appthreshoknowincells ardistribu

0
500 1000 1500 2000 2500 3000 350
Figure 5.1. Measured Times Histogram (MTH).

his presentation has the advantage that it offers a preview of themes for all the channels, enabling preliminary evaluations of theent quality. Among others, it gives information about the purity oflied gas, how correct are the used high voltages and discriminatorslds or about efficiency. The MTH shape can be understoodg the electric field configuration of a drift cell. Assuming that thee hit by particles spatially constant distributed, the drift timestion of the produced electrons will not be anymore constant.


Around the anode wires, where the electric field values are important, thedrift electrons are strongly accelerated and cause the dominant peak of thespectrum at short times. The plateau at intermediate and large drift timesgives the information that the drift velocity decreases very slowly alongthe drift cell. At the end of the spectrum a small bump appeared becauseof a slightly acceleration around the potential wires.

Intuitively, the drift time equal to zero would correspond to ameasured time equal to the internal delay of the Control Module.However, in practice the trigger signal and the anode signal will notnecessarily be simultaneous because of at least two factors: the differentplaces where a particle hit the TOF scintillators and because of timepropagation of the anode signals through the anodes and read-out circuits.Those variations are also proper to each cell due to the physical place werethey are located in the instrument and also due to the attached electronicshaving slightly different behaviour as shown in Chapter 4. An analysis,which is channel oriented, is thus necessary.

As can be seen from Figure 5.1 the main peak which corresponds toa zero drift time is displaced from the 0 point with an offset. This offsetmust be determined in order to calculate the actual drift times. Themethods already used [Menn 91, Kremer 95, Hams 97] mainly consideredthe offset as the point which corresponds to half the value of peakmaximum, calculated on the increasing peak flank. In addition, dependingon how steep is this flank, the point located at 80% from the peak heightcould be chosen as offset. If there is not enough statistics recorded for acell, one could use the above considerations but applied now for a familyof cells that are somehow related, as in the case of the cells from one LogicModule. Less accurate drift times are calculated in this way but the lack ofstatistics can be overcome. Since this was the case for this data set, acombination of the four methods was used. In Figure 5.2 it is shown arelatively correct MTH for which there are all the four methods applied.The differences in this case are minor. The chosen offset corresponds to thecase c).


a)

b)

c)

d)

Figure 5.2. MTH for channel 441 and the calculated offsets in the case of:a) point at 50% of the maximum on the increasing peak flank

b) same as a) but calculated for Logic Module 13 MTH c) point at 80% of the maximum on the increasing peak flank d) same as c) but calculated for Logic Module 13 MTH.

In Figure 5.3 it is presented a MTH which can not be solved with any ofthe four methods. This kind of MTH was not a singular case and it isspecifically either to the channels located at the edges of the drift chambersor to faulty electronics.


a)

b)

c)

d)

Figure 5.3 MTH for channel 302 and the calculated offsets in the same fourcases. The offset was chosen 375 ns.

The offsets calculated as above are presented in Figure 5.4. Thevalues of interest are up to the channel 480 . The other points up to 520 areoffsets calculated for ensembles of cells (logic modules, layers, driftchambers). They are compared with the ones calculated by taking thepoint located at half of the peak maximum of each drift cell MTH. Thevariations of the offsets inside of a logic module are clearly reduced. Thedifferences of offsets from one Logic Module to another can be understoodby considering the order of connection to Bus Extension Module. LogicModules placed closer to the Bus Extension Module will produce largeroffsets, since the measured times are smaller than the ones from moredistant Logic Modules.


a) b)

Figure 5.4 Offsets calculated with a) 50% of the maximum and b) a conjunctionof four methods (the vertical lines delimit logic modules, from 5 to 14).

Once the offsets proper to each drift cell are known, the drift timescan be calculated by subtracting the offsets from the MTH. In Figure 5.5 itis presented the Drift Times Histogram (DTS) obtained for this data setcalculated in this way.

Figure 5

Channel 480

.5 Drift Times Histogram (DTS) for all channels.


5.2 Drift Time - to - Path Relation (DPR)

Once the drift time for a hit cell is known the next step is to inferinformation about track points inside this cell. A certain measured drifttime means that the incident particle trajectory was tangent to one specificline of equal drift time (Figure 3.4). Therefore, a first theoretical approachwould be that for each event, when more cells were hit, a common tangentto the corresponding equal drift time lines should be constructed. Thisapproach was done only in the early phase of testing the capabilities ofsuch a drift cell structure [Christian 90, Menn 91, Bremerich 92]. Itincluded a calculus of the internal electric field structure and of equal drifttime surfaces for a single cell. The knowledge of such surfaces meansnothing else that a theoretical relation between drift times and driftdistances was found for each cell. Such a correspondence is known as DriftTime – to - Path Relation (DPR).

However, for a system of 480 cells this approach causes tremendousdifficulties to arise not only because of the calculus volume but alsobecause of the continuously precise monitoring of all the voltages and ofthe mutual influences between the cells electric fields. From thisperspective it is not realistic to try obtaining 480 DPRs for as many driftcells.

Another way to attempt getting the DPR is to use the measured drifttimes itself. From the very beginning it must be observed that due to thepoor statistics for each cell one has to renounce the goal to get 480 DPRs. Acommon DPR will improve the statistics and make thus this analysispossible at the costs of lowering the resolution.

At a more careful look of Figure 3.4 one can notice that for a largespatial domain the lines of equal drift times are highly symmetric, beingrepresented by circles. A first approximation, which will be correctedthereafter, is to assume that all the equal drift time lines are circles all overthe drift cell. This is equivalent saying that the DPR is an injective functionbecause a drift time corresponds to an unique drift distance. This does notdescribe accurately the real situation but offers a good starting point. Sincethe electric field inside a cell is basically the one of a cylindrical capacitor itis meaningful to apply first as DPR the following relation:

r = ct ⋅ t (5.1)


where r is the drift distance, t the drift time and ct represents a constantthat depends of the cell dimensions.

Proceeding further with the analysis on an event by event basis,circles are constructed, with the radii corresponding to the measured drifttimes. In the next step a procedure which searches possible commontangents of the above mentioned circles will be applied. The distancesfrom the anode wires and those straight lines are calculated and saved asχ2-Sums. The tangent-track that describes the event best will be selected asthe straight line with the smallest χ2. At this point, for each hit cell at onegiven event it is important to calculate the residual, defined in thefollowing relation:

measfitres xxx - = (5.2)

where the involved sizes are illustrated in Figure 5.6.

Figure 5.6. Definition of the res

Xmeas

k

Xfit

Residual (xres)

Fitted trac

idual.


The new calculated xfit distances will better represent the calculateddrift distances than the ones assumed previously xmeas and they will beused to compute a new improved DPR. In Figure 5.7 it was plotted theDPR square root together with its subsequent calculated xfit points.Positive and negative values of xfit are obtained if the drift paths arelocated in different cell halves. One can notice that the first chosen DPRrepresents a poor description of the theoretical one for increased drifttimes, a fact which shows that the electric field symmetries are broken forlarger distances.

Figure 5.7 Square Root DPR (in red) and the calculated xfit points.

Another useful representation is the so-called “ResidualsDistribution”. It shows easily if a certain DPR describes correctly the dataand it is used for the resolution calculus (Figure 5.8). The residuals, whichproceed from a wrong DPR, will not be distributed equally around the X-axis.


Figure 5.8 Residual Distribution for a square root DPR.

Using the new calculated xfit points a better DPR can be inferred.However, since it is compulsory to remain always at the situation whenonly circles are to be fitted one have to make an angle selection in the DPRcalculus. As a consequence, at the obtaining of the new DPR willparticipate only xfit points belonging to perpendicular tracks, namely withthe absolute zenith angles less than 2.5° (0° DPR). This is done because inthe case of perpendicular tracks the distances from anode wires to thetracks are always identical with the drift distances. For the calculus of theDPR, the square root of time axis was first divided in 50 time intervals(from 0 to 2500 ns). For each time interval the corresponding xfit points areaveraged obtaining thus 50 so called support points. A spline fittingprocedure applied to those points will produce the new DPR. In Figure 5.9it is presented the square root DPR, the xfit points calculated from it(belonging to straight tracks) and the new fitted DPR.


Figure 5.9 Square root DPR (blue), calculated xfit points and the new DPR (red).

Using the improved DPR, a new iteration can be initiated with thesame stages as the above ones and better DPRs will be calculated. Thisiteration process is convergent to a stable DPR after at most eightiterations. In Figure 5.10 are presented the differences between square rootDPR and first calculated DPR. As expected they differ at most at the cellsextremities. After seven iterations the differences of the DPRs are againpresented. The variations observed from now on are mainly due to thestatistical fluctuations of the support points in the fitting procedure.

Figure 5.10 Differences between two consecutive DPRs at first iteration (left)and seventh iteration (right).

(µm) (µm)


5.3 Residuals Scatter Plot and the Spatial Resolution

Among other methods, the spatial resolution can be calculatedstarting from the residuals scatter plot [Christian 91, Menn 91]. One needstherefore a correct residuals distribution, which can be obtained only usinga correct DPR. In Figure 5.11 it is presented the way that a residuals scatterplot evolves towards a correct one for three consecutive DPRs. As the DPRis more refined through successive calculations, the residuals are morecorrectly distributed around the X-axis of the scatter plot.

Figure 5.11 Evolution of the residualsthe DPR improveme

For a greater iteration number than thones presented above, the quality of the straced with the naked eye. To obtain more acone has to consider that in the fitting procfinite number of points take part. For this re

DPR 2
DPR 1
SQRT

scatter plots duringnt.

ose presented above, as thecatter plots cannot be easilycurate values of the residualsedure of the tangent-track aason the xfit points from the


exterior drift chamber layers have a greater influence at the fitting than thepoints from the interior layers [Neuhaus 89]. Therefore, for the middlechamber whose spatial resolution will be calculated, the residualsproceeding from different measurement levels will be corrected bymultiplying them with the following values [Kremer 95] :Level 1 and 8 : 1.286Level 2 and 7 : 1.240Level 3 and 6 : 1.072Level 4 and 5 : 1.069

The spatial resolution will be given by the width of the residualshistogram, which must be gaussian distributed. However, since theresolution is not constant for all distances, the 15.6 mm cell width will beseparated in 15 spatial domains and for each domain a residuals histogramis constructed. The standard deviation of the Gaussian fitted curve to thishistogram will give the spatial resolution in this particular distancesdomain.

The choice of the fit interval and the histogram binning must bedone carefully in order to minimise effects as ions clustering or electronsdiffusion. Since those effects are uniformly distributed, its influences areimportant at the tail of the distributions, causing incorrect spreading of thehistograms. In Figure 5.12 a wrong fit is shown where no cut was applied.The quality criterion for a good fit is here the χ2 value.

Figure 5.12 Example of wrong values for b

fitting on the distance interval 5÷6 mm (badoth χ2 and resolution).


With this calculated standard deviation as a first estimate of theresolution on this domain one can make a cut on the fitting interval of ± 3σaround the mean value and a new gaussian fit is done. This choice of the3σ interval is based on the fact that 99.8% of the measured points shouldbe found in this domain. The standard deviation will continuouslydecrease for at most three such iterations until a stable value is reached.The χ2 value improves accordingly. In Figure 5.13 the final fit after threeprocedures is shown. One can notice that both parameters are improved.

Figure 5.13 Final fitting for det5÷6 mm (a resol

Due to the poor statistics15.6 mm) were the most affecteand therefore these distances aUsing the same considerationsto measure times with 1 ns accDPR support points calculation

ermining the spatial resolution on the intervalution of 68 µm was obtained).

for this data set, the large distances (13.5 ÷d. A reasonable gaussian fit was impossiblere no more present in the resolution plots., the new capability of the read-out systemuracy was not totally exploited since at the the time scale was divided in 50 intervals


to preserve good statistics. This situation will not be present anymoreduring the planned 3-days flight.

5.4 The Angle Correction

Before presenting the resolutions for the whole distance domain, onehas to consider the angle correction. Its sense lies in the approximationmade for the DPR calculus, namely that only xfit points belonging toperpendicular tracks were considered. The residuals calculated for thiscategory of points are the correct ones for the whole range of distances.

For short and medium drift times the lines of equal drift times areapproximately circles, which implies that the DPR is not angle dependent.At long distances and for the tracks that have larger angles with respect tothe vertical axis of the instrument other DPRs must be inferred. This factwill be illustrated in the Figure 5.14 where three different DPRs, calculatedat different angles, are identical except at long distances. From a closerlook at the lines of equal drift time from Figure 3.4, one notice that twodifferent tracks, one perpendicular on the drift chambers (with 0° angle inthe analysis) and one bent (with a certain angle), which are tangents to thesame line of equal drift time, corresponds to two different drift distances.In the case of perpendicular tracks the drift distance, which is also identicalwith the distance anode track, is greater than the drift distance in the caseof bent tracks. Accordingly, the distance anode - track in the case of benttracks will be smaller and thus the constructed circles should have smallerradii. If one uses therefore the 0° DPR for tracks with large angles and longdistances then the circles that take part at the fit will be bigger than thecorrect ones. As consequence, the residuals should be negative and willtend to lie below the X-axis on the scatter plot. This is the theoreticalsituation if the electric field inside the cell is as the one presented in Figure3.4 [Bremerich 92].

It is however possible to encounter the opposite residuals behaviourif the high voltages are not exactly as the ones described in Chapter 3. Forexample, if the 570 V voltage on the potential wires decreases to 300 V,than the lines of equal drift times will be pushed towards the anodes, andan electric field configuration similar with the one without potential wireswill be created. As presented in [Bremerich 92] this type of electric field


will lead to an opposite behaviour of the residuals than described in thebeginning of this sub-section.

In Figure 5.14 three DPRs are presented, calculated for tracks atdifferent angles. The one at 0° is already known from the previousconsiderations. The other two DPRs are calculated for tracks at largerangles (10° and 20°). The situation is reversed to the theoretical one, whenwe would have been expected to obtain DPRs at larger angles under the 0°DPR. This behaviour must have been caused, as mentioned, by a drop inthe potential wire voltage.

Figure 5.14 DPRs calculated for different angles.

To be able to correct the residuals scatter plot at large angles andlong distances without the need to compute different DPRs, one can usethe 0° DPR together a with correction matrix. The goal is to find out, for agiven angle and a given distance, what correction should be brought to thecircle radius obtained from the 0° DPR in order to obtain the right circles.This correction can be given by the residuals itself, if they are ordered in anappropriate fashion in a correction matrix. The correction matrix has a30x13 dimension, where the square root of time axis is divided in 30 equalintervals and the angle spectrum is separated in 13 intervals. An angle

DPR 0°

DPR 20°

DPR 10°


interval corresponds to 5° with an overlap of 2.5° between two adjacentintervals. Track points whose drift electrons are originated in the exteriorhalves of the drift chamber levels are distributed to negative angles. Theidea behind this is that the electric field configuration in this part of thecells is influenced by the presence of the guarding wires and thecylindrical symmetries are more affected here. This matrix is filledprogressively with the residuals, as the tracks are resolved. Finally, eachmatrix element is averaged in the three directions: times, angles andresiduals. A new iteration is done where an interpolated value from thecorrection matrix is added to the xmeas point from the 0° DPR and the newresidual is transferred back to the matrix. After at most four iterations thedifferences of the successive correction matrix are only statistically. InFigure 5.15 it is presented the correction matrix after the fourth iteration.

Figure 5.15 Correction matrix after four iterations.

As it was assumed, the corrections are important for large anglesand long distances, reaching up to 400 µm. For negative angles the


corrections are more important than for positive angles, meaning that theelectric field symmetrical configuration in the half cells located at the driftchambers margins will be more affected.

In Figure 5.16 a comparison of residual scatter plots calculated withand without angle correction is presented. The residuals equal distributionaround the X-axis is improved for long distances. Figure 5.17 shows thatthe shape of the residuals distribution tends to a Gaussian distribution ifthe angle correction is applied.

a) b)

Figure 5.16 The residuals distribution calculated in two cases:a) without angle correction and b) with angle correction (in this case, theresiduals at negative distances are represented with the reversed sign).


Figure 5.17 Improvement of the (red without angle corr

Using the angle correctionall distances and all angles. In Fresolutions in both the cases. Thlong distances.

Figure 5.18 The spatial resowith ang

residuals histogram for the interval 12÷13 mmection, blue with angle correction).

, the resolution can now be calculated forigure 5.18 there are compared the obtainede improvement is significant especially at

lution without angle correction (red) andle correction (black).

µµµµm


5.5 3σ Correction

The fact that one knows a first estimation of the spatial resolution ateach distances domain, one can use it to infer even better values than thepresent ones. If we encounter a track with a certain angle and a certaindrift time for a cell, then the distance track-anode wire, given by the DPRand the angle correction, is measured with a resolution σ according to theFigure 5.18. Fitting the tangent-track to the circle, the measured residualshould lie in 99.8% of the cases inside the 3σ interval, which in the worstcase should not be greater than 0.9 mm. If not, then one could assume thatit is a good chance that this measured drift time proceeded from physicaleffects which are not related only to the drift motion of electrons (knock-onelectrons, nuclear scattering, diffusion). As a consequence, the measuredtimes at this cells will gain no weight in the final fit of a tangent-track.With a more precise fitted track, those cells are again considered and theresiduals for them are calculated. With this method, very inaccurate timemeasurements can not establish an overall worsening of the spatialmeasurement. Applying this procedure, some events were totallydiscarded but they represented only 10% of the overall statistics. On theother hand, the improvement over the resolution is significant.

Figure 5.19 shows the improvement of the residuals histogram,plotted for all distances. One can notice that as the width is narrower, thepeak is higher meaning that points from the distribution tails were shiftedto the centre (more accurate measured).


Figure 5.19 The effect of the

In Figure 5.20 the spatial rfunction of drift distance. For abouspatial resolution is better than 9situated between 50 µm and 60 µThose results represent slight imresults obtained with the older read

3σ correction on the residuals histogram.

esolution improvement is plotted as at 60% of the possible drift distances the0 µm. The lowest reached values are

m for middle drift distances (4÷8 mm).provements if one compares similar-out system [Kremer 95, Hams 97].


-0.2 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4

50

100

150

200

250

300

R

eso

lutio

n (

µm)

Distance Anode-Track (cm)

Figure 5.20 The spatial resolution as result of the 3σ correction (red) comparedwith the previous one (black)

The reduced resolution at long drift distances can be explained dueto a loss of symmetry of the electric field and because of electron diffusion.The loss of resolution at short distances has two likely causes. Since thedrift velocity increases rapidly close to the wire, an error in timingtranslates into a larger position error. As previously mentioned, forstatistical reasons, the binning chosen for this analysis at the calculus of theDPR, was not small enough to take full advantage of the time resolution of1 ns. In addition, when a particle passes close to the anode wire, theclustering of ionisation along the path translates into a spatial error sinceelectrons may not be liberated at the point of closest distance.

6. Conclusions 57

Chapter 6

Conclusions

The central point in the present work is constituted by aninvestigation of the AK8092 read-out system capabilities, as part of theISOMAX tracking detector. The analysis includes two main sections: a testsseries which aim to reveal the intrinsic properties of the read-out systemelectronics and a thorough description of a straight tracks calculusprocedure aimed to show which resolution characterises the spatialmeasurements.

In the first section tests concerning the time measurement resolutionand the calibration line proper to the system were performed, both at roomand extreme temperatures. The projected time measurement resolution of1 ns, proved to be slightly underestimated because the measurements withan external trigger, which simulates at best the experimental conditions,were recorded with an accuracy of 0.7 ns in average. Measurements with apulse generator, used both as trigger and as test signal generator, showeda slightly greater time measurement resolution of 1.1 ns in average. Thislast result can be traced in a proper pulse generator contribution at thetotal measurement error. The measurements aimed to obtain thecalibration line shown a linear behaviour (with the slope one) of thesystem over the whole time domain. The same characteristics of the system

6. Conclusions 58

were once again tested at temperatures that ranged from -20°C up to 40°C.At the first attempt to cool down the system the electronics ceased tobehave normally, but the reason for that was some faulty solderings. Whenthose problems were outran the system responded extremely well both atlow and high temperatures. The time resolution presented no variationagainst the temperature, even in the case when the calibration of the TACswas not done. The linearity remains also unchanged with the temperature,meaning that the computing of the DPR (Drift Time to Path Relation) asdone for the old read-out system remain further valid.

The calculus of the spatial resolution for the middle drift chamberimplied new modifications to the older software in order to take in accountthe new data format and the new time resolution. The lack of sufficientstatistics did not allow proving significant improvements over theresolution compared with the old read-out system, especially at longerdistances. However the obtained values are slightly better than previousresults, being under 90 µm in 60% of the possible distances, in the case ofstraight tracks of singly charged particles. It is worth mentioning theefficiency shown by the 3σ correction, which achieved a resolutionimprovement of 15% for most of the distances.

As a final conclusion, the AK8092 read-out system has shown itsvery good capabilities during the investigations, being a reliableinstrument for the next flight of the ISOMAX instrument.

59

Bibliography

[Bremerich 92] M. Bremerich, Simulation der Elektronendrift inhexagonalen Driftkammerzellen und experimenteller Testeines Prototyps. Diplomarbeit, Siegen (1992)

[Bremerich 97] M. Bremerich, Ein Ballonexperiment zur Untersuchung derleichten Isotope in der kosmischen Strahlung. Dissertation,Siegen (1997)

[Christian 91] Test einer DriftKammer mit hexagonaler Zellstruktur imhomogenen Magnetfeld. Diplomarbeit, Siegen (1991)

[Geier 99] S. Geier, et al., In-flight Performance of the ISOMAX TOF,Proceedings 26th ICRC (Salt Lake City), OG 1.1 (1999)

[de Nolfo 99] G.A. de Nolfo, et al., Cosmic Ray Isotope Measurementusing the Cherenkov-Rigidity Technique in ISOMAX,Proceedings 26th ICRC (Salt Lake City), OG 1.1 (1999)

[Göbel 2000] H. Göbel, Further Improvement of the TOF Analysis,Memo, Siegen (2000)

[Hams 96] T. Hams, Aufbau eines Driftkammer-Gassystems und Testeiner leistungsarmen Driftkammerauslese für das ISOMAXExperiment. Diplomarbeit, Siegen (1996)

[Hams 2000] T. Hams, Private Communications (2000)

[Hof 94] M. Hof, et al., Performance of Drift Chambers in aMagnetic Rigidity Spectrometer for Measuring the CosmicRadiation, Nuclear Instruments and Methods in PhysicsResearch A 345 561-569 (1994)

[Kremer 95] J. Kremer, Testmessungen am Spurdetektor und amFlugzeitsystem des ISOMAX Experimentes. Diplomarbeit,Siegen (1995)

[Neuhaus 89] J. Neuhaus, Messung von Teilchenspuren in einemSchwerionen-Experiment mit einer Drift-Influenzkammer.Diplomarbeit, Siegen (1989)

[Menn 91] W. Menn, Messung der Teilchenbahnen vonhochenergetischen Schwerionen mit einer mit CO2gefüllten Driftkammer. Diplomarbeit, Siegen (1991)

[Sauli 84] F. Sauli, A. Peisert, CERN-Report, 84-08 (1984)

[Streitmatter 92] R. E. Streitmatter, A program to study beryllium andother light isotopes in the cosmic radiation. Proposal,Washington (1992)

Acknowledgements

I would like to express my gratitude to Prof. Dr. Manfred Simon for givingme the opportunity to work in his research group, for his patience and hiscontinuous and competent support.

I am indebted to Dipl.-Phys. Thomas Hams for his inspired advice and hisprecious help.

A very big “Thank you” to Dipl.-Phys. Holger Göbel for many helpfuladvices and comments during the whole work.

I am also grateful to the other actual or former members of Prof. Simon’sresearch group for useful discussions about physics: Dr. Michael Hof, Dr.Wolfgang Menn, Dr. Jens Kremer, Dipl.-Phys. Alexander Molnar and BerndDostal.

Last but not least I want to thank to Doug Robinson for his help with thecorrection in English of the thesis.

Erklärung

Hiermit erkläre ich, daß ich die vorliegende Diplomarbeitselbständig verfaßt und keine anderen als die angegebenen Quellen undHilfsmittel benuzt, sowie Zitate und Ergebnisse Anderer kenntlichgemacht habe.

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