TABLE OF CONTENTS
Page No.
Acknowledgements......................................................V
Abstract.............................................................VI
PART I : A RING IMAGING CHERENKOV DETECTOR
Chapter I The Technique of Ring Imaging Cherenkov Detectors
1.1 Introductory Background to Cherenkov Detectors...........1
1.2 Ring Imaging : Some Theoretical Aspects..................3
1.3 Sources of Error in the Determination of qc..............6
a) Photon Localisation...................................8
b) Dispersion...........................................10
c) Energy Loss in the Medium............................12
d) Multiple Coulomb Scattering..........................13
e) Optical Aberrations..................................15
f) Diffraction..........................................15
References..............................................17
Chapter II An Experimental Ring Imaging Detector
2.1 Introduction............................................18
2.2 The Test Beam C13.......................................18
2.3 Experimental Layout.....................................19
a) The Radiator Vessels and Mirror......................21
b) Radiator and Photoionising Gas Systems...............21
2.4 The Time Projection Chamber (TPC).......................23
2.5 On-Line Data Acquisition................................25
a) Trigger Logic........................................25
b) Event Description....................................26
c) On-Line Software.....................................27
References..............................................29
Chapter III An Analysis of the Experimental Data
3.1 Introduction............................................30
3.2 Straight Ionisation Tracks in the TPC...................31
3.3 Efficiency Scan of the Drift Gap........................32
3.4 Cherenkov Rings in the TPC..............................33
3.5 Interpretation of Results...............................38
References..............................................42
PART II : AN ANALYSIS OF THE PHOTOPRODUCTION REACTION
g p ® w p° p
Chapter IV Vector Meson Photoproduction
4.1 Introduction............................................43
4.2 Mesonic Currents from the Photon........................43
4.3 Meson Spectroscopy and the Naive Quark Model............45
4.4 The Vector Mesons.......................................47
4.5 The wp State : Experimental Situation...................48
References..............................................51
Chapter V The Experimental Investigation of Vector Meson States
in Photoproduction
5.1 Introduction............................................52
5.2 The Photon Beam and Tagging System......................52
5.3 The OMEGA Spectrometer and Associated Detectors.........55
a) The Hydrogen Target..................................55
b) The OMEGA MWPCs......................................56
c) The Cherenkov Counter and
Scintillation Hodoscopes.............................57
d) The Photon Detector..................................58
e) The Electron Positron Pair Veto Counters.............59
5.4 Formation of the Experimental Trigger...................61
5.5 Offline Event Reconstruction and Simulation Software....63
a) TRIDENT..............................................64
b) JULIET...............................................65
c) GEORGE...............................................66
d) MAP..................................................66
References..............................................68
Chapter VI Observation of the State wp° in p+p-p°p°(p)
6.1 Introduction............................................69
6.2 Selection of the Data...................................69
6.3 Background Subtraction..................................70
6.4 Overall Features of the Selected Data...................71
6.5 Simulation of the Experimental Acceptance...............72
References..............................................76
Chapter VII A Spin-Parity Analysis of wp°
7.1 Introduction............................................77
7.2 Acceptance Correction of the Experimental Data..........78
7.3 Helicity Formalism and Decay Angular Distributions......79
7.4 Model Independent Fits to the Data Moments..............81
7.5 Model Dependent Fits to the Data Moments................82
a) Details of the Fitting Method........................83
References..............................................87
Chapter VIII Results and Overall Conclusions
8.1 Introduction............................................88
8.2 Spin Parity Analysis using Decay Angular Distributions..88
8.3 Results from the Model Independent Fits.................89
8.4 Results from the Model Dependent Fits...................92
8.5 Summary and Conclusions.................................98
References..............................................100
Appendix A.1 Simulation of a subset of the wp° Data..................101
a) Introduction.........................................101
b) Software Framework...................................101
c) Generation of the Events.............................102
d) Particle Tracking through the Detectors..............103
e) Simulation of the JULIET Software....................104
f) Comparison of Real and Simulated Data................106
References..............................................107
Appendix A.2 Software selection of the total wp° data................108
Appendix A.3 Expressions for the Moments (1).........................109
Appendix A.4 Expressions for the Moments (2).........................110
Appendix A.5 Formalism used in the Model Dependent Fitting Program...111
ACKNOWLEDGEMENTS
I would like to thank the following people for helping me
in one way or another over the last three years.
My supervisor, Professor W. Galbraith, for his good-humoured
assistance and advice throughout my period of research at
the University of Sheffield, and at C.E.R.N.
My parents, for their continuous warm support and encouragement.
My colleague, Dr. John V. Morris, for numerous discussions,
and for remarkably clear explanations of the wp° analysis.
Dr.Peter Sharp and Dr.Tom Ypsilantis, for instilling some of their
own enthusiasm for the Ring Imaging technique in me.
Dr. Jean Richardson, for making the last months of my research
particularly enjoyable.
Drs. Richard McClatchey and Colin Paterson, for conversations
both on high energy physics, and largely off it, which I
consistently found enjoyable.
The following members of the EGAMMA collaboration, who
helped me in various ways:
Drs. George Lafferty, Glenn Patrick, Martyn Davenport,
John Lane and John A.G. Morris.
The S.E.R.C. for the provision of a research studentship,
and C.E.R.N. for the use of its superb facilities.
ABSTRACT
The work described in this thesis covers two distinct
aspects of high energy particle physics, and was undertaken
mainly at the C.E.R.N. laboratory, Geneva, Switzerland.
In the first part of the thesis, an experimental
investigation of the properties of a detector based on the
emission of Cherenkov light in a gaseous radiating medium (argon) is
described.
A charged particle beam of selected momentum
in the range 4-18 GeV/c was allowed
to pass through the radiating medium.
The Cherenkov light so produced was collected by a spherical
mirror and brought to a focus as a ring image in the focal
plane within the active area of a Time Projection Chamber.
Electrons created in the photoionisation of a sensitive gas
in this chamber drifted to a plane of 48 wires, the signals
from which were decoded to reconstruct the ring image.
The results clearly show the capability of the detector for distinguishing
between different charged particle types in the beam.
The second part of the thesis is concerned with the study of
the photoproduction of the so-called higher vector meson states
using a plane-polarised photon beam, of well measured energies
within the range 20-70 GeV, which interacted in a target of
liquid hydrogen.
This target was situated inside a region of magnetic field (1.8 Tesla)
which was produced by the Omega magnet.
Also within the magnetic field volume was a system of MultiWire
Proportional Chambers, which afforded the reconstruction of the
charged particle tracks produced in the interaction and the
location of the interaction vertex within the target.
Neutral pions were detected by identifying photons from the
decay p° ® gg in a large lead-glass array.
An electronic trigger selected events of the type gp ® p+p-p°p°(p)
where the symbol (p) signifies that the recoil proton was sometimes
detected.
Events of this type were recorded onto magnetic tape, and
subsequently analysed offline.
The analysis presented in the thesis refers to the specific
channel gp ® wp°(p) ® p+p-p°p°(p),
where the w is seen in its p+p-p° decay mode,
the total
cross-section for which is shown to be 0.86 ± 0.27 mb.
A determination is made of the spin-parity content of the wp°
state, using both a model dependent and also a model independent
fit to the double moments of the sequential decay (X ® w + p°,
w ® p+p-p°).
The results indicate that an enhancement in the mass spectrum of
wp° events occurs at @1.21 GeV/c², and is shown to be due to
the dominant presence of the Jp=1+ B(1.23) meson.
The results also show that the data are consistent with the presence
of a small contribution from a 1- signal, which may be interpreted
either as the tail of the r(0.77), or as a resonance above
wp° threshold, or as the result of some other process, such as
the Deck mechanism.
Chapter I The Technique of Ring Imaging Cherenkov Detectors
1.1 Introductory Background to Cherenkov Detectors
From a consideration of Maxwell's equations, Heaviside [1]
predicted the possibility of observing a special form of
radiation when a charged particle passed through matter.
Nearly sixty years later, in 1934, Cherenkov and Vavilov [2]
described such an effect, where the nature of the light
seen depended on the gross structure of the medium and
on the momentum of the incident particle.
Tamm and Frank [3] developed the
classical theory which accounts for this light, now
referred to as Cherenkov radiation.
The time variation of the
polarisation induced by the passage of a charged particle through
matter leads in principle to a radiation field at some point distant
from the particle's instantaneous position.
For slowly moving particles,
this field has global symmetry, and,
as a result of interference between the various radiating elements
of the medium, no net field is observed some
distance away.
However, for fast particles the polarisation is axially
asymmetric, and at a threshold velocity where the particle velocity, b,
exceeds that of light in the medium;
b = c / n (1.1)
(n is the refractive index), coherence between the induced
polarisation at different points along the particle trajectory is
achieved.
This gives rise to emission of light along
the direction of coherence (Figure 1.1).
The radiation is emitted in a forward cone of half-angle qc
given by;
cosqc = 1 / bn (1.2)
where b is the ratio of the particle velocity in the medium
to the speed of light
in vacuo.
Light is emitted
from all points along the particle's path,
the electric
vector of the radiation being in a direction perpendicular to
the surface of the Cherenkov cone.
The use of this effect in experimental high energy physics is
in determining the velocity of a charged particle and, in some cases,
its direction through a detector.
Cherenkov detectors in general consist of some
transparent medium (either gaseous, liquid or solid) in which the
particles produce Cherenkov radiation,
and some form of electronic detector which responds
to this light.
In most applications to date the electronic detector has been
a photomultiplier.
From Equation 1.2 it is seen that no light is emitted unless
b > 1 / n (1.3)
and this determines a lower limit on the particle velocity for detection in
a given medium.
Detectors which respond to light from particles
with b above this threshold are termed 'threshold' Cherenkov
detectors.
Those which detect radiation over a small range of cone
angles qc are called 'differential' Cherenkov detectors.
Finally,
the 'ring imaging' Cherenkov detector preserves the spatial information
from the photons emitted around the light cone by detecting the spatial
position of each photon in two dimensions.
For a long time it was impossible to detect Cherenkov rings from
single particles.
In 1963, Butslov[4] et al., photographed the first rings from single
cosmic ray particles.
However, the low quality of the images, which was due to distortions,
prevented a reliable estimate of the ring size to be made.
At Princeton in the same year, Poultney [5] et al. detected whole rings
from a negative pion beam of momentum 820 MeV/c.
The experiment used a system of lenses which focussed the radiation to
a ring of radius approximately 90 mm,
which was then detected by
a photomultiplier.
Three years later, in 1966,
Iredale [6] et al., detected rings produced by radiation from protons of
momentum 5.8 GeV/c in the NIMROD machine.
In that experiment a least squares fit to at least ten detected
photons around a ring was made to determine the ring radius.
By this method the Cherenkov angle qc was determined to within ±9
mrad.
The attraction of these experiments was that both the
velocity and the direction of the particle were measured.
Since then, much interest has been aroused in the possibility
of extracting enough information from Cherenkov rings to make
threshold Cherenkov counters obsolete, except for relatively
crude particle identification.
A description of the construction and testing of a small
ring imaging Cherenkov detector constitutes part of this thesis.
The remainder of this chapter is concerned with the theoretical
background of the technique.
1.2 Ring Imaging : Some theoretical aspects.
A ring imaging Cherenkov detector essentially measures the
angles of emission of the photons
around the Cherenkov light cone and the
intersection at some plane of this cone.
Figure 1.2 shows a simple ring imaging detector.
Photons emitted by the charged particle while travelling through
the radiator vessel are reflected at the spherical mirror to form
a focussed ring at the plane of the detector D.
From the photon positions
a determination may be made of the particle direction;
for single
particles this requires at least three detected photons.
Since the photon positions in general are affected by the
experimental resolution, there is a pattern recognition
problem in determining the size of the ring or other conic
section detected.
However,
the quantity of information extracted for each detected particle
is larger, for example, than that for a threshold Cherenkov detector.
The photons produced in the radiator vessel
are emitted uniformly along the particle trajectory at the angle
qc, Equation 1.2.
These photons are focussed by the spherical
mirror of focal length f to a ring image of radius R at the focal
surface;
R = f tanqc (1.4)
In the present example the focal surface is approximated to the
detector plane D.
The two-dimensional position of each photon on the ring must then
be measured to determine the ring size and position to the best
attainable accuracy.
In practice this can be achieved by converting the photons to
photoelectrons in some suitable gas mixture, then causing these
electrons to drift in an electric field and enter a
multiwire proportional
chamber (MWPC).
Within this chamber the avalanche at a wire, caused by an
impinging photoelectron, determines the position of the initial
photon in one dimension (this is simply the wire address).
From the overall time taken for the photon to convert, the produced
photoelectron to drift and the avalanche to cause a pulse on the
hit wire, and a knowledge of the drift velocity in the gas, the
other space co-ordinate of the Cherenkov photon can be determined.
The Tamm-Frank [3] expression for the Cherenkov radiation loss per
unit length of radiator is;
dW e² w2 1
¿¿ = ¿ Ú (1 ¿ ¿¿¿¿¿¿¿).wdw (1.5)
dl c² w& s'1. n(w)²b²
where n(w) denotes that the medium may be dispersive.
Substituting w=2pc/R above gives;
dW 1 dR
¿¿ = 4p²e² Ú(1 ¿ ¿¿¿¿) ¿¿
dl n²b² R³
and it is seen that the intensity of radiation is inversely proportional to
the third power of the wavelength.
Thus Cherenkov light is mainly concentrated in the
short wavelength region
of the spectrum.
Since;
W = NphT (1.6)
where Npis the number of photons emitted, h is Planck's constant
and T the photon frequency,
Npcan be determined for a given length of radiator.
The proportion of these photons actually detected by the
apparatus per unit energy range is given by;
LA
N = 2p ¿¿ sin²qc Ú Ï dEp
hc
Here L is the length of radiator in metres,
A is the fine structure constant
(= 1/137), Epis the photon energy, and Ï is the energy
dependent acceptance of the apparatus.
The factor Ï might, for instance, comprise the quantum efficiency of the
photoionising gas, the photon reflection efficiency
of a mirror and the transmission factors of any windows in the
detector:
it is clearly wavelength dependent.
The integral must
be taken over the range of wavelengths to which the detector is
sensitive.
Defining Np per unit energy interval as;
2pA
Np = ¿¿¿ Ú Ï dEp (1.7)
hc
then in S.I. units, and per electron volt (eV), Np has the value;
Np = 37000 Ú Ï dEp
and the detected number of photons may be expressed as;
N = NpL sin²qc (1.8)
Np may usefully be thought of as a constant which
characterises the efficiency of
the detector.
1.3 Sources of error in the determination of qc
From the Cherenkov relation (Equation 1.2) it is deduced that the error in
measuring b is related to the r.m.s. errors in qc and n
by;
ìb/b = Ê {(ìn/n)² + tan²qc.ìqc²}
In a particle beam of momentum 10 GeV/c for instance,
the values of b for pions, kaons and protons are;
b(proton) = 0.9966
b(kaon) = 0.99878
b(pion) = 0.999902
Thus to separate these three types of particle an
accuracy ìb/b of less than one part in 10³ is required.
Since b is related to g by;
g = 1 / Ê(1-b²)
this accuracy in b corresponds to one in g of;
ìg/g = b².g² ìb/b
Hence;
ìg
¿¿ = g²b²tanqc ìqc
g
This equation holds when there is no dispersion
or when a measurement is made of g from a single photon.
If N photons are detected, then this error is reduced to 1/ÊN
of its single photon value, given that the refractive index is
constant over the energy range of the detected photons.
N is
derived from Equation 1.8 by integrating over the energy
acceptance of the detector.
For a detector with a characteristic
Np, and with N photons detected;
ìg g²b³n
¿¿ = ¿¿¿¿¿ ìqc (1.9)
g ÊNpL
The angular spread, ìqc, will comprise contributions from;
{a} the accuracy in the localisation of the Cherenkov photons,
{b} the dispersion of the radiator medium,
{c} the energy loss in the medium,
{d} the multiple scattering of the charged particle
in the medium,
{e} optical aberrations in mirrors, and
{f} diffraction due to the finite length of the radiator.
It will be useful (for later purposes) to describe each of these
contributions in a little more detail now.
1.3(a) Photon Localisation
Since the multiplicity of Cherenkov photons radiated per
particle may be as low as one or two in a given detector,
the efficient conversion and detection of such photons is essential.
Depending on the event sampling rate required, several methods
for detecting single photons in two dimensions exist.
At low rates, for example, image-intensifiers may be used [7],
as may a charge-coupled-device (CCD)[8] or Time-Projection-Chamber
(TPC) [9].
Time Projection Chambers and Charge Coupled Devices are also able to
operate at high sampling rates,
although in the case of the CCD, the expense of making the
device sufficiently large to detect whole rings, or sufficiently
good optically to reduce the ring size, is often
prohibitive.
The TPC, on the other hand, is a
well-proven single photon detector in the ring
imaging context [10,11,12], and has the advantage of being relatively
simple and easy to operate.
TPC operation is discussed in detail below (Chapter 2),
and essentially
involves the conversion of single photons to photoelectrons, which
then drift under the influence of an electric field to
enter a Multiwire Proportional Chamber (MWPC),
where they are detected spatially (see Figure 1.3).
The spatial accuracy and detection efficiency depend upon
factors which include
the quantum efficiency of the photo-ionising gas,
the transmissivity of the windows,
the MWPC wire spacing,
the frequency at which the TPC is read out electronically,
the diffusion constants of the photo-ionising gas and
the localisation of the avalanches within the MWPC.
The last four points relate to errors in the measured position
of each photon.
For an MWPC with inter-wire separation s, the r.m.s. error ìx
in the determination of an avalanche position at a hit wire
is given by;
ìx = s/Ê12
If the chamber is read out electronically every ìt seconds,
and the nominal electron drift velocity in the applied electric field
is bd,
then the computed drift length y
contains an error term;
ìyeec. = bd ìt
which holds if the pulse duration is short compared with ìt.
The drift velocity itself contains an
error due to electron diffusion.
In general, the spatial resolution of drift chambers is mainly
limited by density fluctuations in the primary ionisation,
and the
electron's transverse and longitudinal diffusion over the
drift length y.
Variations in the characteristics of the avalanches, and in their
formation rate, will occur
around the MWPC anode wires.
Delta rays (see below), together with the gas pressure and
ambient temperature can also affect the TPC performance.
The r.m.s. displacement ìy due to diffusion is given by [13];
ìydff. = Ê(2Dy/mE)
where D is the diffusion constant, m is the mobility (m²s-±V-±)and
E is the applied drift field (Vm-±).
The quantity D/m is approximately equal to the
average vibrational energy
of the gas electrons.
The radius of the Cherenkov (detected) ring,
given by R² = x²+y²,
is determined to within ìR;
ìR = 1/R ((xìx) + (yìy))
ìx contains the term in s above, and also a term due to the
transverse diffusion of the photoelectron in the drift region.
To a good approximation the transverse and longitudinal
errors due to diffusion may be set equal.
ìxtt. = s/Ê12 + Ê(2Dx/mE)
ìytt. = ìtbd + Ê(2Dy/mE) (1.10)
The error in qc is just ìR/f, where f is the focal length
of the optical system.
1.3(b) Dispersion
In terms of the relative permeability, m, and the
relative permittivity, Ï, of a dielectric medium, the
refractive index is defined to be;
n = Ê(m.Ï)
With the exception of ferromagnetic materials, and in the
vast majority of cases, m deviates from unity by a few parts
in 10´.
Ï defines the constant of proportionality between the electric
field in a medium, E, and the polarisation, P;
(Ï - Ï0).E = P
Ï0 is the permittivity of the vacuum.
If an electromagnetic wave of frequency w is incident on the
dielectric, then the molecules within the medium undergo forced
oscillations.
For large values of w the molecules are unable to follow the
forcing vibrations, and their contributions to the polarisation
field will decrease.
The polarisation field P is thus weaker, and Ï is smaller.
By a classical treatment, the polarisation
field is considered as being the product of the number of contributing
electrons per unit volume and the dipole moments of each.
The sizes of the dipole moments vary with the forcing electromagnetic wave.
Since n² may be expressed in terms of Ï, and hence in terms
of w, it is found [14];
Nmqe² fjFONT FACE=SYMBOL>
n(w)² = 1 + ¿¿¿¿.û ¿¿¿¿¿¿¿¿¿¿¿¿¿ (1.11)
Ï0me j (w0.²-w²+ig jw)
where qeis the electronic charge,
Nm is the number of molecules per unit volume, and meis the mass of
the electron.
The sum is taken over the number of different oscillators j
with natural frequencies w0., in the medium.
The number of summations and the w0 will change from
medium to medium.
&jare the damping coefficients, and the fjlabel the
oscillator strengths.
Colourless transparent gases have their w0 outside
the visible region of the spectrum; this is the reason for such gases
being
colourless.
When w << w0 the refractive index is constant.
The refractive index will slowly rise as w approaches
one of the regions of resonance, w0..
This is the so-called 'normal' dispersion condition.
The regions in the spectrum around w0
are called the absorption bands of the material.
In these areas, dn/dw is negative and the dispersion is termed
'anomalous'.
For many gases at low pressure, and when w is far from w0.,
n-1 is small, and the approximation
n²-1 @ 2(n-1)
holds. Then Equation 1.11 becomes;
Nme² fjFONT FACE=SYMBOL>
n-1 = ¿¿¿¿ û ¿¿¿¿¿¿¿¿¿¿¿ (1.12)
2Ï0m w0.²-w²-igjw
Nm is proportional to the density of the gas.
Figure 1.4 shows the variation of the quantity n-1 for argon
at NTP for photon energies in the range 7.5 to 9 eV,
this range being the one of interest in the present work.
1.3(c) Energy loss in the medium
The main process by which charged particles lose energy
when passing through matter is through Coulomb interactions with
atomic electrons.
(The loss of energy to nuclei in this way is small by
comparison.)
The direct removal of electrons from neutral atoms by the
incident particle is termed 'primary' ionisation.
The knocked-out electrons, if of sufficient energy, may then
cause 'secondary' ionisation, such electrons being called 'delta-rays'.
Ionisation loss has a minimum at relativistic energies,
and to a good approximation is the same for particles of equal
charge and velocity.
In addition to ionisation loss, the close encounters between fast
charged particles and nuclei result in decelerations with the
emission of radiation, and this process, 'bremsstrahlung' (BR),
is an important process by which electrons lose energy in matter.
The critical energy, Ïc, is usefully defined as the energy
at which, in unit length of material, the particle loses
the same energy by ionising atoms as it does by radiating.
The radiation length, X0, is then defined for energies
much larger than Ïc to be the thickness of material which
causes a reduction by 1/e of the particle's incident energy.
It is found that, for the ionisation part, -dE/dx (the rate
of kinetic energy loss in the medium) is independent of particle rest
mass, and inversely proportional to b².
For BR, -dE/dx is given by;
dE
- ¿¿ = Na W Z² f(Z,E) (1.13)
dx
where W is the total energy of the particle, Na is the
number of atoms per unit volume and
Z is the charge on the nuclei in the medium.
The bremsstrahlung radiation is emitted into a cone of
semi-angle q, given by;
m
q = ¿¿¿
m+E
where m is the particle rest mass.
From a knowledge of the rate of energy loss undergone by the
particle in traversing the length of the radiator, a determination
may be made of the change in Cherenkov angle ìqc, since
b is energy dependent.
1.3(d) Multiple Coulomb Scattering (MCS)
As a charged particle moves through a medium it interacts
in the Coulomb field of each nucleus passed.
This results in some deviation from the particle's initial direction.
Each deviation may be considered as a small
angular shift, and
several such interactions result in lateral scattering of the particle.
In practice, the largest and smallest scattering angles likely
to occur are limited by the finite size of the nucleus and the
effects of nuclear screening, respectively.
Nuclear screening is the reduction of the nuclear Coulomb field at
large distances by the presence of the atomic orbital
electrons.
By treating the scattering process statistically (making the
assumption that all deviations are small), the root mean square
scattering angle may be expressed as [15];
Ê<q²> = 1/Ê2b².(Es/E).Ê(X/Xp) (1.14)
where X is the length of the medium traversed, Xp the radiation length
in the medium, E the total energy of the particle,
and Es is given by;
Es= mc².Ê(4p.137)
= 0.023 GeV
The radiation length, Xp is given by the expression;
1/X0 = 4A (N/A) Z² re² lne(183 1/³ÊZ)
where N is Avogadro's number, A is the atomic mass of the medium, Z is its
charge number and re is the classical electron radius.
Approximately, the mean square scattering angle per unit radiation
length is
<q²> = (Es/E)²
The contribution to the error in qc is simply twice this value,
being, as an example, for a particle of momentum 10 GeV/c (the
principal beam momentum used in the detector tests Chapter 2);
ìqc = 2 (0.023/10)² = 10-µ radians
Thus the total contribution to ìqc is small when
gases at low pressure are used, since linear radiation lengths are
considerable in such cases.
1.3(e) Optical Aberrations
In differential and ring imaging Cherenkov detectors
the preferred mirrors are spherical.
Such mirrors have smaller aberrations and are more easily
manufactured than parabolic mirrors.
If the radius of the formed image at the focal plane of
the detector mirror is R (Equation 1.4), then the radial
spread on R due to spherical and coma
aberrations, is given by [16];
DR/R = -(1/8).(d/f)³ + (1/8).(d/f)².qc (1.15)
where d is the diameter of the mirror, and f its focal length.
The contribution to the error in qc from the optical aberrations
is thus simply DR/f.
1.3(f) Diffraction
Since the observed light in the detector originates from
a finite length of radiator, account must be taken of the
incoherence of photons from different points along
the particle trajectory.
The image of a point source of light when focussed by an
optical system takes the form of an Airy disc, when viewed
through a circular aperture.
Often, unless the mirror is of very high quality, the
aberrations will mask observation of this disc.
However, the width, w, of the central fringe in the Airy disc
(where the majority of light is concentrated) can be
expressed in terms of the aperture, and the focal length
of the system [17];
w = 1.22 R.f/d
where d is the aperture, f the focal length, and R the
wavelength of the light.
This is manifest as an error in the radius of the focussed
ring, R, and may thus be translated to an error in qc;
ìqc(Airy) = 1.22 R/(b²n²d)
This takes a maximum value when the Cherenkov light is just
collected by the optical system, that is when qc = d/(2L).
Hence;
ìqc(Airy)mx. = 1.22 R/(2Lqc) (1.16)
which is of order 10-· m-±.
In conclusion, the total error ìqc on the Cherenkov angle
is given by the sum in quadrature of the individual errors
discussed above;
(ìqc)² = (ìqg)²+(ìqd)²+(ìqm.)²
+(ìqe)²+(ìR/f)²+(ìqa)² (1.17)
Some other sources of error, which depend on details of the detector
used, will be discussed where appropriate below.
Having outlined the physical principles underlying a Cherenkov Ring Imaging
detector, the next chapter describes a prototype of such a device, which
was constructed and used successfully in a particle
beam of principal momentum 10 GeV/c to locate Cherenkov rings and prove
the technique as viable.
The final chapter in the first part of this thesis presents
results obtained with this device, and an analysis of the particular errors
arising in the technique.
REFERENCES
[1] O.Heaviside, see T.Kaiser, Nature 247(1974)400
[2] P.A.Cherenkov, Doklady 2(1934)451
[3] I.E.Tamm and I.M.Frank, Doklady 14(1937)107
[4] A.Butslov et al., N.I.M. 33(1962)574
[5] S.K.Poultney et al., Rev.Sci.Ins. 20(1963)267
[6] A.Iredale et al., IEEE Trans.Nucl.Sci. 13(1966)339
[7] B.Robinson, Phys.Scripta 23(1981)716
[8] R.S.Gilmore et al., N.I.M. 206(1983)189
[9] T.Ekelof et al., Phys.Scripta 23(1981)718
[10] T.Ypsilantis et al., N.I.M. 173(1980)283
[11] R.S.Gilmore et al., N.I.M. 157(1978)507
[12] M.Davenport et al., IEEE Trans.Nucl.Sci. 30(1983)35
[13] W.Farr et al., N.I.M. 154(1978)175
[14] J.V.Jelley., 'Cherenkov radiation and its applications.'
(Pergamon Press,1958)
[15] B.Leontic, CERN 14(Yellow Report,1959)
[16] E.Hecht and A.Zajak, 'Optics' (Addison-Wheley,1974)
[17] W.A.Fincham and M.H.Freeman, 'Optics' (Butterworths,1974)
Chapter II An Experimental Ring Imaging Detector
2.1 Introduction
This chapter describes the experimental details and arrangement
of a small ring imaging Cherenkov detector.
The detector as a whole was assembled and operated during the period
June to December 1982 in the C13 test beam, derived from the
CERN Proton Synchrotron (PS) machine.
High energy pions passed through a length of argon radiator.
Cherenkov light produced in the radiator
was collected by a spherical mirror and
brought to a focus within the active area of a TPC.
The component parts of the ring imaging detector had
previously been constructed and
partially tested at the Rutherford Appleton Laboratory.
2.2 The Test Beam , C13
This was a secondary beam located in the East Hall of the
PS machine and derived from the extracted
proton beam striking a secondary target.
The target itself could be changed, but was usually a 5 mm diameter
rod of aluminium of length 250mm
This target gave the highest electron flux in the beam (about 7%
of the total particles).
The normal intensity incident upon
the target was 2.10±± protons per pulse.
At 10 GeV/c there were approximately 5.10´ pions per 10±± protons
incident on the target.
The momentum of the particles could be adjusted between the
limits 4 and 20 GeV/c, by varying the strength of the field in
a momentum-selecting magnet.
The experimental area where the ring imaging detector
was set up was approximately 16 m. in length, and the final
focus of the beam could be moved along this length by
adjusting collimators and steering magnets.
In front of the area available to users were situated two scintillation
counters, two gas threshold Cherenkov counters, and one MWPC.
A second MWPC was installed at the rear of the area.
Each Cherenkov counter was 3 m. in length, could withstand
3 bar of overpressure, and
both were normally filled with helium.
2.3 Experimental layout
The apparatus used in the prototype ring imaging detector
is shown in Figure 2.1.
This consisted of two large radiator vessels
each of length 2m and of diameter 30 cm.
The first of these could
be bolted to the second to obtain a radiator medium of length 4m.
The second vessel had a side arm to which the Time Projection Chamber
(TPC) could be attached.
Within the second radiator, provision was
made for mounting a mirror whose axis could be moved to point at an
angle to the radiator's long axis.
In this way Cherenkov light from the beam particles
could be reflected along the side arm to the TPC
for detection.
Upstream of the first radiator sat four MWPCs,
two of a type which measured positions of tracks
in one dimension, and two which measured tracks orthogonally.
For convenience these were labelled either 'x-chambers'
or 'y-chambers'.
Downstream of the second radiator vessel sat a
similar group of four MWPCs.
At each end of this equipment were
positioned a group of scintillation counters, three counters upstream and two
counters downstream.
Each scintillation counter was constructed using discs of
plastic scintillator
coupled to phototubes.
One counter of the upstream group, and one of the downstream group,
used discs of diameter 1 cm.
The remaining counters contained discs of diameter 5 cm.
In this arrangement S1, S2 and S5 were of the larger diameter
and S3, S4 the smaller.
By defining a hardware trigger T5 as being the coincidence between
signals from all five counters viz.,
T5 = S1.S2.S3.S4.S5 (2.1)
one could restrict the size of the beam 'seen' by the rest of the
apparatus to a small angular width (Figure 2.2).
Conversely, by defining, for example,
the hardware trigger T4 as being;
T4 = S1.S2.S4.S5 (2.2)
the effective size of the beam so defined was larger in area than that
selected by the trigger T5 (Figure 2.3).
Given the hardware trigger from the scintillation counters, the
eight MWPCs yielded the spatial information to determine the track of the
charged particle.
The MWPCs were of two types, as already mentioned.
The 'x-chambers'
consisted of wires which ran vertically and hence provided a measurement
in x; the 'y-chambers', on the other hand, measured y.
Each wire plane was separated from the adjacent plane by
1 cm, each wire was of diameter 100 mm,
and the inter wire separation was 1 mm.
(The number of wires in each chamber varied between 24 and
64 depending on its position and type.)
With this arrangement
a charged particle entering the apparatus, and satisfying the angular
requirements of the hardware trigger, could, in principle, deposit energy
in one or more of the MWPCs.
For at least two digitisings from each end of the system of MWPCs,
and from like chambers, a determination could be made
of the particle direction in at least one of the two dimensions.
2.3(a) The Radiator Vessels and Mirror
Each radiator vessel was constructed from stainless steel
piping of large bore with flanges welded onto the pipe
at both ends for connection to other apparatus.
Each pipe was baked at 200°C before use in the experiment, to
remove occluded surface impurities.
This was done to minimise out-gassing at low gas pressures.
The downstream vessel, as well as having a side arm to which the TPC might
be attached, also had a port to which the pumping system was
bolted (Figure 2.1).
For some tests, it was desired to reduce the length of radiator
gas through which the beam particles passed,
in order to investigate the reduction in N for the detector (Equation 1.8).
This was achieved by detaching the upstream vessel (Figure 2.1).
and then sealing off the downstream vessel with the stainless steel
flange (marked F in Figure 2.1).
The mirror had a focal length of 80 cm, a diameter
of @30 cm.
and it was coated with a layer of magnesium
fluoride deposited on the reflective
surface of aluminium.
The coatings were of such a thickness that optimal reflectivity in
the wavelength region of interest was achieved.
The mirror was so positioned within the rear radiator vessel that its focal
axis bisected the angle between the side arm axis and the beam axis, i.e.
the mirror was rotated about the vertical so that its focal axis was
at an angle of approximately 15
degrees to the beam axis.
2.3(b) Radiator and Photoionising Gas Systems
The gas system may be divided into two parts, one which
regulated the flow of radiator gas to the radiator vessels, and the other
which provided the TPC with the photoionising gas mixture.
The radiator gas system is shown schematically in Figure 2.4.
To remove all traces of oxygen (which has a short absorbtion length
for photons in the wavelength region of interest), the radiator
vessels were initially evacuated to a pressure of 10-· Torr using a
rotary and a diffusion pump.
The vessels were then filled to just above atmospheric pressure with argon,
which was passed
through Messer Griesheim GMBH 'OXYSORB' filters,
and the oxygen concentration metered (Meter type BOC Z-OX).
The meter could be coupled either to the
input or return gas lines (Figure 2.4).
The purified gas flowed into the radiator vessel(s) at the
upstream end, and out at the downstream end.
With this system, the oxygen concentration in the radiator
gas flowing to
the vessels was measured to be < 1 p.p.m., and
remained at this level throughout the tests.
The substance TEA (Tri-Ethyl-Amine) was used as a photoionising gas
because of its low ionisation potential (7.52 eV) for
conversion of photons to photoelectrons.
It exists as a liquid at 4°C with a partial vapour pressure
of 20 Torr.
The quantum efficiency for conversion of photons in TEA is
shown versus photon energy in Figure 2.5, together with the transmission
of the CaF2 windows used in the detector.
An admixture of TEA and methane (CH4) was created using the
mixing system shown in Figure 2.6.
The relative amount of TEA in the final mixture fed in to the
TPC determined the conversion
length for photons, A, within the drift volume.
For 10% of the CH4 flowing through the TEA 'bubbler' (Figure 2.6),
with the TEA at a temperature of 4°C, the resulting conversion length A,
was 6 mm.
2.4 The Time Projection Chamber (TPC)
A TPC essentially comprises two regions;
the first region is a drift volume in which ions drift towards the
second region, an MWPC, in which the ions are
detected (Figure 1.3).
The information received from the associated electronics
gives the drift times of the ions in the first region,
hence the term 'time projection'.
The device thus measures the two dimensional position of any ion
in the drift region by
converting the time of drift to a linear displacement;
yin. = bdift..t (2.3)
where bdift is the drift velocity of the photoelectrons in the gas.
The TPC used in the present investigations was constructed at
the Rutherford Appleton Laboratory , and details of its
construction exist elsewhere [1].
Figure 2.7 shows both a plan view and a side elevation of the
device.
Referring to this figure,
field shaping wires of diameter 100 mm surround
a cage of dielectric material of dimensions
100x100x40 mm³.
These wires were wound as separated wire loops, each at a distance of 2
mm from the adjacent loop:
the windings ran along the interior and exterior sides of the cage.
The electric potential between each
successive loop was constant and graded by
a resistor chain.
Two circular holes in opposite sides of the cage contained windows
through which the Cherenkov photons passed to be converted in the
photoionising gas within the chamber.
One of these windows was made from calcium fluoride, the other
from fused silica (quartz).
Both had a thickness of 3 mm.
The drift field wires lay flat against, and on both sides of,
each window.
A variable resistor was connected between the field shaping wire
nearest the MWPC plane and earth, in order that the drift field
could be varied to optimise conditions.
The furthermost field shaping wire was held at a high negative
potential (usually 10 KV).
Thus any photoelectrons (or other negatively charged particles)
within the conversion gap (the space between the two windows)
were constrained to drift towards the MWPC plane.
This MWPC consisted of 48 wires each of 20 mm
diameter, and spaced by 2 mm.
These wires lay between two cathode wire planes at earth potential and
separated from each other by 10 mm.
Each of these wires was coupled to a 0.2 mA threshold amplifier
attached directly to the exterior frame of the TPC.
The drift region and MWPC were housed in a fibre-glass box
through which the photoionising gas flowed.
A second calcium fluoride window pressed against the one fitted
in the drift cage (with the cage orientated as shown) and existed
to isolate the photoionising gas from the exterior.
In the case where the TPC was clamped to a radiator vessel under
vacuum, the stainless-steel support seen in Figure 2.7 ensured
that this second calcium fluoride window did not break.
The support was held at earth potential and consequently some small distortion
of the electric field at the entrance windows occured.
The loss of collection efficiency due to this effect was measured to be
@10%.
2.5 On-Line Data Acquisition
2.5(a) Trigger Logic
Figure 2.8 shows a logic diagram of the electronic circuitry used
in the acquisition of the data.
Two types of experimental trigger were implemented, the first being
a 'real' event trigger derived from the detection of a charged
particle in the detector, and the second being a 'random' event trigger
derived from a pulse generator.
The 'random' trigger generated background events for analysis, and
for comparison with real events.
Signals from the five scintillation counters Si were
fed to AND gates, where a coincidence was demanded between some
combination to define the trigger, T (see above).
The desired coincidence was scaled, and fed to an OR gate together
with the random trigger (Trn.).
The output signal (an 'event trigger', EV,)
from this OR gate was fanned-out for use by a
variety of elements;
EV = T4(T5).OR.Trn. (2.4)
The beam-line MWPCs were strobed in on reception of EV, and the
detected signals fed to CAMAC.
The Time-to-Digital-Converters (TDCs) for the
TPC were started by a delayed
EV signal.
Each TDC channel (1 - 48) was
then stopped when a pulse was detected from
the appropriate wire.
Whilst the signals were being accumulated by CAMAC the reception of
other events by the acquisition system was inhibited.
As soon as the event had been read in, this veto was removed, so that
the next event could be received.
A start-of-burst (SOB) signal was fed directly to the on-line
computer together with an end-of-burst (EOB) signal.
2.5(b) Event Description
Event records as provided by the on-line software
were characterised by one or more
digitisings in the beam-line MWPCs, together with information
from the TDCs associated with the TPC.
In addition to this information, several scalers were
incremented at each event, and added to the data record.
The type of event ('real' or 'random') could be determined
by examining two such TDC values on the event record.
Each of the 48 TDC channels associated with the TPC
was present on the record as an integer number running from
0 to 1024.
The numbers were proportional to the time which had elapsed
since the common start signal from EV via CAMAC,
and as such gave a description of the drift time spectrum
over all wires.
There was no capability for storing more than one digitising
on any given wire per event .
Each TDC channel thus contained either an in-range time
(0 - 1023) or a 'run-out' (1024) corresponding to no hit on
the wire.
Calibration of the TDCs associatd with the TPC was accomplished in the
following way (Figure 2.9).
A pulse-train of frequency 100 MHz
was produced using a gate-generator.
One of the pulses from this train was used to form a coincidence
with a pseudo-random 1 KHz signal from a pulse generator.
The coincidence was fanned out and used as a common TDC start signal.
Another pulse from the 1 MHz train was then fanned out and used as
a common TDC stop signal.
In this way the difference between start and stop signals was an
integral number of 10 ns time bites.
Thus in each of the 48 TDC channels examined off-line there was a series
of spikes, separated in TDC channels by the equivalent of 10 ns.
A fit in each TDC channel to the inter-spike separation yielded the
calibration constants ìti (nanoseconds per TDC channel), and
to (the dead time in nanoseconds for channel i).
Thus for a given digitising Ni read by CAMAC at wire
number i, the equivalent time which had elapsed since the common
start signal was given by;
t = Ni.ìti + to (2.5)
From a survey of the beam-line MWPC positions, and a
knowledge of the wire configuration in each MWPC, a
determination of the particle position could be made at
each MWPC plane, given a digitising in the corresponding ordinate.
Multiple hits (>1) in each MWPC were discriminated against
in the on-line and off-line software.
Straight line fits to digitised information of the single
hit variety enabled a rather accurate determination of the
particle trajectory through the detector to be made.
At normal intensities about 2000 particles per
burst were read by CAMAC with T defined as
in Equation 2.2.
With T defined as in Equation 2.1, about
200 particles per burst were recorded.
2.5(c) On-Line Software
The purpose of the on-line software was to provide enough
information during the running periods to enable qualitative
decisions to be made on the performance of the detector.
A determination of the efficiency of the detector could be made
but the statistical accuracy was poor.
Depending on the section of the detector being evaluated,
such as the TPC, the beam-line MWPCs or the trigger,
several different analysis programs could be invoked to
provide the relevant
distributions of interest and corresponding statistics.
An important feature of the capability of the
computer (Digital Equipment Corp. type PDP-11/34),
on which these programs were stored, was
the possibility of sharing the data between several programs
all accumulating data simultaneously.
The events were 'shared out' depending on the specific priority
of each program,
the higher the priority of the program,
the more events per unit time being passed
for analysis to that program.
In addition to the programs used for on-line evaluation of the
detector, it was possible to send experimental data via a
cable link, to one of the CERN mainframe computers.
Here the data were initially stored on disc, then copied to
tape (6250 b.p.i.) by an automatic process.
In this way more sophisticated software could be used to analyse
the experimental data.
Thus the on-line software, coupled with the tape-writing
facility, enabled a rather complete check to be made on the
operation of the detector, and on the state of the particle beam itself.
REFERENCES
[1] Omega Photon Collaboration, CERN SPSC/P140 Add.3(1982)
Chapter III An Analysis of the Experimental Data
3.1 Introduction
In this chapter the analysis of the data obtained using the
detector described in Chapter 2 is presented.
Topics of particular concern will be the efficiency of the device for
the detection of the ring images, and the accuracy with which the
photoelectrons were detected spatially.
The device was used in two distinct modes.
First, the TPC was positioned such that the particle beam
directly passed through the
drift region, and tests were carried out to determine the charge collection
efficiency of the chamber, the drift velocity of the ions in the
drift region for different gas mixtures, and the spatial accuracy in
the localisation of ionisation due to beam particles in this region.
Secondly, with the TPC positioned on the side arm of the downstream radiator
vessel (Figure 2.1), Cherenkov ring images were observed for various
concentrations of the photoionising gas (TEA), and for
various particle momenta.
Measurements were made of the observed ring images in terms of
their radius and sharpness in definition, as a function of these variables.
The results of the tests enabled a calculation to be made for
Np (Equation 1.8), together with an assessment of the effectiveness
of the device in distinguishing between two types of particle
present in the beam.
3.2 Straight Ionisation Tracks in the TPC
The apparatus was initially set up with the TPC positioned at A
in Figure 2.1.
A traversing table allowed the TPC to be moved a known distance
either in the up-down or left-right directions by remote control.
The scintillators S1 -S5 were timed in, together with the
eight beam line MWPCs.
Adjustment of the time delay in the TDC signals
associated with the TPC ensured that
the electronic acquisition system strobed all 48 wires after the
correct time had elapsed since reception of the event signal EV (Section 2.5a).
In this arrangement, the beam particles travelled through the
TPC drift region parallel to the plane containing the TPC sense wires,
and at right-angles to the wires themselves (Figure 2.7).
Figure 3.1 shows the wake of ionisation left by a beam particle
which traversed the TPC drift region.
After calibration corrections had been made (Equation 2.5), straight
line fits to such events were made to determine the spatial position
of each track in the following way.
First, events with signals from less than 5 of the 48 MWPC wires were
rejected.
The digitisings from the remaining good events were fitted to straight
lines.
In the fitting procedure, if the sum of the
residuals of each track point to the
fitted track point was too large, then the track point with the
largest residual was removed, and the fit repeated.
This procedure was used a maximum of ten times, or until the number
of track points was reduced to five.
Finally, the errors on the fitted tracks were used to determine the
accuracy to which their positions could be located within the TPC.
Figure 3.2 shows a plot of the RMS error on the fitted times
to all wires, after the fitting procedure.
The peak at @7 ns corresponds to a time resolution
of an ionisation point within the drift region of the TPC.
The rise seen up to the cut-off point at @25 ns is due
to extra tracks within the TPC which did not satisfy the trigger
requirements.
To interpret this time resolution in terms of a spatial resolution required
a knowledge of the drift velocity of ionisation in the
drift volume.
Measurements of the beam particle directions from the beam line
MWPCs were used to determine the gradients of these directions in
the y plane.
The gradients, together with the measured position of the TPC, were used to
derive the positions of intersection of the beam particles with the TPC.
Each derived position was plotted against the fitted drift times for
the resulting ionisation in the TPC.
Figure 3.3 shows such a plot, where the drift field was 0.7 kV/cm.
The inverse of the gradient of the
straight line in Figure 3.3 is the drift velocity
of ionisation in the chosen gas mixture, at the chosen drift field.
By measuring the gradients of the lines in such plots, the drift
velocity was determined for various values of the drift field Ed.
Figure 3.4 shows the results of this analysis, and indicates a
spatial error of ±0.6 mm at a drift velocity of 90 mm/ms.
3.3 Efficiency Scan of the Drift Gap
To measure the charge collection efficiency of the TPC as a function
of the point of ionisation in the drift region, the TPC was
positioned in the beam so that the beam particles were
perpendicular to the MWPC sense wires, but did not pass through either
entrance window (see Figure 3.5).
By moving the TPC in the left-right or up-down directions, and
measuring the charge collected on a particular wire (chosen
centrally in the chamber), the efficiency scan was performed.
The wire numbered 25 had been previously measured to
have an efficiency of 75%, and was
arbitrarily selected to be the test wire.
The TPC was initially positioned so that the centre of the beam was
20 mm nearer the MWPC wire plane than the centre of the drift
region (see Figure 3.5, position marked 'A').
The TPC was then moved from a position where the beam centre was
just below the CaF2 windows (see Figure 2.7) to a position where it
was just above the quartz window.
This move was completed in several steps, and the charge collected
on wire #25 measured at each step.
Subsequently, the TPC was moved so that the beam centre was
positioned at the centre-line of the drift volume
(Figure 3.5, position marked 'B'), and the scan
performed again.
The results are shown in Figure 3.6, where the entrance window
regions are shown shaded.
The chamber is seen to be more efficient for ionisation points closer
to the MWPC wires than to the centre of the TPC.
3.4 Cherenkov Rings in the TPC
To operate the detector in its ring-imaging mode, the
TPC was attached to the side-arm of radiator vessel 2, such that
the area of drift volume just behind the entrance windows was
in the focal plane of the spherical mirror (Figure 2.1).
Some distortion of the reconstructed rings was expected with this
configuration, and a Monte Carlo simulation of this effect [1]
gave an indication of its extent.
Cherenkov photons from those beam particles with velocities above
the threshold, were collected and reflected by the mirror to the
TPC.
Within the TPC, the photons converted in the TEA/CH4 mixture
at some point behind the entrance windows.
The probability of conversion was governed by the mean free path
of the photons, A, in the mixture, and this was short (<6 mm) compared with the length of the conversion space (@32 mm).
After conversion, the resulting photoelectrons drifted through the
gas mixture in a field determined by the voltage applied to wire
#50 of the drift field cage.
Upon reaching the edge of the drift region, the photoelectrons
were accelerated over the remaining centimetre to the MWPC wire
plane by the potential difference between wire #50 and the
cathode plane of the MWPC.
(The anode wires in the MWPC were at earth potential).
This transfer of photoelectrons between the drift region and the
MWPC region could be inhibited by applying negative bias across the
gap.
In practice, of course, the optimum transfer efficiency was required.
This was achieved by measuring the number of photoelectrons collected
at the MWPC as a function of both the drift field, Ed, and of the
transfer gap bias field, Eb.
Figure 3.7 shows a plot of the mean number of photoelectrons collected,
np., versus Ed, for a setting of Eb= 30 Volts/mm.
This plot reveals a clear plateau for values of Ed above 55 Volts/mm,
and in accordance Ed was fixed at this value while other effects were
investigated.
The optimum value of Eb was arrived at by a similar procedure.
The photoelectron collection efficiency having been optimised,
the properties of the observed ring-images were then examined.
Figure 3.8 shows a plot of measured time versus wire number for several
thousand events in the TPC, where the beam particle momentum was
10 GeV/c.
At this momentum, the majority (@95%) of the beam particles were pions,
the remaining few percent being electrons
(above Cherenkov velocity threshold), muons
(above threshold) and kaons (below threshold).
The observed width of the ring image is large, partly due to the divergence of
the beam; the particle directions were not coincident.
Other effects which increased the observed ring width are discussed
below.
An inactive wire is seen at position 36; no times were recorded at this
value of x.
To correct for the effect of the beam divergence, the gradient of the
fitted beam track, dx/dz, (from the beam line MWPC information) was plotted
versus the time digitisings on the TPC wires.
Figure 3.9 shows two such plots (for wires #21 and #28), where the two
regions of high density in each plot
correspond to digitisings from opposite sides of the Cherenkov ring.
The straight lines shown, demonstrate the variation of the position of the
ring image as a function of the beam divergence.
Vertical lines, in these plots, would indicate co-incident beam particles
in the apparatus from event to event.
To impose zero divergence in the software, the time digitisings on all the TPC
wires were corrected using the slope of the best lines through each of
the two regions.
Figure 3.10 thus shows the corrected time spectra on wires #28 and #21
for beam momenta of 4 and 7 GeV/c.
Although the statistics are poor at 4 GeV/c, the two spikes clearly
indicate the presence of a ring.
At this momentum, (see Table 3.1), only electrons and muons are above
threshold, so this is likely to be a b=1 electron ring.
At 7 GeV/c the ring projection on both wires is clearly seen, with
improved statistics.
At this momentum, electrons, muons and pions are all above threshold
(Table 3.1), and the beam particles were predominantly pions.
TABLE 3.1 : Radii of Ring Images at the Selected Beam Momenta
P(GeV/c) R(e-) R(m-) R(p-) R(K-) mm.
&
nbsp;
4 22.2 6.90 below below
7 22.2 18.7 15.5 below
10 22.2 20.6 19.2 below
14 22.2 21.4 20.7 below
16 22.2 21.6 21.1 below
18 22.2 21.7 21.3 below
This table assumes a refractive index for argon of n=1.000368
at the peak of the TEA quantum efficiency curve, and at a
temperature of 22°C.
Indicated in Figure 3.10 are the two smaller spikes corresponding to the
electron ring at 7 GeV/c (which has the same radius as that at 4 GeV/c).
With higher electron statistics, these would be better defined, but
notwithstanding, demonstrate the capability of the device for
discriminating between electrons and pions at this momentum.
To observe the behaviour of the device as a function of particle
momentum, several thousand events were recorded at beam momenta of
4,7,10,14,16 and 18 GeV/c.
In Figure 3.11 are plotted the accumulated rings at each
momentum setting.
At 4 GeV/c the statistics are poor; only electrons and muons
produce light in the radiator vessel.
The shadow of the 'Mercedes Benz' support (see Section 2.4)
is seen as a depletion of events at three points around the ring,
accounting for a loss of @10% of the incident Cherenkov photons.
Here again, wire #36 was inactive, and this is seen as an
absence of events at x=7.0 cm.
At 7 GeV/c, the electron ring is discernible as a faint background
surrounding the more intense pion ring.
At 10 GeV/c and above, the electron rings are absorbed into the
pion rings, which gradually have increased in
diameter with increasing momentum.
(The apparent variation in the observed widths of the accumulated images is
accounted for by different total numbers of particles for which data were
accumulated at the various momenta.)
To investigate the ring sizes at these momenta settings, single
events with three or more observed photoelectrons were fitted
to circles (the assumption being that the reconstructed spatial
positions of the photons lay on a circle), and the
computed value of the radius plotted.
Figure 3.12 shows the results, which are tabulated in Table 3.2, to
be compared with Table 3.1.
TABLE 3.2 : Fitted Radii of Ring Images at the Selected
Beam Momenta
P(GeV/c) R(e-) R(m-) R(p-) R(K-) mm.
;
4 19.0 below
7 19.0 14.0
10 19.0 17.0
14 19.0 18.0
16 19.0 18.0
18 19.0 &nb