Abstract 1

Abstract  1
Proton, electron, and heavy ion collisions have produced a wealth of
information about subatomic particles. Historically, high energy physics (HEP)
has pushed the energy frontier. Limitations of the proton and electron beams
may make the muon beam a good candidate for the future of HEP. The large
hurdle for the muon beam is cooling. Conventional cooling methods are too
slow for the muon beam due to its short lifetime, so new methods must be
used. Ionization and frictional cooling are the alternatives because they have
the potential to cool the beam in adequate time. Frictional cooling, the
process under study at Nevis, will be tested initially on a proton beam.
Particle Colliders
Electron-positron (lepton) collisions are much cleaner than Proton-antiproton (hadron) collisions. The highest energy lepton only collision seen so
far was at LEP in 2000 where a 104.5 GeV e+ and e- beam was collided,
resulting in a 209 GeV center-of-mass energy collision. 1 The quest for higher
center-of-mass energy electron collisions continues, but is inherently
hindered in circular accelerators by the effects of synchrotron radiation.
Synchrotron radiation is the release of energy by charged particles on an
orbital or curved path, a path induced in a circular accelerator by the
magnetic field. A charged particle’s radiation due to transverse acceleration
scales with the inverse of the mass to the fourth power.
 2c 
 1  E 
P =  e 2 β 4  2  2 
 3
 r  mc 
Equation for the radiated power of a charged particle in a relativistic, accelerated orbit.
The electron beam requires a great deal more power to sustain the beam’s
energy than the heavier proton. This is because the electron beam loses
energy at a rate 20004 times more quickly than the proton. Therefore, the
next energy increase for electron collisions will most likely come from the
NLC, a 20 mile long linear accelerator that’s in its conceptual phase. 2 Linear
accelerators eliminate the synchrotron radiation issue, but they are limited in
the amount of linear gradient they can achieve. Technological limits do not
limit the beam energy; financial limits impose space and accelerating
chamber number restrictions.
For the proton beam, almost 2000 times more massive than the
electron beam, the effects of synchrotron radiation at high energies are
negligible. Proton’s can therefore take advantage of the circular accelerator
to higher energies and attain extremely high energy collisions. CERN’s LHC
hopes to reach 7 TeV proton beams by 2005, with a 14 TeV center-of-mass
energy collision. 3 The energies attainable for a proton beam in a circular
accelerator are in fact so high that there is a struggle to produce sufficiently
powerful magnets. 4 However, because a proton is not a point particle, not all
the energy goes into the hard scatter. Only one tenth to one seventh of the
energy in a hadron beam is used in the desirable parton-parton collision. The
valence quarks only carry a fraction of the momentum of the hadron beam,
yielding 1.5 to 2.3 TeV center-of-mass energies. 5 Another drawback of the
hadron collisions are the less clean environments than those of the lepton
collisions. This is due to the excess background from the breakup of
spectator particles.
There are two problems and two solutions, but neither is paired to
annihilate both problems in one particle. The best solution would be a particle
that was more massive than the electron, so it would be negligibly affected
by synchrotron radiation, but remain a point particle.
The muon is 200 times more massive than the electron and is a point
particle, thus yielding cleaner collisions than protons with less energy loss
due to synchrotron radiation than electrons when accelerated. With a muon
collider we could push the energy frontier, while using less power and space
than electron and proton colliders require. The muon collider is the ideal
particle for Higgs studies, as the probability for Higgs production goes with
the mass of the lepton squared. Another great benefit is the production of
neutrinos as a by-product of the muon beam, providing a convenient source
for further neutrino study. However, there are a number of problems facing
the use of muons that must be addressed. Where will the muons come from?
How will they be focused into a beam? Perhaps most challenging: how can
muons be used if their mean life is 2.2 microseconds before decaying into
Muons are like heavy electrons because they share many
characteristics with electrons, such as spin, charge, and behavior during
interactions, but they are 200 times the mass of the electron. High energy
cosmic rays are mostly composed of protons that produce high-energy pions
when they collide with gas in the atmosphere. These high-energy pions in
turn decay into high-energy muons, antimuons, and neutrinos.6 The method
to get muons for collisions is modeled after this phenomenon. While we can’t
use muons that decayed from cosmic rays, we can make pion beams from
impinging a proton beam on a target, and those pion beams will then decay
into muons. However, the resultant beam occupies a large phase space that
is too large for collision in an accelerator by a factor of 106. This phase
volume must be reduced for a muon collider to be feasible. 7
Phase space is the size of the beam not only in physical space, but
also in momentum space. Phase space is six-dimensional, determining the
location and momentum of particles in four-dimensional space -time.8
e6D = s (x)s (Px)s (y)s (Py)s (z)s (Pz)
Equation for Phase Space
A reduction of the phase volume is called cooling a beam. This entails
the reduction of transverse-momentum and a decrease in the energy spread.
Historically, beams have utilized stochastic cooling or electron cooling. The
muon lifetime is 2 microseconds, so the cooling must take place within that
amount of time. Stochastic and electron cooling are too slow to work on a
muon beam.9 A new method of cooling is called for to chill the muons, and
two proposals have been put forward: ionization and frictional cooling.
Ionization cooling entails passing the beam through an absorber thus
reducing the transverse - and longitudinal-momentum. A muon beam is a
good candidate for this method because of its low interaction with matter.
The cooling cavities consist of solenoids and focus the beam, Hydrogen
absorbers to reduce transverse energy spread, and RF cavities to reaccelerate the particle.10 The longitudinal-momentum would be restored in
this accelerating region. This scheme requires beam energies of hundreds of
MeV. The energy rate loss at these high levels is not ideal because higher
energy particles lose energy more quickly than lower energy particles (see
energy rate loss diagram below).
http://prst-ab.aps.org/pdf/PRSTAB/v2/i8/e081001 p.2
Energy rate loss diagram
So far, reduction factors of only 100 have been achieved via ionization
cooling. This is far from the factor of 106 required to collide the muon beam.
Frictional cooling is another alternative. It is done below the ionization
peak and takes advantage of the high energy loss rate at those low kinetic
energies. In this region an E field is applied, so when in combination with a B
field, creates an equilibrium situation whereby the energy spread narrows to
almost zero. This narrow spread is independent of how wide the energy
spread was in its initial condition.
Muons enter the cooling cell (diagram below). The B field confines the
particles to process around the magnetic field lines. The gas simply slows the
particles down, reducing the impact that the B field can have on them,
allowing them to exit the chamber once the transverse momentum is
Frictional Cooling System
This system is successful because it relies on the Lorentz force
F = q( E + v × B)
Lorentz force equation
When ? goes to zero because of energy reducing inelastic collisions with the
gas, the E field will be the dominant contributor to force, and will pull the
muon out of the chamber. When the E field moves the muon, this will create
a velocity and a force from the B field. The v will then be subdued via
inelastic collisions, thus enabling the E field to be the dominant contributor to
the force again. The muon will have achieved an equilibrium condition with a
narrow energy spread when it exits the system, regardless of its initial
condition, and the phase space will be reduced. 11
Summer Activities
At NEVIS this summer, the frictional cooling of a muon beam was our
primary interest. This is a preliminary stage, so various triggering devices
and detectors that will be used to verify if the beam has been cooled were
investigated. The plan is to test the frictional cooling principle on a proton
beam. Our triggering devices couldn’t be tested with a proton beam readily,
so we used alpha and beta sources.
Radioactive Sources
Radionuclides are unstable nuclides that are radioactive. The instability
of a nuclide depends on the ratio between number of protons and neutrons.
Radionuclides emit three kinds of radiation: alpha, beta, and gamma. 12 A
beta source has excess neutrons, and ejects an electron from inside the
nucleus when a neutron decays into a proton. Our beta source is Strontium90 with a 10 µC strength (a micro-curie is roughly 37,000 decays per
second) and a mean energy of 200 keV and a maximum of 595 keV. An
alpha source ejects large subatomic alpha particles, consisting of two protons
and two neutrons. Our alpha source is Americium-241 with a 5 µC strength
and a decay energy of 5.6 MeV. 13 The alpha has the benefit of higher decay
energy than the beta, but has a smaller range in material. I n addition to its
lower rate, the alpha does not travel great distances. This is similar to the
behavior of the proton, so the alpha best emulates the particle we will test
our detectors on.
The detectors we investigated were microchannel plates (MCP), a
silicon detector, and scintillators attached to photomultiplier tubes (PMT).
The goal was to set-up a double-trigger system in order to measure a
particles time-of-flight. The object was to detect non-random coincidence of
particles triggering on two detectors that were aligned along the particle
Scintillators give off light when charged particles pass through them.
When attached to a PMT (PMTs convert photons into an electrical signal and
then amplifies the signals) the generated signal can be triggered on to
produce a rate. Scintillators are generally made of plastic with small
elements that excite easily and decay, quickly in the release of photons. 14 We
used a Bicron® organic BCF-12 blue emitting scintillator with a polystyrenebased core and a layer of PolyMethylMethaAcrylate cladding. 15 These
scintillators are manufactured expressly for alpha, beta, and charged particle
detection, which serve our purposes ideally.
Schematic of scintillator from Bicron®
The low stopping energy of the alpha compelled us to reduce the
thickness of the scintillator. This was to ensure that the particle would trigger
on the scintillator and retain enough energy to arrive at the second detector
and trigger there as well. The alpha is similar in stopping energy to the
proton, so this precaution was essential for when these triggers were to be
used on the proton beam. The machine shop removed the PMMA cladding
from the scintillator and drilled a hole that left a depth of only 200 microns.
The hole had a 3mm diameter and the scintillator had a 5mm square width.
The removal of the cladding most likely increased the angle of total internal
reflection, thus making it easier for photons to refract and escape without
being measured by the PMT.
Diagram of the drilled scintillator.
A collimator was used to direct the radiation towards the hole to
reduce background caused by trigger from non-hole scintillation.
I wrote a program that projected what the expected trigger rate would
be based on the collimator height, radius, and distance from the scintillator.
This program was adapted to show how this rate changed when the source
was scanned across the scintillator. The diagram below illustrates that rate
change as a function of position. This helped determine the ideal dimensions
for the collimator.
Scanning source across scintillator.
x-axis: position (cm) y-axis: rate (Hz)
Beta source with .25 cm diameter collimator
Source 1.45 cm from target, collimator 1.3 cm tall
Despite great potential, the scintillating stick did not prove to be a
useful triggering device. This was because of a high attenuation length. We
found that when a source was scanned at the location of our shallow section
on the stick, it was so great a distance from the PMT that the rate did not
rise above background. Although the stick was shortened, increasing the rate
at the shallow point, the rate changed dramatically with very small changes
in distance from the PMT, smaller even than the width of the collimator or
the hole’s diameter.
To Tip
Rate falloff diagram
Another problem with the PMT scintillator set-up was an increase in
rate with time when all variables were held constant. It was discovered that
there were two culprits for this. First, there was a faulty power supply that
increased its output voltage with time, thus increasing the voltage applied to
the PMT with time. The second culprit was the heating up of the PMT in
vacuum. The vacuum was essential in order to increase the distance the
alpha could travel. The solution for this was to place the PMT in a heat sink.
Our heat sink was a large piece of aluminum with a great deal of surface area
that was fit around the PMT like a glove, and helped dissipate the heat with
its large surface area. A new power supply and the heat sink eliminated the
rate increase with time.
All I did was
change with time
after the red line,
why did my rate
Rate increase diagram
Another triggering device that was used to detect particles in the
double trigger system was a microchannel plate (MCP). An MCP is like many
small PMTs on a grid with small distances between them. The walls of the
MCP tubes are clad with lead oxide. Alphas and protons are ideal for MCPs
because they do not penetrate deeply before triggering the release of
secondary electrons from the clad tubes. We yield a full gain of the MCP with
these particles because of their short penetration distance. Electrons can
penetrate the plates entirely, never triggering a cascade of secondary
electrons, reducing the signal. Since the tubes are so small and segregated
from one another, the MCP can project the position of the particles entry to
the plate. For our purposes, we were only concerned with the rate, so the
location of the signal on the plate was unimportant. Electrons, ionized
particles, and high energy photons (X-rays and UV) can be detected by
MCPs. 16 These particles enter one of the channels, and are accelerated
through the channel by a bias voltage that is applied across the plate (see
following diagram). The amplification occurs when the particles hit the walls
of the channel during their journey.
The walls emit electrons when hit. The precise amplitude gain varies based
on the bias voltage and the plate. Our plate had a gain of 104 to 105 with a
bias voltage of 1000V. However, our set-up had two plates aligned in a
chevron pattern and doubled to 2000V across both plates, thus making the
total gain 108 to 1010. With these amplifications, our signal was very easy to
observe when present. However, the plates are very delicate. The surface
can be easily cracked and tarnished, and therefore cause shorts on the plate.
The final detector that we investigated was a Silicon detector. They are
not commonly produced as thinly as we had them made, partially because it
is very difficult to guarantee uniformity in thickness across the surface. 17 The
non-uniformity on the order of thickness we obtained (15 µm) is ±0.5 µm.
That is a 3% variation in energy depletion of the particle being detected.
Silicon detectors work when a particle interacts with the semiconducting silicon as it passes through the detector. The particle interacts
with valence and conduction band electrons. 18 The excited electrons
accumulate charge, and induce a current. Based on an alteration of the
current, the detector notes the presence or absence of a particle. The
magnitude of the current change can indicate the energy of the particle.
The silicon detector and the MCP are the best detectors for our
purposes. However, we have yet to test them together. These detectors will
enable us to determine time of flight measurements for a beam. Once we
have the time of flight, and knowing the length of the drift region, we will be
able to determine the velocity, the momentum, the energy and, should we
include a material in the particles path, the energy loss as well. This will
enable us to verify if frictional cooling is effective, initially with a proton beam
at RARAF, eventually with a muon beam.
Window on Gas Chamber
Low energy protons do not penetrate very deeply, so we must take
into consideration the boundaries of the gas cell that will be cooling the
beam. If the end walls, or windows, are too thick, the proton beam will lose a
great deal of energy during its flight and perhaps not make it to the final
detector. Extremely thin windows were selected to be on the ends of the
chamber. However, despite the low impact these windows have on the
proton beam energy, they make it difficult to keep an amount of helium in
the chamber, and a vacuum around the chamber, without a leak. A leak
would be further catastrophic because it would be difficult to remove all the
helium from the vacuum chamber, and it would be a long time before a low
pressure vacuum could be achieved. The situation is further complicated by
the fact that it is very difficult to mount the windows (As they are small in
diameter as well as depth) on the gas chamber. Our current method is to
epoxy the window to washers that will be epoxied to the gas chamber. This
method has not yet been tested.
Energy Loss Program
I edited a program that had been developed to indicate ideal energies
and gas chamber densities for the frictional cooling system. I altered it to
indicate what the anticipated kinetic energy would be at various positions
within the system with varieties of the E field, B field, gas chamber, and
window set-up.
It is expected that frictional cooling will be successful. The real
mystery that lies ahead for the muon collider is going to come when we look
for the capture cross section of the muon. It is not known at the low energies
where we plan to operate. If it is too high, we may lose too much of our
beam in the process of cooling, and the colliding of muon beams would be
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