Muon Drift Tube GasesMuon Drift Tube GasesChris Clark Chris Clark Advisors: Rachel Avramidou, Rob VeenhofAdvisors: Rachel Avramidou, Rob Veenhof

Muon Drift TubesMuon Drift Tubes

Incoming muons Incoming muons ionize gasionize gas moleculesmolecules

Electrons Electrons produced in produced in ionizations are ionizations are acceleratedaccelerated toward the anode toward the anode wire by the wire by the electric fieldelectric field

Electron AvalancheElectron Avalanche

Fast electrons can Fast electrons can cause cause additional additional ionizationsionizations near wire near wire

Exponential growthExponential growth of electronsof electrons

Repulsive force of Repulsive force of many electrons near many electrons near the wire causes the wire causes displacement of displacement of electronselectrons in the wire in the wire

GARFIELDGARFIELD

Simulates passage Simulates passage of a muon through a of a muon through a drift tube and drift tube and generates the generates the resulting resulting drift-linesdrift-lines of electrons and ionsof electrons and ions

Produces a Produces a distribution of drift distribution of drift timestimes (the time it (the time it takes for an electron takes for an electron to reach the wire*)to reach the wire*)

*Actually it takes about 20 electrons due to the discriminator

Simulation ResultsSimulation Results

We recorded the We recorded the maximum timemaximum time from a from a drift time distribution for electrons that drift time distribution for electrons that started just inside the tube wallstarted just inside the tube wall

We did this many times after tweaking the We did this many times after tweaking the temperature, pressure, or COtemperature, pressure, or CO22 fraction of fraction of the gas and found the gas and found linear fitslinear fits for the for the drift drift timestimes..

ConclusionsConclusions

The slopes of the linear fits were The slopes of the linear fits were farther from the experimental farther from the experimental valuesvalues than previous simulations than previous simulations

We ran all the simulations again We ran all the simulations again with with 10x higher statistics10x higher statistics and the and the slopes were only slightly affectedslopes were only slightly affected

Possibly this means that the Possibly this means that the experiments are experiments are not controlled not controlled tightly enoughtightly enough

Penning IonizationPenning Ionization Penning Ionization Penning Ionization

occurs when an occurs when an excited moleculeexcited molecule ionizesionizes another another molecule by molecule by collisioncollision

In this section I will In this section I will explain the ideas explain the ideas behind a behind a simple simple equationequation that I that I developed to developed to predict predict the probabilitythe probability of of Penning ionizationPenning ionization

DefinitionDefinition

OnlyOnly some excited statessome excited states actually have actually have enough potential energy to ionize another enough potential energy to ionize another gas speciesgas species

We define the probability of Penning We define the probability of Penning ionization to be the ionization to be the fraction of the fraction of the energyenergy in in the molecules in these excited states that the molecules in these excited states that will will eventuallyeventually end up causing end up causing ionization by ionization by the Penning processthe Penning process

We use the terms ‘energy’ and ‘eventually’ We use the terms ‘energy’ and ‘eventually’ so that the so that the energy can be transferredenergy can be transferred to to another molecule before Penning ionizationanother molecule before Penning ionization

Sample GasesSample Gases

We used the gas that will be found We used the gas that will be found in the in the ATLASATLAS muon drift tubes: muon drift tubes: 93% Argon, 7% CO 93% Argon, 7% CO22

Another gas with good information Another gas with good information already available is the gas in already available is the gas in ALICEALICE: 90% Neon, 10% CO: 90% Neon, 10% CO22

For both of these gases there is For both of these gases there is only one typeonly one type of Penning ionization: of Penning ionization: Ar*+CO Ar*+CO22 and Ne*+CO and Ne*+CO22

Energy DestinationsEnergy Destinations

A good way to understand the A good way to understand the problem is to look at where the problem is to look at where the energy can energy can end up in a stable formend up in a stable form (excited states will deexcite)(excited states will deexcite)

Conceivable optionsConceivable options are: are: Ionization of COIonization of CO22

Kinetic EnergyKinetic Energy Escape from the systemEscape from the system

Photon DeexcitationPhoton Deexcitation

Natural Radiative LifetimeNatural Radiative Lifetime of Argon of Argon in the D-Level excited state is in the D-Level excited state is probably around probably around 3.7 ns3.7 ns (given by inverse of Transition (given by inverse of Transition Probability or Einstein A Coefficient)Probability or Einstein A Coefficient)

The The mean free timemean free time of an Argon of an Argon atom in this gas is about atom in this gas is about 1.5 ns1.5 ns

Somewhere around Somewhere around 1/31/3 of excited of excited Argon atoms will deexcite before Argon atoms will deexcite before undergoing any collisionsundergoing any collisions

Photon DeexcitationPhoton Deexcitation A photon sees roughly the A photon sees roughly the same cross same cross

sectionssections as an excited Argon atom as an excited Argon atom because the cross sections are because the cross sections are primarily determined by the targetprimarily determined by the target

The photons The photons won’t escape the systemwon’t escape the system because of their short mean free because of their short mean free paths and because the walls of the paths and because the walls of the tube are Aluminum, which is very tube are Aluminum, which is very reflectivereflective

Can Can pretendpretend that photon deexcitation that photon deexcitation never happensnever happens and it won’t affect the and it won’t affect the Penning ionization probabilityPenning ionization probability

ConcernsConcerns

Kinetic-Assisted IonizationKinetic-Assisted Ionization – If a – If a lower energy excited state had lower energy excited state had enough kinetic energyenough kinetic energy it could still it could still cause ionization, but this will cause ionization, but this will never never happenhappen at our temperatures at our temperatures

Associative IonizationAssociative Ionization – If – If two two excited moleculesexcited molecules collide then their collide then their combined excitation energy can combined excitation energy can cause an ionization, but this type of cause an ionization, but this type of collision seems collision seems less probableless probable

Collisions of the 2Collisions of the 2ndnd Kind Kind Inelastic collisions of the second kind are Inelastic collisions of the second kind are

collisions in which the collisions in which the excitation energyexcitation energy of of one molecule is released and ends up in one molecule is released and ends up in the the kinetic energykinetic energy of the other molecule of the other molecule

After such a collision ionization will After such a collision ionization will probably not happen because it is probably not happen because it is thermodynamically unfavoredthermodynamically unfavored

Together with inelastic collisions of the Together with inelastic collisions of the first kind, these collisions are responsible first kind, these collisions are responsible for maintaining the relation specified by for maintaining the relation specified by the the Boltzmann factorBoltzmann factor

SummarySummary

The energy from the D-Level excited The energy from the D-Level excited states can only end up as states can only end up as Penning Penning ionization or kinetic energyionization or kinetic energy

Penning ionization only occurs if an Penning ionization only occurs if an excited Argon atoms excited Argon atoms collides with a collides with a COCO22

Inelastic Collisions of the second kind Inelastic Collisions of the second kind are relegated to occurring upon are relegated to occurring upon collision with another collision with another Argon atomArgon atom

No energy escapes and these are the No energy escapes and these are the only significant processesonly significant processes

Penning Ionization Penning Ionization ProbabilityProbability

Here, f is the fraction of COHere, f is the fraction of CO22, , σσPenningPenning is the cross is the cross section for Penning ionization, and section for Penning ionization, and σσInelasticInelastic is the cross is the cross section for inelastic collisions of the second kindsection for inelastic collisions of the second kind

σσInelasticInelastic is approximated by the van der Waals radius is approximated by the van der Waals radius of Argonof Argon

σσPenningPenning is taken from experimental values, which are is taken from experimental values, which are hard to findhard to find

Empirical ComparisonEmpirical Comparison

** EquationEquation EmpiricalEmpirical

ATLAS GasATLAS Gas 0.24499**0.24499** 0.231560.23156

ALICE GasALICE Gas 0.417190.41719 0.4-0.5***0.4-0.5***

*This is so theoretical there are no significant figures!

**The Penning cross section for Ne*+CO2 was used here

***This value was produced by Rob Veenhof using a more sophisticated method that yields a range values

ConclusionConclusion

The equation for Penning ionization The equation for Penning ionization probability is probability is not ready to be used not ready to be used as a toolas a tool – it needs further testing, – it needs further testing, further consideration of some further consideration of some factors, and more precise cross factors, and more precise cross section measurementssection measurements

However, with the ideas in place, However, with the ideas in place, hopefully the hard part is overhopefully the hard part is over

AcknowledgementsAcknowledgements

Funding Sources:Funding Sources: University of University of

MichiganMichigan National Science National Science

FoundationFoundation Ford Motor Ford Motor

CompanyCompany

Help Sources:Help Sources: Rachel AvramidouRachel Avramidou Rob VeenhofRob Veenhof Peter CwetanskiPeter Cwetanski Adrian FabichAdrian Fabich Homer NealHomer Neal Jean KrischJean Krisch Jeremy HerrJeremy Herr