PHYS%575% Autumn%2015 ! Radia&on!and!Radia&on!Detectors! ! Course!home!page: ! h6p://depts.washington.edu/physcert/radcert/575website/ % 5:!cross!sec&ons,!a6enua&on;!calorimetry;!! coun&ng!sta&s&cs;!sta&s&cs!for!analysis! R.%Jeffrey%Wilkes%% Department%of%Physics% B305%PhysicsEAstronomy%Building% 206E543E4232 % wilkes@u.washington.edu%
Course%calendar% Tonight % 2%
Announcements% • All%but%2%have%sent%me%proposed%topics% • PresentaPon%dates:%Tues%Dec%1,%Tues%Dec%8,%and%Thurs%Dec%10% – See%class%web%page%for%link%to%signup%sheet% % I%will%arbitrarily%assign%slots%for%those%not%signed%up%by%November%29%% As%of%today:% %% 11/3/15% 3%
Colloquium%of%interest % See%sharepoint.washington.edu/phys/newsevents/Pages/ViewEEvent.aspx? • eid=4702% – Any%week:%Go%to%Physics%Dept%home%page,%click%on% events ,% events %/% this(week( ;%every% Monday%there%is%a%generalEinterest%colloquium%open%to%the%public,%in%AE102% Watch%the%talk % Small town near Fukushima (post-tsunami nuclear reactor disaster in March, 2011) took steps to protect its citizens, independent of central government: distributed sodium- iodide pills, dosimeters for school children. 11/3/15% 4%
ChiEsquared%distribuPon% Last time N ( x i − µ ) 2 0.3 χ 2 ≡ ∑ , sum of deviations squared, in units of σ 2 σ 2 0.25 i = 1 � =1 1 2 ν /2 Γ ( ν / 2)( χ 2 ) ν /2 − 1 exp( − χ 2 / 2) p ( χ 2 ; ν ) = 0.2 2 p( χ 2 ; ν ) f(x) 0.15 = χ 2 PDF for ν degrees of freedom 5 0.1 10 ν = number of independent variables in sum 0.05 Example:%if%we%average%N%data%points%to%esPmate% µ, ν =NE1% χ 2 0 • Chisq%distribuPon%is% 0 2 4 6 8 10 12 14 16 18 – Monotone%decreasing%for% ν <2% x – Peaks%at% ν E2%for% ν >%2% 0.03 – Has%mean= ν , σ 2 =2 ν %and% ! %N( ν ,2 ν ) for% ν %E>% � %% 0.025 � =100 2 χ α %% p(chisq; N=100) 0.02 2 ; ν ) = p ( χ 2 ; ν ) d χ 2 ∫ Integral distribution: P ( χ α = 1 − α 0.015 0 So χ 2 > χ α 2 occurs with probability = α 0.01 0.005 Use to test for N( µ , σ 2 ) behavior: 0 60 70 80 90 100 110 120 130 140 Example: test hypothesis that { x i } come from N( µ , σ 2 ) chisq N ( x i − x ) 2 2 ( ν = N − 1) Then we should have χ 2 ≡ Area = prob that χ 2 will ∑ ≤ χ α p( χ 2 ; ν ) σ 2 randomly be > χ α 2 i = 1 to have confidence level α in our hypothesis χ 2 2 ≅ ν → χ 2 2 χ α Rule of thumb: for ν ≥ 10, ν ≈ 1 is 50% probable χ 0.5 5
Example:%counPng%staPsPcs%and%limits%of%detectability % How%can%we%tell%if%a%significant%signal%exists%in%the%presence%of%background?%% • N T %=%number%of%counts%observed%in%Pme%T,%% N B %=%background%counts%(measured%in%a%separate%run,%with%no%source),%%% then%N T %=%N S %+%N B %%where%N S %=%true%signal%counts% Case%where%N S %>>%N B %is%trivial,%but%what%if%N S %~%N B% ?% Assume%T%is%long%enough%so%all%count%values%are% � not%small �� (%>5)% Then%we%expect%N � s%to%be%GaussianEdistributed,%with% σ %= √ %N% % %N S %=%N T %E%N B %,%so%% σ ! S 2 !=! σ ! T 2 !+! σ ! B 2 ! % – Suppose%there%is (no(real(ac0vity %present,%so%N S %really%=%0%% • % σ % T 2 %=% σ % B 2 %so%% σ % S 2 %=% 2 % σ % B 2 %%or% σ % S %=% √ ( 2 N B )% So%we%expect%N S %to%be%drawn%from%a%Gaussian%centered%on%0%with%width% σ % S %=% √ ( 2 N B )% Then%we%should%reject%hypothesis%that%there%is%no%acPvity%present%if%% %N T %>%L C% %=% � cut%level � %for%decision% What%should%L C% %be?%
Cuts%and%significance%level%decisions % We%set%L C% %by%deciding%on%a% significance(level( =%acceptable%probability%for%being% fooled%by%a%random%fluctuaPon%( � Type%1%error � ,%falseEposiPve%rate)% If%we%want,%eg,%%<5%%probability%of%false%posiPve%result,%we%must%set%L C% %at%the%5%% tail%of%Gaussian%distribuPon.% Separate%issue:%rejecPng%hypothesis%when%it%is%actually%true%( � Type%2%error � ,%miss% rate,%falseEalarm%rate)%–%more%later% 1000 experiments with mean count 0 and standard deviation 3.5 Harder!case :%Suppose%real%acPvity%is% present,%but%below%background%level,%% 120 100.00% so%N S %actually%>%0%(but%<<%N B )% 100 80.00% N T %is%larger%than%N B %,%but%by%very%limle!% 80 Frequency 60.00% % 60 • For%a%provocaPve%look%at%staPsPcal% 40.00% 40 dilemma%posed%by%lowEsignal% 20.00% 20 experiments,%see%talk%by%Gary%Feldman% 0 .00% at% e 9 7 5 3 1 1 3 5 7 9 r - - - - - o M http://www.hepl.harvard.edu/~feldman/Journeys.pdf N S
Gas%ionizaPon%detectors% • Gaseous%ionizaPon%detectors%have%many%applicaPons%in% nuclear%/%parPcle%physics%experiments% – Charged%parPcles%leave%ionizaPon%trail%in%a%gas%volume%% • IonEelectron%pairs%produced%by%charged%parPcle%collisions%with%atomic%e’s% • Electrons%are%collected%on%an%anode%wire%(and/or%ions%on%cathode)% • Random%process%with%mean%free%path%between%collisions%given%by%% λ=1/(N e σ e ),%where%σ e %=%collision%crossEsecPon%per%electron%and%N e %=%e%density% • The%mean%number%of%collisions%per%unit%length%is%L/λ%% • Original%electrons%may%be%accelerated%by%E%field%and%cascade%before% collecPon:%gas%amplificaPon% • Gas%detectors%can%provide%precise%measurements%of%spaPal% coordinates%on%charged%parPcle%tracks%% – Low%density%gas%causes%limle%scamering% – Coordinate%measurements%of%less%than%0.1%mm%are%possible%% – DetecPon%efficiencies%(N tracks%detected /N actual )%%99%%or%bemer%are%possible% 11/3/15% 8%
Categories%of%gas%ionizaPon%detectors% Classify%by%gas%amplificaPon%factor,%which%depends%on%voltage%gradient%used% IonizaPon%detectors% • – RelaPvely%low%E%field%between%electrodes%–%does%not%mulPply%electrons% – Useful%in%highErate%applicaPons%(eg,%beam%monitors)%where%signal%is%large,%or% for%precision%measurements%(eg,%calibraPons)%% – Output%charge%is%direct%measure%of%ionizaPon%deposited % • Directly%related%to%parPcle%properPes%(charge,%mass,%speed)% • Useful%for%calibraPon%or%parPcle%idenPficaPon,%but%small%signals% • ProporPonal%counters% – Moderate%voltage%accelerates%electrons,%small%electron%amplificaPon%factor% • %output%signal%remains%proporPonal%to%original%ionizaPon%deposited% – High%efficiency%E%small%signals,%but%very%fast%output%and%recovery% Geiger%counters% • – High%voltage%accelerates%e’s,%causes%cascades% ! %gas%breakdown,%spark%path% • Binary%signal:%yes%or%no%–%properPes%of%original%track%are%lost%in%avalanche% – High%efficiency,%big%fat%signal%–%but%long%recovery%Pme%for%gas%(deadEPme)% % 11/3/15% 9%
Gas%counters:%3%zones % 1. Ionization : low V, no multiplication 2. Proportional: linear behavior, signal proportional to original ionization 3. Geiger: breakdown, signal unrelated to original ionization 11/3/15% 10%
IonizaPon%created%by%charged%parPcle%in%a%gas % • Assume:%Encounters%with%gas%atoms%are%random,%and%characterized%by% mean%free%path%(mfp)% λ =%avg%distance%between%collisions% Avg%number%of%collisions%along%path%length%x:%%<n>%=%x/ λ % • Collision%probability%is%Poisson%process:%exponenPal%distribuPon% • – P(x)%=probability%of% not %having%a%collision%in%distance%x% x dx – w%dx%=%probability%of% having %a%collision%between%x%and%x+dx% – So%%probability%of% not %interacPng%between%x%and%x+dx%% %is%P(x+dx)%=%P(x)[1%–%wdx]%%%%{P%of%surviving%x}{P%of%surviving%dx}% – So%dP/dx=%EwP%%%%% – Applying%some%calculus%we%get%P(x)%=%Cexp(Ewx),%where%C=1%% Note%that%probability%of%collision%between%x%and%x+dx%a|er%no%collisions%in% distance%x%is%exp(Ewx)dx%%% • Mean%distance%between%collisions% λ =%1/w%% • From%definiPon%of%a%cross%secPon,%w=N σ % ! % λ = %1/N σ % ' 11/3/15 11%
IonizaPon%Mechanisms% • Primary(ioniza0on %caused%by%detected%parPcle% • Secondary(ioniza0on( due%to% – IonizaPon%electron%colliding%with%neighboring%atoms% e E A% ! %e E A + e E ,%.%.%.%.%% – Intermediate%excited%states%A * %of%atom%in%a%gas%molecule% • e E A% ! %e E A *% ,%followed%%by%A * B% ! %AB + e E%% – IonizaPon%caused%by%UV%photons%emimed%when%excited%states%relax,%eg%% A * % ! %A % %+% γ ' • Mean%energy%to%create%an%ionEelectron%pair%is%~%20E30%eV% – Examples:%%%Ar%%%%%CO 2%%%% Air%%%H 2 O%%%{Ar(99.6%)%+%C 2 H 6 (0.4%),%ArEethane}%%% %%%%%%%%% %26eV%%%%33%%%%%35%%%%30%%%%%%%%%%%%%%%%%%%%20 11/3/15 12%
Electron%yields% • The%number%of%collisions,%k,%in%a%distance%L%is%Poisson% distributed%with%frequency%distribuPon%% P(L/ λ ,k)%=%(1/k!)(L/ λ ) k exp(EL/ λ )% – The%probability%of%at%least%one%ionizing%collision%is%1%–%exp(L/ λ )% – Yield%of%ionizing%collisions%for%minimum%ionizing%parPcles%(m.i.p.)%are% shown%in%the%table%below% Gases at STP, t 99 is thickness of gas layer for 99% efficiency, and last column gives average number of free electrons produced by a m.i.p. 11/3/15 13%
IonizaPon%chamber%applicaPons % • Air%IonizaPon%Dosimeters% Lauritsen pocket dosimeter (c. 1937) – quartzEfiber%electroscopes% • One%of%the%earliest%radiaPon%detectors:%measure%ionizaPon%in%air% by%rate%of%discharge%of%sensiPve%electroscope% • Wulf%Electroscope%(c.%1900)% Fluke%451%Ion%chamber%survey%meter% 349%cc%air%volume%% Observe ionizaPon%Chamber%wall:%% spacing of 246%mg/cm2%thick%phenolic%% threads decrease as Chamber%window:%% charge leaks 6.6%mg/cm2%Mylar% away Initially- charged Measures%Alphas%above%7.5%MeV,%% silk Beta%above%100%keV,%and%% threads Gamma%above%7%keV%% 11/3/15% 14%
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