Outli Ioizig Radiatio Chaptr F.A. Attix, Itroductio to Radiological Physics ad Radiatio Dosimtry Radiological physics ad radiatio dosimtry Typs ad sourcs of ioizig radiatio Dscriptio of ioizig radiatio filds Radom atur of radiatio o-stochastic quatitis Summary Itroductio Radiological physics studis ioizig radiatio ad its itractio with mattr Bga with discovry of x-rays, radioactivity ad radium i 890s Spcial itrst is i th rgy absorbd i mattr Radiatio dosimtry dals with quatitativ dtrmiatio of th rgy absorbd i mattr Ioizig radiatio By gral dfiitio ioizig radiatio is charactrizd by its ability to xcit ad ioiz atoms of mattr Lowst atomic ioizatio rgy is ~ V, with vry littl ptratio Ergis rlvat to radiological physics ad radiatio thrapy ar i kv MV rag Typs ad sourcs of ioizig radiatio -rays: lctromagtic radiatio (photos) mittd from a uclus or i aihilatio ractio Practical rgy rag from.6 kv (K from lctro captur i 37 8 Ar) to 6. ad 7. MV (-rays from 6 7 ) x-rays: lctromagtic radiatio (photos) mittd by chargd particls (charactristic or brmsstrahlug procsss). Ergis: 0.-0 kv soft x-rays 0-0 kv diagostic rag 0-300 kv orthovoltag x-rays 300 kv- MV itrmdiat rgy x-rays MV ad up mgavoltag x-rays Typs ad sourcs of ioizig radiatio Fast lctros (positros) mittd from ucli (rays) or i chargd-particl collisios (-rays). Othr sourcs: Va d Graaf grators, liacs, btatros, ad microtros Havy chargd particls mittd by som radioactiv ucli (-particls), cyclotros, havy particl liacs (protos, dutros, ios of havir lmts, tc.) utros producd by uclar ractios (caot b acclratd lctrostatically)
Typs of itractio ICRU (Th Itratioal Commissio o Radiatio Uits ad Masurmts; stablishd i 95) trmiology Dirctly ioizig radiatio: by chargd particls, dlivrig thir rgy to th mattr dirctly through multipl Coulomb itractios alog th track Idirctly ioizig radiatio: by photos (x-rays or - rays) ad utros, which trasfr thir rgy to chargd particls (two-stp procss) Dscriptio of ioizig radiatio filds To dscrib radiatio fild at a poit P d to dfi o-zro volum aroud it Ca us stochastic or o-stochastic physical quatitis Stochastic quatitis Valus occur radomly, caot b prdictd Radiatio is radom i atur, associatd physical quatitis ar dscribd by probability distributios Dfid for fiit domais (o-zro volums) Th xpctatio valu of a stochastic quatity (.g. umbr of x-rays dtctd pr masurmt) is th ma of its masurd valu for ifiit umbr of masurmts for Stochastic quatitis For a costat radiatio fild a umbr of x-rays obsrvd at poit P pr uit ara ad tim itrval follows Poisso distributio For larg umbr of vts it may b approximatd by ormal (Gaussia) distributio, charactrizd by stadard dviatio (or corrspodig prctag stadard dviatio S) for a sigl masurmt S Stochastic quatitis ormal (Gaussia) distributio is dscribd by probability dsity fuctio P(x) Ma dtrmis positio of th maximum, stadard dviatio dfis th width of th distributio P( ) / Stochastic quatitis For a giv umbr of masurmts stadard dviatio is dfid as S will hav a 68.3% chac of lyig withi itrval of, 95.5% to b withi, ad 99.7% to b withi itrval 3. o xprimt-rlatd fluctuatios
Stochastic quatitis I practic o always uss a dtctor. A stimatd prcisio (proximity to ) of ay sigl radom masurmt i i i i / Dtrmid from th data of such masurmts Stochastic quatitis A stimat of th prcisio (proximity to ) of th ma valu masurd with a dtctor tims i i / is as corrct as your xprimtal stup Stochastic quatitis: Exampl A -ray dtctor havig % coutig fficicy is positiod i a costat fild, makig 0 masurmts of qual duratio, t=s (xactly). Th avrag umbr of rays dtctd ( couts ) pr masurmt is.00x0 5. What is th ma valu of th cout rat C, icludig a statmt of its prcisio (i.., stadard dviatio)? 5.00 0 3 C.00 0 c/s t 3 C.00 0 C c/s 0 3 C.00 0 c/s Hr th stadard dviatio is du tirly to th stochastic atur of th fild, sic dtctor is % fficit o-stochastic quatitis For giv coditios th valu of o-stochastic quatity ca, i pricipl, b calculatd I gral, it is a poit fuctio dfid for ifiitsimal volums It is a cotiuous ad diffrtiabl fuctio of spac ad tim; with dfid spatial gradit ad tim rat of chag Its valu is qual to, or basd upo, th xpctatio valu of a rlatd stochastic quatity, if o xists I gral dos ot d to b rlatd to stochastic quatitis, thy ar rlatd i dscriptio of ioizig radiatio Dscriptio of radiatio filds by o-stochastic quatitis Fluc Flux Dsity (or Fluc Rat) Ergy Fluc Ergy Flux Dsity (or Ergy Fluc Rat) o-stochastic quatitis: Fluc A umbr of rays crossig a ifiitsimal ara surroudig poit P, dfi fluc as d da Uits of m - or cm -
o-stochastic quatitis: Flux dsity (Fluc rat) A icrmt i fluc ovr a ifiitsimally small tim itrval d d dt da Uits of m - s - or cm - s - Fluc ca b foud through itgratio: d dt t 0, t t dt t t 0 o-stochastic quatitis: Ergy fluc For a xpctatio valu R of th rgy carrid by all th rays crossig a ifiitsimal ara surroudig poit P, dfi rgy fluc as dr da Uits of J m - or rg cm - If all rays hav rgy E R E E o-stochastic quatitis: Ergy flux dsity (Ergy fluc rat) A icrmt i rgy fluc ovr a ifiitsimally small tim itrval d dr dt da Uits of J m - s - or rg cm - s - Ergy fluc ca b foud by itgratio: d dt t t t dt 0, t t0 Diffrtial distributios Mor complt dscriptio of radiatio fild is oft dd Grally, flux dsity, fluc, rgy flux dsity, or rgy fluc dpd o all variabls:,, or E Simplr, mor usful diffrtial distributios ar thos which ar fuctios of oly o of th variabls Diffrtial distributios by rgy ad agl of icidc Diffrtial flux dsity as a fuctio of rgy ad agls of icidc: distributio,, E Typical uits ar m - s - sr - kv - Itgratio ovr all variabls givs th flux dsity: Emax,, EsidddE 0 0 E0 (x,y,z) (r,,) Diffrtial distributios: Ergy spctra If a quatity is a fuctio of rgy oly, such distributio is calld th rgy spctrum (.g. E ) Typical uits ar m - s - kv - or cm - s - kv - Itgratio ovr agular variabls givs flux dsity spctrum E,, Esidd 0 0 Similarly, may dfi rgy flux dsity E
Diffrtial distributios: Ergy spctrum xampl E E A flat distributio of photo flux dsity Ergy flux dsity spctrum is foud by E E E Typically uits for E ar joul or rg, so that [ ] = Jm - s - kv - Exampl: Problm.8 A x-ray fild at a poit P cotais 7.5x0 8 photos/(m -sc-kv), uiformly distributd from 0 to kv. a) What is th photo flux dsity at P? b) What would b th photo fluc i o hour? c) What is th corrspodig rgy fluc, i J/m ad rg/cm? Exampl: Problm.8 Ergy spctrum of a flux dsity (E) 7.5x0 8 photos/m -sc-kv a) Photo flux dsity E E E 8 max 7.5 0 90 6.75 0 photos/m s b) Th photo fluc i o hour t hour t 0 4 6.75 0 3600.43 0 photos/m c) Th corrspodig rgy fluc, i J/m ad rg/cm mi 0 E E t E EdE t 0 E 0 8 6 3600 7.5 0 0.336 0 kv/m 6 6 3.336 0.60 0.4 J/m.4 0 rg/cm Diffrtial distributios: Agular distributios a) b) Azimuthal symmtry: a) acclrator bam aftr primary collimator; b) brachythrapy surfac applicator Full diffrtial distributio itgratd ovr rgy lavs oly agular dpdc Oft th fild is symmtrical with rspct to a crtai dirctio, th oly dpdc o polar agl or azimuthal agl Diffrtial distributios: Agular distributios If th fild is symmtrical with rspct to th vrtical (z) axis, it is idpdt of azimuthal agl This rsults i distributio pr uit polar agl ( ) Emax 0 E0 (,, E) si d de Altrativly, ca obtai distributio pr uit solid agl for particls of all rgis Diffrtial distributios: Agular distributios Distributio pr uit polar agl, azimuthal symmtry Fild isotropic pr uit solid agl, d si dd sphrical symmtry
Plaar fluc Plaar fluc Plaar fluc: umbr of particls crossig a fixd pla i ithr dirctio (i.., summd by scalar additio) pr uit ara of th pla Vctor-sum quatity givs t flow umbr of particls crossig a fixd pla i o dirctio mius thos crossig i th opposit dirctio (usd i MC calculatios) Fluc vs. plaar fluc dfiitio mattrs Assum that th rgy impartd is ~ proportioal to th total track lgth of th rays crossig th dtctor For ptratig radiatio both dtctors will rad mor blow th foil, E~ /cos tims th umbr strikig it abov foil For o-ptratig rays th flat dtctor rspods th sam abov ad blow th foil (~to oly th umbr of x-rays strikig it; track lgth is irrlvat) Th rgy dpositd i this cas is rlatd to th plaar fluc Sphrical ad flat dtctors of qual cross-sctio ara (foil) Summary Typs ad sourcs of ioizig radiatio -rays, x-rays, fast lctros, havy chargd particls, utros Dscriptio of ioizig radiatio filds Stadard dviatio du radom atur of radiatio; accuracy of a masurmt o-stochastic quatitis: fluc, flux dsity, rgy fluc, rgy flux dsity, diffrtial distributios