chrenkov theory

8/14/2019 Chrenkov Theory

1/15

Radiasi Cerenkov

Minggu, 07 Februari 2010 15:48

Radiasi cerenkov adalah radiasi elektromagnetik ang di!an"arkan ketika suatu !artikelbermuatan #se!erti elektron$ mele%ati sebuah medium insulator !ada ke"e!atan ang konstannamun lebih "e!at dari!ada ke"e!atan "ahaa !ada medium& 'arakteristik !endaran ber%arna

biru dari suatu reaktor nuklir adalah dikarenakan mun"ulna radiasi "erenkov& (inamakan

demikian berdasarkan nama seorang ilmu%an asal rusia ang !ertama kali menelitina aitu,

)avel *lekseevi"h Cherenkov, meru!akan !emenang nobel !ada tahun 1+58

htt!:%%%&batan&go&id!tnbrinde-&!h!ensiklo!edia54.!engetahuan71.radiasi."erenkov&html
http://www.batan.go.id/ptnbr/index.php/ensiklopedia/54-pengetahuan/71-radiasi-cerenkov.htmlhttp://www.batan.go.id/ptnbr/index.php/ensiklopedia/54-pengetahuan/71-radiasi-cerenkov.htmlhttp://www.batan.go.id/ptnbr/images/gambar/ensiklopedia/250px-cerenkov_effect.jpghttp://www.batan.go.id/ptnbr/index.php/component/mailto/?tmpl=component&link=aHR0cDovL3d3dy5iYXRhbi5nby5pZC9wdG5ici9pbmRleC5waHAvZW5zaWtsb3BlZGlhLzU0LXBlbmdldGFodWFuLzcxLXJhZGlhc2ktY2VyZW5rb3YuaHRtbA%3D%3Dhttp://www.batan.go.id/ptnbr/index.php/ensiklopedia/54-pengetahuan/71-radiasi-cerenkov.html?tmpl=component&print=1&page=http://www.batan.go.id/ptnbr/index.php/ensiklopedia/54-pengetahuan/71-radiasi-cerenkov.pdfhttp://www.batan.go.id/ptnbr/index.php/ensiklopedia/54-pengetahuan/71-radiasi-cerenkov.htmlhttp://www.batan.go.id/ptnbr/index.php/ensiklopedia/54-pengetahuan/71-radiasi-cerenkov.html


2/15

Takhion(bahasa Inggris: tachyon /tki.n/) adalah partikelhipotetis yang selalu

bergerak lebih cepat dari cahaya. 'arena takhion selalu bergerak lebih "e!at dari "ahaa,

!engamat tak akan da!at melihatna mendekat& /etelah takhion mele%ati !engamat, ia akan bisa

melihatna sedang mun"ul dan !ergi ke arah ang berbeda& aris hitam meru!akan gelombang

radiasi Cherenkovang ditunukkan hana dalam satu %aktu&

htt!:id&%iki!edia&org%ikiakhion
http://id.wikipedia.org/wiki/Bahasa_Inggrishttp://id.wikipedia.org/wiki/Wikipedia:IPA_untuk_Bahasa_Inggrishttp://id.wikipedia.org/wiki/Wikipedia:IPA_untuk_Bahasa_Inggrishttp://id.wikipedia.org/wiki/Wikipedia:IPA_untuk_Bahasa_Inggris#Kuncihttp://id.wikipedia.org/wiki/Wikipedia:IPA_untuk_Bahasa_Inggris#Kuncihttp://id.wikipedia.org/wiki/Wikipedia:IPA_untuk_Bahasa_Inggris#Kuncihttp://id.wikipedia.org/wiki/Wikipedia:IPA_untuk_Bahasa_Inggris#Kuncihttp://id.wikipedia.org/wiki/Wikipedia:IPA_untuk_Bahasa_Inggris#Kuncihttp://id.wikipedia.org/wiki/Wikipedia:IPA_untuk_Bahasa_Inggris#Kuncihttp://id.wikipedia.org/wiki/Wikipedia:IPA_untuk_Bahasa_Inggris#Kuncihttp://id.wikipedia.org/wiki/Wikipedia:IPA_untuk_Bahasa_Inggris#Kuncihttp://id.wikipedia.org/wiki/Wikipedia:IPA_untuk_Bahasa_Inggris#Kuncihttp://id.wikipedia.org/wiki/Wikipedia:IPA_untuk_Bahasa_Inggris#Kuncihttp://id.wikipedia.org/wiki/Wikipedia:IPA_untuk_Bahasa_Inggrishttp://id.wikipedia.org/wiki/Partikelhttp://id.wikipedia.org/w/index.php?title=Lebih_cepat_dari_cahaya&action=edit&redlink=1http://id.wikipedia.org/wiki/Radiasi_Cherenkovhttp://id.wikipedia.org/wiki/Bahasa_Inggrishttp://id.wikipedia.org/wiki/Wikipedia:IPA_untuk_Bahasa_Inggrishttp://id.wikipedia.org/wiki/Wikipedia:IPA_untuk_Bahasa_Inggris#Kuncihttp://id.wikipedia.org/wiki/Wikipedia:IPA_untuk_Bahasa_Inggris#Kuncihttp://id.wikipedia.org/wiki/Wikipedia:IPA_untuk_Bahasa_Inggris#Kuncihttp://id.wikipedia.org/wiki/Wikipedia:IPA_untuk_Bahasa_Inggris#Kuncihttp://id.wikipedia.org/wiki/Wikipedia:IPA_untuk_Bahasa_Inggris#Kuncihttp://id.wikipedia.org/wiki/Wikipedia:IPA_untuk_Bahasa_Inggris#Kuncihttp://id.wikipedia.org/wiki/Wikipedia:IPA_untuk_Bahasa_Inggris#Kuncihttp://id.wikipedia.org/wiki/Wikipedia:IPA_untuk_Bahasa_Inggris#Kuncihttp://id.wikipedia.org/wiki/Wikipedia:IPA_untuk_Bahasa_Inggrishttp://id.wikipedia.org/wiki/Partikelhttp://id.wikipedia.org/w/index.php?title=Lebih_cepat_dari_cahaya&action=edit&redlink=1http://id.wikipedia.org/wiki/Radiasi_Cherenkov


3/15

Theory

Cerenkov radiation has been generated b means similar to those !ro!osed here, but not in thelo%.energ regime %e %ill be %orking in& 3or have the "al"ulations or a inite %idth,

"lindri"all smmetri"al beam !assing over a lat va"uum.diele"tri" boundar been done beore

no%, even though Cerenkov radiation has been studied sin"e the earl 1+00s 16&

n general, Cerenkov radiation #es!e"iall the emission angle$ "an best be e-!lained b theugens "onstru"tion& * better analog "an be made b "onsidering the !olari9ation indu"ed in

the diele"tri" as the !arti"le !asses through it& For a more uantitative treatment, an analsis o

the radiated ele"tromagneti" ields o the beam must be undertaken&

Huygens construction

he ugens "onstru"tion e-!lains Cerenkov radiation as a !henomena ver similar to thesho"k%ave !rodu"ed b su!ersoni" ets& /u!!ose a !arti"le emits a %ave !ulse ever time t, and

also that these !ulses move out s!heri"all at s!eed c'& 3o% allo% the !arti"le to move %ith

s!eed v& v;c', then the %ave"rests merel bun"h u! in the dire"tion o motion, but do not"ross&


4/15

"reate a sho"k%ave& hinking about the !olari9ation o the diele"tri" "an hel! to e-!lain this

as!e"t o Cerenkov radiation a little better 16& Consider that a "harged !arti"le, in !assing b the

atoms in the diele"tri", momentaril !olari9es them #!ushing like "harges in the atom a%a, andindu"ing a di!ole state$& @n"e the !arti"le has !assed, this !olari9ed state "olla!ses, "ausing ea"h

atom to emit Cerenkov radiation #i the velo"it "onstraint is met, o "ourse$& For slo% moving

!arti"les, the !olari9ation is !ere"tl smmetri"al, resulting in no ele"tri" ield at long distan"es#and thus no radiation$& "one? o di!loes develo!s behind the ele"tron$& here %ould no% be distin"t di!ole ield

established in the diele"tri", one that "an onl be "olla!sed %ith the emission an ele"tromagneti"

!ulse #Cerenkov radiation$& Radiation %ould be emitted !er!endi"ular to the sura"e o this "one,

%ith the angle o the "one ound using the ugens "onstru"tion&

Theoretical Analysis
http://mxp.physics.umn.edu/s04/projects/s04cherenkov/ref.htmhttp://mxp.physics.umn.edu/s04/projects/s04cherenkov/ref.htm


5/15

he ollo%ing treatment o the !roblem makes several sim!liing assum!tions #rom the Frank

and amm theor detailed in 16$:

#i$ he diele"tri" is "onsidered as a "ontinuum, in as mu"h as the material is deined sim!l bits diele"tri" "onstant %ith all mi"ro.stru"ture ignored&

#ii$ (is!ersion is ignored&

#iii$ Radiation rea"tion is ignored&

#iv$ he material is "onsidered to be a !ere"t isotro!i" diele"tri", %ith no absor!tion o radiation

#"ondu"tivit is 9ero, !ermeabilit is unit$&

#v$ he beam is "onsidered to move at a "onstant velo"it #no slo%ing due to ioni9ation, oCoulomb s"attering$&

#vi$ he material is unbounded and the beam !ath is ininite&

Ale"tron sheet !assing over a diele"tri"&

Aven given these assum!tions, there has been relativel little theoreti"al %ork done on thee-!erimental geometr "onsidered here& he "losest %ork %ould be that o (anos 2,B6, %ho"onsidered the motion o an ininitesimall thin sheet o "harge moving at some distan"e rom

the va"uum.diele"tri" boundar& he ollo%ing derivations ollo% the %ork !resented in 26&

@ne begins b deining a "harge densit

%here

and, as beore,
http://mxp.physics.umn.edu/s04/projects/s04cherenkov/ref.htmhttp://mxp.physics.umn.edu/s04/projects/s04cherenkov/ref.htmhttp://mxp.physics.umn.edu/s04/projects/s04cherenkov/ref.htmhttp://mxp.physics.umn.edu/s04/projects/s04cherenkov/ref.htmhttp://mxp.physics.umn.edu/s04/projects/s04cherenkov/ref.htmhttp://mxp.physics.umn.edu/s04/projects/s04cherenkov/ref.htmhttp://mxp.physics.umn.edu/s04/projects/s04cherenkov/ref.htmhttp://mxp.physics.umn.edu/s04/projects/s04cherenkov/ref.htmhttp://mxp.physics.umn.edu/s04/projects/s04cherenkov/ref.htm


6/15

*lso, is the Fourier "oei"ient o the "harge densit "orres!onding to the reuen"

, and is the average (C "harge densit& @ "ourse, this is or a bun"hed sheet, movingin the 9.a-is, %ith 9ero e-tent in the -.a-is #!er!endi"ular to the sura"e o the diele"tri"$&

he !otentials in ree s!a"e #above the va"uum.diele"tri" boundar$ are

%here is "onstant and is the 9.a-is unit ve"tor&

Considering onl the *C !art o the "harge densit, one arrives at

%here

o solve the homogeneous euation one makes the trial solution

the Dorent9 "ondition, , it ollo%s that & hus

he va"uum ields that go %ith the ele"tron beam are

From above


7/15

ere sign- is deined as

and

*bove, the uantities and are !arameters that "an be adusted to mat"h the boundar"onditions&

he ve"tor !otential inside the diele"tri" is ust

%here

From this the ields "an be "al"ulated

3o% one "an im!ose the boundar "ondition #the tangential ield must mat"h$ at

From here one "an ind the euations o the outgoing %ave


8/15

%here

and

he ele"tron beam radiates an average energ deined b the )onting ve"tor

%here

)onting ve"tor de"om!osition&

he normal "om!onent o this ve"tor "orres!onds to the energ radiated into the diele"tri":

%here

%ithNbeing the number o ele"trons in one "oulomb # $& hus this "om!onent o the

)onting ve"tor is in %atts !er "entimeter suared iIis in am!s !er "entimeter&


9/15

@ne should also note that the angle o the radiation #$ is given b

o sim!li things, lets !ut the above derivation in terms o kno%n uantities:

the beam sheet in this e-am!le has %idth, this "an be a!!lied in the )onting ve"tor as su"h #in

sim!liied notation$

%here is measured rom the sura"e o the diele"tri"&

* similar analsis %as "ondu"ted b Dinhart 46 or a single ele"tron !assing over an ininite

!lane intera"e bet%een a va"uum and a diele"tri" #%ith similar "onstraints as above %ith the

addition o and $& he total radiation out!ut %as ound to be

%here eis the "harge o the ele"tron, and the energ radiated !er unit angular reuen" is

/ket"h o reuen" de!enden"e o !o%er&


10/15

Conseuentl, there e-ists a reuen", and thus a %avelength, at %hi"h most o the radiation is

emitted:

Summary

t has been sho%n that the general design used in this e-!eriment, namel the !assing o anele"tron beam over a diele"tri", %ill !rodu"e Cerenkov radiation given the "orre"t diele"tri"&

his %as done b (anos B6 %hen he generated mi"ro%ave Cerenkov radiation b !assing a 10

'eE ele"tron beam over a !late o titanium dio-ide & /in"e %e are using a lo%.energ beam oB'eE, %e need a diele"tri" "onstant o at least 85& his is ound b

@ "ourse, one "an move easil rom a !otential dieren"e like B'E to a value or using

/olving one gets

http://mxp.physics.umn.edu/s0/pro!ects/s0cherenko"/theory.htm


11/15

Cerenkov Radiation

Cerenkov #or Cherenkov$ radiation is a bit o nineteenth "entur !hsi"s that stumbled into the

t%entieth& t "ould have been #and to some degree %as, b the !hsi"ist eaviside$ !redi"ted inthe 1880s, but this ee"t %as dis"overed b a""ident, !erha!s b the Marie and )ierre Curie& t

%as studied in detail b )avel Cerenkov in the 1+B0s, and e-!lained a e% ears later b la

Frank and gor amm& he three o them %on the 1+58 3obel !ri9e or their %ork&


12/15

this t!e o radiation, in"luding some o those that have !laed a maor role in studing the

!ro!erties o neutrinos, e&g& /u!er'amiokande&

Cerenkov radiation is also ver useul in "he"king %hether AinsteinHs theor o relativit is ana""urate des"ri!tion o nature& Cosmi" ras, !arti"les ling in rom outer s!a"e #%hi"h oten hit

something in the atmos!here and make a large sho%er o !arti"les that "an be dete"ted bobservers on the ground$, "an in rare "ases "arr e-traordinaril high energ, as mu"h as 100

million times more energ than the !rotons at theDarge adron Collider& hese !arti"les are #asar as %e "an tell$ !rodu"ed man light ears a%a rom earth, in !o%erul astronomi"al events

su"h as su!ernovas& 3o% su!!ose the s!eed o light %ere not an ultimate s!eed limit, and those

!arti"les traveled aster than the s!eed o light in the va"uum o outer s!a"e& hen these ultra.high.energ !arti"les %ould undergo Cerenkov radiation too& *nd be"ause the have so ar to

travel, the %ould lose mu"h o their energ to this radiation& t turns out this energ loss "an be

ver ra!id, and that these !arti"les "ould not travel astronomi"al distan"es and kee! their ultra.high.energ unless their s!eed remained e-tremel "lose to or belo% the s!eed o light&

n short, i "osmi" ras at ultra.high.energies "ould move aster than the s!eed o light, then weshouldnt observe any cosmic rays at ultra-high-energies at all, be"ause the should all lose

most o their energ long beore the rea"h earth& ut %e do observe them& "Tiny loophole, Ithink# we are almost certain most of them are charged# their properties indicate they feel the

strong nclear force, and the only stable particles that cold travel sch distances are protons

and more generally atomic nclei, all of which have electric charge! If yo open this loophole abit, yo wold redce the constraint somewhat, bt it wold still be pretty strong!$/o thereore

%e "an "on"lude: the ultra.high.energ "osmi" ras #as %ell as an "osmi" ras at lo%er energ$

"annot e-"eed the s!eed o light b more than a ver tin number& Astimates rom the late 1++0s

due to the ver amous !hsi"ists /idne Coleman and /heldon lasho% %who were the first Iam aware of to make this argment, bt who might well have been preceded by other athors;

please let me know if yo are familiar with earlier papers!ut this tin number at about ten !artsin a trillion trillion& he "onstraints rom e-!eriment have !robabl im!roved sin"e then& "illtry to find pdated nmbers, and ones withot any possible loopholes!$

/imilarl, the sim!le a"t that %e observe high.energ ele"trons !uts limits on their s!eed

relative to that o light& he most re"ent "laim Hve read #still tring to igure out its sour"e$ is

that observation o ele"trons %ith energies u! to hal a eE im!l that ele"trons "annot e-"eedthe s!eed o light b more than a !art !er thousand trillion&

http://pro#mattstrassler.com/articles$and$posts/particle$physics$basics/cerenko"$

radiation/
http://www-sk.icrr.u-tokyo.ac.jp/sk/index-e.htmlhttp://www-sk.icrr.u-tokyo.ac.jp/sk/index-e.htmlhttp://profmattstrassler.com/articles-and-posts/largehadroncolliderfaq/introduction-to-the-large-hadron-collider/http://profmattstrassler.com/articles-and-posts/largehadroncolliderfaq/introduction-to-the-large-hadron-collider/http://profmattstrassler.com/2011/09/20/supernovas-and-neutrinos/http://profmattstrassler.com/articles-and-posts/particle-physics-basics/cerenkov-radiation/http://profmattstrassler.com/articles-and-posts/particle-physics-basics/cerenkov-radiation/http://www-sk.icrr.u-tokyo.ac.jp/sk/index-e.htmlhttp://profmattstrassler.com/articles-and-posts/largehadroncolliderfaq/introduction-to-the-large-hadron-collider/http://profmattstrassler.com/2011/09/20/supernovas-and-neutrinos/http://profmattstrassler.com/articles-and-posts/particle-physics-basics/cerenkov-radiation/http://profmattstrassler.com/articles-and-posts/particle-physics-basics/cerenkov-radiation/


13/15

Cerenkov Radiation

Andrew J. Keller

arch !" #$%%

Su&mitted as coursework 'or Physics #(%" Stan'ord )niversity" *inter #$%%

he notion o glo%ing radioa"tive material is %ell established in !o!ular "ulture, but as %ith

man as!e"ts o nu"lear energ, the to!i" is rie %ith misinormation& *s it turns out, t%o distin"t

!hsi"al "auses give rise to %hat "ould be loosel termed as Knu"lear blue glo%,K the blue lightgiven o in "ertain environments %ith sui"ientl intense radiation& he blue glo% seen in

Fig. 1:%erenko" radiation #rom the &eed &esearch &eactor' ortland' &. (%ourtesy

o# the *.+. ,uclear &egulatory %ommission.) +ource: -ikimedia %ommons
http://large.stanford.edu/courses/2011/ph241/http://en.wikipedia.org/wiki/File:Cerenkov_Effect.jpghttp://large.stanford.edu/courses/2011/ph241/keller2/images/cerenkov.gifhttp://large.stanford.edu/courses/2011/ph241/http://en.wikipedia.org/wiki/File:Cerenkov_Effect.jpg


14/15

%ater.moderated rea"tors and the blue glo% observed in "riti"alit a""idents in the laborator

setting ma seem related, but %hereas in "riti"alit a""idents a blue glo% in air is due to the

emission o light in the rela-ation o e-"ited gas mole"ules, the blue glo% o a rea"tor has moree-oti" origins&

3u"lear rea"tors are oten !i"tured %ith a "loud o beautiull disuieting blue light #see igure1$, termed Cerenkov radiation& Cerenkov began his irst "ontributions to the understanding o

this radiation in 1+B4 %hen he observed light rom the gamma.ra irradiation o a !ure solventb a radium sour"e& his observation %as une-!e"ted, as he %as initiall attem!ting to stud the

light emitted rom uranl salt solutions under gamma.ra irradiation, %ith no e-!e"ted

ba"kground rom the solvent& Moreover, the lumines"en"e "ould not be uen"hed, b varing thetem!erature or other%ise, as is !ossible in the "ase o light emitted rom the de"a o an e-"ited

state& CerenkovHs advisor Eavilov !ostulated that the radiation might be due to the motion o

ele"trons, and urther e-!eriments using beta de"as !rovided su!!orting eviden"e& 16

3ot more than three ears later, amm and Frank !ublished a theor elu"idating CerenkovHs

observations, determining its "ause to be the motion o "harged !arti"les %ith !hase velo"itgreater than the s!eed o light in the traversed medium& 16 /everal salient eatures o the

radiation ma be observed rom the radiation intensit s!e"trum the derived, %here %e assumethe "harged !arti"le is an ele"tron and v is the s!eed o the ele"tron, e is the ele"tron "harge, " is

the s!eed o light, and n is the inde- o rera"tion o the medium:

First, it is a!!arent that the e-!ression is negative and thereore meaningless unless v = "n, the

!hase velo"it o the medium& /e"ond, it is interesting to note that Cerenkov radiation is readildierentiated rom remsstrahlung radiation be"ause the intensit does not de!end on the mass

o the "harged !arti"le, %hereas remsstrahlung radiation does& 26 Finall, given that the inde-o rera"tion o %ater does not var mu"h over the visible s!e"trum, the intensit goes linearl

%ith reuen", e-!laining %h Cerenkov radiation a!!ears blue& B6 Dater e-!erimental studies

"orroborated agreement %ith the Frank and amm theor, a!art rom understood deviations su"h

as ultraviolet absor!tion in %ater and se"ond order ee"ts& 46

t is interesting to "onsider %hat the energ o an ele"tron %ould need to be in order to observe

Cerenkov radiation in air& *ssuming a "onstant inde- o rera"tion o 1&000B over the visible

s!e"trum, the threshold velo"it %ould be roughl 0&+++7"& n this "ase, a sim!le "al"ulation o

the relativisti" kineti" energ ields the threshold o 20&B5 MeE, higher than all but the mostenergeti" beta de"as, man o %hi"h onl o""ur %ith rare isoto!es& 56 t is then "lear %h

Cerenkov radiation is !rimaril asso"iated %ith the !ools o %ater surrounding rea"tor "oresL

the threshold kineti" energ in %ater, assuming an inde- o rera"tion o 4B, ma be readil"al"ulated to be onl about 20 keE, an energ s"ale readil a""essible to "ommon beta de"as&

Furthermore, it is obvious that a blue glo% in the air as seen in "riti"alit a""idents "annot be

e-!lained b Cerenkov radiation& his is not to sa that Cerenkov radiation is onl ound at the
http://large.stanford.edu/courses/2011/ph241/keller2/images/latex.gif


15/15

"ore o nu"lear rea"torsN interestingl, Cerenkov radiation has been im!li"ated in the lashes o

light that astronauts have re!orted seeing %ith their ees "losed %hile in transit to the moon& 6

http://large.stan#ord.edu/courses/0/ph/keller/

chrenkov theory

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